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Newbe question: pitch and octave frequency ratio?
ras wrote:
I understand that a octave have 12 'intervals' as well as how you do the math (twelfth root of 2) but not why an octave: "is itself a frequency ratio of 2:1". Any help will be most appreciated, thanks Mike And octave below A 440 is 220, and an octave higher is 880. The octave above and below those is 110 and 1660Hz.. Not sure if that relationship is naturally musical, or whether it is a thing learned by us. geoff |
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#2
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Newbe question: pitch and octave frequency ratio?
ras wrote:
I understand that a octave have 12 'intervals' as well as how you do the math (twelfth root of 2) but not why an octave: "is itself a frequency ratio of 2:1". Any help will be most appreciated, thanks Mike And octave below A 440 is 220, and an octave higher is 880. The octave above and below those is 110 and 1660Hz.. Not sure if that relationship is naturally musical, or whether it is a thing learned by us. geoff |
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#3
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Newbe question: pitch and octave frequency ratio?
ras wrote:
I understand that a octave have 12 'intervals' as well as how you do the math (twelfth root of 2) but not why an octave: "is itself a frequency ratio of 2:1". Any help will be most appreciated, thanks Mike And octave below A 440 is 220, and an octave higher is 880. The octave above and below those is 110 and 1660Hz.. Not sure if that relationship is naturally musical, or whether it is a thing learned by us. geoff |
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#4
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Newbe question: pitch and octave frequency ratio?
Pitch math ... can somebody explain what that: "an octave ... which itself is a frequency ratio of 2:1" means? This is an excerpt from the book: "Audio Explained" by Michael Talbot-Smith: ------ Pitch ... the frequency ratio between two adjacent semitones is approximately 6%. In scientific terms the exact number is ¹²V2 (the twelfth root of 2). [V = suppose to the root char, cannot find the key combination for it on the windows system.] The reasoning behind this is that there are 12 equal semitone ‘intervals’ in an octave, which itself is a frequency ratio of 2:1. Each step must therefore be ¹²V2. ------ I understand that a octave have 12 ’intervals‘ as well as how you do the math (twelfth root of 2) but not why an octave: "is itself a frequency ratio of 2:1". Any help will be most appreciated, thanks Mike |
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#5
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Newbe question: pitch and octave frequency ratio?
"Geoff Wood" -nospam wrote in message ... | ras wrote: | I understand that a octave have 12 'intervals' as well as how you do | the math (twelfth root of 2) but not why an octave: "is itself a | frequency ratio of 2:1". | | Any help will be most appreciated, thanks | Mike | | And octave below A 440 is 220, and an octave higher is 880. The octave | above and below those is 110 and 1660Hz.. | | Not sure if that relationship is naturally musical, or whether it is a thing | learned by us. | | | geoff | | It is indeed naturally musical. The ratio 2:1 is quite simple, no? Let's say that we hear two notes simultaneously. If we hear A above middle C (440) and A an octave above that (880), this ratio sounds calm and peaceful. However, if we hear a whole series of a few hundred different notes, all accompanied by another synchronized series an octave above that, we might become irritated. But play both notes one after the other and we can experience the sequence as expressive. The psychology of music is indeed complex. Many harpsichordists like to couple up the mechanism so that they're constantly playing simultaneous octaves, even one octave above and one below, so that three pitches are sounding. It makes the instrument louder, an advantage for a naturally quiet instrument when playing a concerto with an orchestra. However, I find such coupling obnoxious: to me, it ruins the musicality -- the sound is bright, but it's also really annoying. I'd prefer a proper Baroque situation: one string at a time or two strings in unison (1:1). This is an authentic 18th Century configuration. To bring the ensemble into balance, just make the orchestra really small. We lose majesty and brightness; we gain subtlety, excitement, and warmth. Classical music becomes more like jazz. Wow: which would you choose? As these ratios become more and more complex (7:1, 23:1), we perceive them as being increasingly dissonant, interesting, raucous, wonderful, exciting, horrible (take your pick). The history of music is a continuous series of one generation's dissonance becoming the consonance of the next generation. Each generation bends the envelope of the last one. And so the artist's pallette progresses with more colors. In practice, musical ratios are not as simple as I've presented above. I've given you the general, theoretical ideal. After a certain point in musical history, many of these ratios don't work out quite "right." Bach wrote The Well-Tempered Clavier in an attempt to promote a modern tuning system in which the ratios were stretched very slightly. Our modern "equal temperament" gives all musical keys the same characteristics as one another, allowing a profound, innovative composer such as Bach the ability to modulate from one key to another almost without limits. In the world since the Baroque period, musical physics has been bent to suit the art -- the ratios are subtly altered. In fact, piano tuners have been tuning the entire instrument slightly wide, obtaining a brightness of sound as a result (which drives woodwind players insane when they try to match the pitches of that piano). And Charlie Parker blew some very complicated music, making use of it: believe it! The piano tuner is much more of a trickster than you thought, huh? However, the sound of an un-tempered organ or harpsichord is subtly and fascinatingly different. Every key has its own coloration, its own character. A concerto in D major is happy, for example; in the old world, it was a happy key. We're not used to this in modern times. That's why authenticity in performing baroque music can really matter. I'm going to stop dead in my tracks right now because this subject is just so intricate. It's worthy of a book. So, yes, an octave is 2:1. Richard |
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#6
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Newbe question: pitch and octave frequency ratio?
"Geoff Wood" -nospam wrote in message ... | ras wrote: | I understand that a octave have 12 'intervals' as well as how you do | the math (twelfth root of 2) but not why an octave: "is itself a | frequency ratio of 2:1". | | Any help will be most appreciated, thanks | Mike | | And octave below A 440 is 220, and an octave higher is 880. The octave | above and below those is 110 and 1660Hz.. | | Not sure if that relationship is naturally musical, or whether it is a thing | learned by us. | | | geoff | | It is indeed naturally musical. The ratio 2:1 is quite simple, no? Let's say that we hear two notes simultaneously. If we hear A above middle C (440) and A an octave above that (880), this ratio sounds calm and peaceful. However, if we hear a whole series of a few hundred different notes, all accompanied by another synchronized series an octave above that, we might become irritated. But play both notes one after the other and we can experience the sequence as expressive. The psychology of music is indeed complex. Many harpsichordists like to couple up the mechanism so that they're constantly playing simultaneous octaves, even one octave above and one below, so that three pitches are sounding. It makes the instrument louder, an advantage for a naturally quiet instrument when playing a concerto with an orchestra. However, I find such coupling obnoxious: to me, it ruins the musicality -- the sound is bright, but it's also really annoying. I'd prefer a proper Baroque situation: one string at a time or two strings in unison (1:1). This is an authentic 18th Century configuration. To bring the ensemble into balance, just make the orchestra really small. We lose majesty and brightness; we gain subtlety, excitement, and warmth. Classical music becomes more like jazz. Wow: which would you choose? As these ratios become more and more complex (7:1, 23:1), we perceive them as being increasingly dissonant, interesting, raucous, wonderful, exciting, horrible (take your pick). The history of music is a continuous series of one generation's dissonance becoming the consonance of the next generation. Each generation bends the envelope of the last one. And so the artist's pallette progresses with more colors. In practice, musical ratios are not as simple as I've presented above. I've given you the general, theoretical ideal. After a certain point in musical history, many of these ratios don't work out quite "right." Bach wrote The Well-Tempered Clavier in an attempt to promote a modern tuning system in which the ratios were stretched very slightly. Our modern "equal temperament" gives all musical keys the same characteristics as one another, allowing a profound, innovative composer such as Bach the ability to modulate from one key to another almost without limits. In the world since the Baroque period, musical physics has been bent to suit the art -- the ratios are subtly altered. In fact, piano tuners have been tuning the entire instrument slightly wide, obtaining a brightness of sound as a result (which drives woodwind players insane when they try to match the pitches of that piano). And Charlie Parker blew some very complicated music, making use of it: believe it! The piano tuner is much more of a trickster than you thought, huh? However, the sound of an un-tempered organ or harpsichord is subtly and fascinatingly different. Every key has its own coloration, its own character. A concerto in D major is happy, for example; in the old world, it was a happy key. We're not used to this in modern times. That's why authenticity in performing baroque music can really matter. I'm going to stop dead in my tracks right now because this subject is just so intricate. It's worthy of a book. So, yes, an octave is 2:1. Richard |
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#7
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Newbe question: pitch and octave frequency ratio?
"Geoff Wood" -nospam wrote in message ... | ras wrote: | I understand that a octave have 12 'intervals' as well as how you do | the math (twelfth root of 2) but not why an octave: "is itself a | frequency ratio of 2:1". | | Any help will be most appreciated, thanks | Mike | | And octave below A 440 is 220, and an octave higher is 880. The octave | above and below those is 110 and 1660Hz.. | | Not sure if that relationship is naturally musical, or whether it is a thing | learned by us. | | | geoff | | It is indeed naturally musical. The ratio 2:1 is quite simple, no? Let's say that we hear two notes simultaneously. If we hear A above middle C (440) and A an octave above that (880), this ratio sounds calm and peaceful. However, if we hear a whole series of a few hundred different notes, all accompanied by another synchronized series an octave above that, we might become irritated. But play both notes one after the other and we can experience the sequence as expressive. The psychology of music is indeed complex. Many harpsichordists like to couple up the mechanism so that they're constantly playing simultaneous octaves, even one octave above and one below, so that three pitches are sounding. It makes the instrument louder, an advantage for a naturally quiet instrument when playing a concerto with an orchestra. However, I find such coupling obnoxious: to me, it ruins the musicality -- the sound is bright, but it's also really annoying. I'd prefer a proper Baroque situation: one string at a time or two strings in unison (1:1). This is an authentic 18th Century configuration. To bring the ensemble into balance, just make the orchestra really small. We lose majesty and brightness; we gain subtlety, excitement, and warmth. Classical music becomes more like jazz. Wow: which would you choose? As these ratios become more and more complex (7:1, 23:1), we perceive them as being increasingly dissonant, interesting, raucous, wonderful, exciting, horrible (take your pick). The history of music is a continuous series of one generation's dissonance becoming the consonance of the next generation. Each generation bends the envelope of the last one. And so the artist's pallette progresses with more colors. In practice, musical ratios are not as simple as I've presented above. I've given you the general, theoretical ideal. After a certain point in musical history, many of these ratios don't work out quite "right." Bach wrote The Well-Tempered Clavier in an attempt to promote a modern tuning system in which the ratios were stretched very slightly. Our modern "equal temperament" gives all musical keys the same characteristics as one another, allowing a profound, innovative composer such as Bach the ability to modulate from one key to another almost without limits. In the world since the Baroque period, musical physics has been bent to suit the art -- the ratios are subtly altered. In fact, piano tuners have been tuning the entire instrument slightly wide, obtaining a brightness of sound as a result (which drives woodwind players insane when they try to match the pitches of that piano). And Charlie Parker blew some very complicated music, making use of it: believe it! The piano tuner is much more of a trickster than you thought, huh? However, the sound of an un-tempered organ or harpsichord is subtly and fascinatingly different. Every key has its own coloration, its own character. A concerto in D major is happy, for example; in the old world, it was a happy key. We're not used to this in modern times. That's why authenticity in performing baroque music can really matter. I'm going to stop dead in my tracks right now because this subject is just so intricate. It's worthy of a book. So, yes, an octave is 2:1. Richard |
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#8
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Newbe question: pitch and octave frequency ratio?
Quoth Geoff Wood ...
Aha, it is because it doubles the frequency. Thank you kindly for helping, mike ras wrote: I understand that a octave have 12 'intervals' as well as how you do the math (twelfth root of 2) but not why an octave: "is itself a frequency ratio of 2:1". Any help will be most appreciated, thanks Mike And octave below A 440 is 220, and an octave higher is 880. The octave above and below those is 110 and 1660Hz.. Not sure if that relationship is naturally musical, or whether it is a thing learned by us. geoff |
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#9
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Newbe question: pitch and octave frequency ratio?
Quoth Geoff Wood ...
Aha, it is because it doubles the frequency. Thank you kindly for helping, mike ras wrote: I understand that a octave have 12 'intervals' as well as how you do the math (twelfth root of 2) but not why an octave: "is itself a frequency ratio of 2:1". Any help will be most appreciated, thanks Mike And octave below A 440 is 220, and an octave higher is 880. The octave above and below those is 110 and 1660Hz.. Not sure if that relationship is naturally musical, or whether it is a thing learned by us. geoff |
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#10
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Newbe question: pitch and octave frequency ratio?
Quoth Geoff Wood ...
Aha, it is because it doubles the frequency. Thank you kindly for helping, mike ras wrote: I understand that a octave have 12 'intervals' as well as how you do the math (twelfth root of 2) but not why an octave: "is itself a frequency ratio of 2:1". Any help will be most appreciated, thanks Mike And octave below A 440 is 220, and an octave higher is 880. The octave above and below those is 110 and 1660Hz.. Not sure if that relationship is naturally musical, or whether it is a thing learned by us. geoff |
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#11
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Newbe question: pitch and octave frequency ratio?
"Richard Steinfeld" wrote in message ...
Many harpsichordists like to couple up the mechanism so that they're constantly playing simultaneous octaves, even one octave above and one below, so that three pitches are sounding. Having built 11 harpsichords, all based on historical models, having examined maybe 30 others from antiquity, and many dozens more modern instruments, I must say that have NEVER EVER seen an instrument that can be "coupled up" as you describe. The largest common instruments, from then and now, are two manual instruments with three sets of strings. The lower manual plays two strings, on sounding at unisin, the other sounding at an octave, while the upper manual plays the second unison choir. The ONLY "coupling up" such instruments are capable of is coupling the uppoer manual to the lower. This does not couple up or down an octave, but rather at unison, so you have the capability of playing the 2 unison choirs together, or adding the octave choir to the unison. The occasional and, in fact, rare example of instruments based on the large Hass model will have two more choirs on the lower manual, tuned and octave down and two octaves up, but such instrument are, by far, exceedingly rare exceptions to the rule. But, once again, there simply is no such thing in harpsichords, modern or ancient, of "coupling up" by octaves. It makes the instrument louder, an advantage for a naturally quiet instrument when playing a concerto with an orchestra. However, I find such coupling obnoxious: to me, it ruins the musicality -- the sound is bright, but it's also really annoying. I'd prefer a proper Baroque situation: one string at a time or two strings in unison (1:1). This is an authentic 18th Century configuration. Sorry, but you're ignoring the entire class of authentic Baroque instruments that include the octave (4') choir. Included in that class are most double manual instruments of the era, from France, Flanders, Germany and England. To bring the ensemble into balance, just make the orchestra really small. We lose majesty and brightness; we gain subtlety, excitement, and warmth. Classical music becomes more like jazz. Wow: which would you choose? I would choose authenticity to the original than something, uhm, "jazzed up." :-) As these ratios become more and more complex (7:1, 23:1), we perceive them as being increasingly dissonant, interesting, raucous, wonderful, exciting, horrible (take your pick). Uh no, not exactly. There are entire sets of small whole-number ratios that are quite consonant. You chose ratios that are, in fact consonant. The latter example is, well, wierd in that it is so widely separated as to be heard as two distinct tones. In practice, musical ratios are not as simple as I've presented above. That much I'll certainly agree on. I've given you the general, theoretical ideal. After a certain point in musical history, many of these ratios don't work out quite "right." Bach wrote The Well-Tempered Clavier in an attempt to promote a modern tuning system in which the ratios were stretched very slightly. Our modern "equal temperament" gives all musical keys the same characteristics as one another, allowing a profound, innovative composer such as Bach the ability to modulate from one key to another almost without limits. Please, I REALLY hope you are not equating "well-temperement" with "equal-temperment." They are most decidely NOT the same thing, as bach and many before and since nknew full well. However, the sound of an un-tempered organ or harpsichord is subtly and fascinatingly different. I should say, never, ever having heard and "untempered" keyboard instrument. That would suggest Pythogrean intonation, something that is physically impossible on a fretted or keyed instrument with a finite number of freat or keys. I suspect you mean "just intoned" or "well-tempered" or other tuning schemes which are not "equally tempered." Yes, such, on the appropriate instrument playing the appropriate repertoire can be most enjoyable. I'm going to stop dead in my tracks right now because this subject is just so intricate. It's worthy of a book. Several of which I have on the shelf beside me as we speak, from a reprint of Pietro Aron to Barbour's eanalysis of this and other just intonations, to Helmholtz's Sensation of Tone, discussing aural consonance and sissonance and the role of hole-number ratios to Fespermann Equal-Beating Temperments and many others. So, yes, an octave is 2:1. Yes, it is, but you utterly failed to answer the question as to why. Here's a moe general explanation as to why small, simple whole-number ratios, such as 2:1 (the octave), 3:2 (the pure 5th), 4:3 (the fourth) 5:4 (a justly intoned major third), and so on, sound pleasing. It has to do with the concept of "coincident partials". Except in the case of pure sine waves, musical tones have overtones or "partials" that are whole number ratios of the original frequency. For example, play the middle A note on a piano, organ or harpsichord, look at it with a high-resolution spectrum analyzer, and not only will you find fundamental tone at 440 Hz (or, 415 if you have it tuned, like my harpsichords, about a semitone low), but you'll find prominent tones at whole-number multiples of that, 2 times, 3 times, 4 times and so on, at frequencies of 880, 1320, 1760 Hz and so on. This is true of each and every one of the notes you play. Indeed, on some instruments, such as the harpsichord, MOST of the energy is in these uppper partials or harmonics. Now, play the octave above A440, together with A440. See what happens? the 2nd harmonic of A440 is "coincident" with the fundamental of the note 1 octave up (or double the frequency), at 880: A440 * 2 = 880 A880 * 1 = 880 -------------- Difference 0 These two notes, assuming the instrument is tuned properly, coincide and reinforce on another. But, let's take the upper A sightly off-tune. Let's make it 881 instead: A440 * 2 = 880 Hz A881 * 1 = 881 -------------- Deff: 1 Hz That difference will be heard in a wavering of the note at a rate of 1 second. tune it further away, and the wavering gets faster, until about the time when the difference is 6-10 Hz, when it stops being perceived as a waver and starts being perceived as "fuzz" make it far enough away, the difference tone perceived sounds quite discordant. Let's look at another example. As I mentioned, an interval of a pure fifth has the ratio of 3:2. IN our example, the fifth above A is E. It has a frequency 3:2 times that of the fundamenatl, or: 440 * 3/2 = 660 Hz Now, watch what happens. Take the THRID harmonic af the A and the SECOND hamonic of the E: A440 * 3 = 1320 Hz E660 * 2 = 1320 Hz Voila! coincident partials! And the same rule applies. As long as they are close in frequency, they sound "in tune" because of the lack of wavering. You can extend this to more complex rations, like, as mentioned, 4:3 (4th), 5:4 (major 3rd), and so forth. The problem is that, generally, the amount of energy diminshes as the harmonic number increases and the efect of out-of-tuneness is less apparent. This is one reason why music with strange interbvals may sound fine on a piano, but intlerable on a harpsichord: there's FAR more energy in these upper partials in a harpshord then a piano. Of ALL these intervals, those that have small whole-number ratios, the simplest and most obvious is the unison 1:1. Next is the octave (2:1). Now, the next question is, why is it called "an octave" if it's ratio is 2:1? The word derives form the Latin for "eight." |
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#12
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Newbe question: pitch and octave frequency ratio?
"Richard Steinfeld" wrote in message ...
Many harpsichordists like to couple up the mechanism so that they're constantly playing simultaneous octaves, even one octave above and one below, so that three pitches are sounding. Having built 11 harpsichords, all based on historical models, having examined maybe 30 others from antiquity, and many dozens more modern instruments, I must say that have NEVER EVER seen an instrument that can be "coupled up" as you describe. The largest common instruments, from then and now, are two manual instruments with three sets of strings. The lower manual plays two strings, on sounding at unisin, the other sounding at an octave, while the upper manual plays the second unison choir. The ONLY "coupling up" such instruments are capable of is coupling the uppoer manual to the lower. This does not couple up or down an octave, but rather at unison, so you have the capability of playing the 2 unison choirs together, or adding the octave choir to the unison. The occasional and, in fact, rare example of instruments based on the large Hass model will have two more choirs on the lower manual, tuned and octave down and two octaves up, but such instrument are, by far, exceedingly rare exceptions to the rule. But, once again, there simply is no such thing in harpsichords, modern or ancient, of "coupling up" by octaves. It makes the instrument louder, an advantage for a naturally quiet instrument when playing a concerto with an orchestra. However, I find such coupling obnoxious: to me, it ruins the musicality -- the sound is bright, but it's also really annoying. I'd prefer a proper Baroque situation: one string at a time or two strings in unison (1:1). This is an authentic 18th Century configuration. Sorry, but you're ignoring the entire class of authentic Baroque instruments that include the octave (4') choir. Included in that class are most double manual instruments of the era, from France, Flanders, Germany and England. To bring the ensemble into balance, just make the orchestra really small. We lose majesty and brightness; we gain subtlety, excitement, and warmth. Classical music becomes more like jazz. Wow: which would you choose? I would choose authenticity to the original than something, uhm, "jazzed up." :-) As these ratios become more and more complex (7:1, 23:1), we perceive them as being increasingly dissonant, interesting, raucous, wonderful, exciting, horrible (take your pick). Uh no, not exactly. There are entire sets of small whole-number ratios that are quite consonant. You chose ratios that are, in fact consonant. The latter example is, well, wierd in that it is so widely separated as to be heard as two distinct tones. In practice, musical ratios are not as simple as I've presented above. That much I'll certainly agree on. I've given you the general, theoretical ideal. After a certain point in musical history, many of these ratios don't work out quite "right." Bach wrote The Well-Tempered Clavier in an attempt to promote a modern tuning system in which the ratios were stretched very slightly. Our modern "equal temperament" gives all musical keys the same characteristics as one another, allowing a profound, innovative composer such as Bach the ability to modulate from one key to another almost without limits. Please, I REALLY hope you are not equating "well-temperement" with "equal-temperment." They are most decidely NOT the same thing, as bach and many before and since nknew full well. However, the sound of an un-tempered organ or harpsichord is subtly and fascinatingly different. I should say, never, ever having heard and "untempered" keyboard instrument. That would suggest Pythogrean intonation, something that is physically impossible on a fretted or keyed instrument with a finite number of freat or keys. I suspect you mean "just intoned" or "well-tempered" or other tuning schemes which are not "equally tempered." Yes, such, on the appropriate instrument playing the appropriate repertoire can be most enjoyable. I'm going to stop dead in my tracks right now because this subject is just so intricate. It's worthy of a book. Several of which I have on the shelf beside me as we speak, from a reprint of Pietro Aron to Barbour's eanalysis of this and other just intonations, to Helmholtz's Sensation of Tone, discussing aural consonance and sissonance and the role of hole-number ratios to Fespermann Equal-Beating Temperments and many others. So, yes, an octave is 2:1. Yes, it is, but you utterly failed to answer the question as to why. Here's a moe general explanation as to why small, simple whole-number ratios, such as 2:1 (the octave), 3:2 (the pure 5th), 4:3 (the fourth) 5:4 (a justly intoned major third), and so on, sound pleasing. It has to do with the concept of "coincident partials". Except in the case of pure sine waves, musical tones have overtones or "partials" that are whole number ratios of the original frequency. For example, play the middle A note on a piano, organ or harpsichord, look at it with a high-resolution spectrum analyzer, and not only will you find fundamental tone at 440 Hz (or, 415 if you have it tuned, like my harpsichords, about a semitone low), but you'll find prominent tones at whole-number multiples of that, 2 times, 3 times, 4 times and so on, at frequencies of 880, 1320, 1760 Hz and so on. This is true of each and every one of the notes you play. Indeed, on some instruments, such as the harpsichord, MOST of the energy is in these uppper partials or harmonics. Now, play the octave above A440, together with A440. See what happens? the 2nd harmonic of A440 is "coincident" with the fundamental of the note 1 octave up (or double the frequency), at 880: A440 * 2 = 880 A880 * 1 = 880 -------------- Difference 0 These two notes, assuming the instrument is tuned properly, coincide and reinforce on another. But, let's take the upper A sightly off-tune. Let's make it 881 instead: A440 * 2 = 880 Hz A881 * 1 = 881 -------------- Deff: 1 Hz That difference will be heard in a wavering of the note at a rate of 1 second. tune it further away, and the wavering gets faster, until about the time when the difference is 6-10 Hz, when it stops being perceived as a waver and starts being perceived as "fuzz" make it far enough away, the difference tone perceived sounds quite discordant. Let's look at another example. As I mentioned, an interval of a pure fifth has the ratio of 3:2. IN our example, the fifth above A is E. It has a frequency 3:2 times that of the fundamenatl, or: 440 * 3/2 = 660 Hz Now, watch what happens. Take the THRID harmonic af the A and the SECOND hamonic of the E: A440 * 3 = 1320 Hz E660 * 2 = 1320 Hz Voila! coincident partials! And the same rule applies. As long as they are close in frequency, they sound "in tune" because of the lack of wavering. You can extend this to more complex rations, like, as mentioned, 4:3 (4th), 5:4 (major 3rd), and so forth. The problem is that, generally, the amount of energy diminshes as the harmonic number increases and the efect of out-of-tuneness is less apparent. This is one reason why music with strange interbvals may sound fine on a piano, but intlerable on a harpsichord: there's FAR more energy in these upper partials in a harpshord then a piano. Of ALL these intervals, those that have small whole-number ratios, the simplest and most obvious is the unison 1:1. Next is the octave (2:1). Now, the next question is, why is it called "an octave" if it's ratio is 2:1? The word derives form the Latin for "eight." |
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#13
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Newbe question: pitch and octave frequency ratio?
"Richard Steinfeld" wrote in message ...
Many harpsichordists like to couple up the mechanism so that they're constantly playing simultaneous octaves, even one octave above and one below, so that three pitches are sounding. Having built 11 harpsichords, all based on historical models, having examined maybe 30 others from antiquity, and many dozens more modern instruments, I must say that have NEVER EVER seen an instrument that can be "coupled up" as you describe. The largest common instruments, from then and now, are two manual instruments with three sets of strings. The lower manual plays two strings, on sounding at unisin, the other sounding at an octave, while the upper manual plays the second unison choir. The ONLY "coupling up" such instruments are capable of is coupling the uppoer manual to the lower. This does not couple up or down an octave, but rather at unison, so you have the capability of playing the 2 unison choirs together, or adding the octave choir to the unison. The occasional and, in fact, rare example of instruments based on the large Hass model will have two more choirs on the lower manual, tuned and octave down and two octaves up, but such instrument are, by far, exceedingly rare exceptions to the rule. But, once again, there simply is no such thing in harpsichords, modern or ancient, of "coupling up" by octaves. It makes the instrument louder, an advantage for a naturally quiet instrument when playing a concerto with an orchestra. However, I find such coupling obnoxious: to me, it ruins the musicality -- the sound is bright, but it's also really annoying. I'd prefer a proper Baroque situation: one string at a time or two strings in unison (1:1). This is an authentic 18th Century configuration. Sorry, but you're ignoring the entire class of authentic Baroque instruments that include the octave (4') choir. Included in that class are most double manual instruments of the era, from France, Flanders, Germany and England. To bring the ensemble into balance, just make the orchestra really small. We lose majesty and brightness; we gain subtlety, excitement, and warmth. Classical music becomes more like jazz. Wow: which would you choose? I would choose authenticity to the original than something, uhm, "jazzed up." :-) As these ratios become more and more complex (7:1, 23:1), we perceive them as being increasingly dissonant, interesting, raucous, wonderful, exciting, horrible (take your pick). Uh no, not exactly. There are entire sets of small whole-number ratios that are quite consonant. You chose ratios that are, in fact consonant. The latter example is, well, wierd in that it is so widely separated as to be heard as two distinct tones. In practice, musical ratios are not as simple as I've presented above. That much I'll certainly agree on. I've given you the general, theoretical ideal. After a certain point in musical history, many of these ratios don't work out quite "right." Bach wrote The Well-Tempered Clavier in an attempt to promote a modern tuning system in which the ratios were stretched very slightly. Our modern "equal temperament" gives all musical keys the same characteristics as one another, allowing a profound, innovative composer such as Bach the ability to modulate from one key to another almost without limits. Please, I REALLY hope you are not equating "well-temperement" with "equal-temperment." They are most decidely NOT the same thing, as bach and many before and since nknew full well. However, the sound of an un-tempered organ or harpsichord is subtly and fascinatingly different. I should say, never, ever having heard and "untempered" keyboard instrument. That would suggest Pythogrean intonation, something that is physically impossible on a fretted or keyed instrument with a finite number of freat or keys. I suspect you mean "just intoned" or "well-tempered" or other tuning schemes which are not "equally tempered." Yes, such, on the appropriate instrument playing the appropriate repertoire can be most enjoyable. I'm going to stop dead in my tracks right now because this subject is just so intricate. It's worthy of a book. Several of which I have on the shelf beside me as we speak, from a reprint of Pietro Aron to Barbour's eanalysis of this and other just intonations, to Helmholtz's Sensation of Tone, discussing aural consonance and sissonance and the role of hole-number ratios to Fespermann Equal-Beating Temperments and many others. So, yes, an octave is 2:1. Yes, it is, but you utterly failed to answer the question as to why. Here's a moe general explanation as to why small, simple whole-number ratios, such as 2:1 (the octave), 3:2 (the pure 5th), 4:3 (the fourth) 5:4 (a justly intoned major third), and so on, sound pleasing. It has to do with the concept of "coincident partials". Except in the case of pure sine waves, musical tones have overtones or "partials" that are whole number ratios of the original frequency. For example, play the middle A note on a piano, organ or harpsichord, look at it with a high-resolution spectrum analyzer, and not only will you find fundamental tone at 440 Hz (or, 415 if you have it tuned, like my harpsichords, about a semitone low), but you'll find prominent tones at whole-number multiples of that, 2 times, 3 times, 4 times and so on, at frequencies of 880, 1320, 1760 Hz and so on. This is true of each and every one of the notes you play. Indeed, on some instruments, such as the harpsichord, MOST of the energy is in these uppper partials or harmonics. Now, play the octave above A440, together with A440. See what happens? the 2nd harmonic of A440 is "coincident" with the fundamental of the note 1 octave up (or double the frequency), at 880: A440 * 2 = 880 A880 * 1 = 880 -------------- Difference 0 These two notes, assuming the instrument is tuned properly, coincide and reinforce on another. But, let's take the upper A sightly off-tune. Let's make it 881 instead: A440 * 2 = 880 Hz A881 * 1 = 881 -------------- Deff: 1 Hz That difference will be heard in a wavering of the note at a rate of 1 second. tune it further away, and the wavering gets faster, until about the time when the difference is 6-10 Hz, when it stops being perceived as a waver and starts being perceived as "fuzz" make it far enough away, the difference tone perceived sounds quite discordant. Let's look at another example. As I mentioned, an interval of a pure fifth has the ratio of 3:2. IN our example, the fifth above A is E. It has a frequency 3:2 times that of the fundamenatl, or: 440 * 3/2 = 660 Hz Now, watch what happens. Take the THRID harmonic af the A and the SECOND hamonic of the E: A440 * 3 = 1320 Hz E660 * 2 = 1320 Hz Voila! coincident partials! And the same rule applies. As long as they are close in frequency, they sound "in tune" because of the lack of wavering. You can extend this to more complex rations, like, as mentioned, 4:3 (4th), 5:4 (major 3rd), and so forth. The problem is that, generally, the amount of energy diminshes as the harmonic number increases and the efect of out-of-tuneness is less apparent. This is one reason why music with strange interbvals may sound fine on a piano, but intlerable on a harpsichord: there's FAR more energy in these upper partials in a harpshord then a piano. Of ALL these intervals, those that have small whole-number ratios, the simplest and most obvious is the unison 1:1. Next is the octave (2:1). Now, the next question is, why is it called "an octave" if it's ratio is 2:1? The word derives form the Latin for "eight." |
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Newbe question: pitch and octave frequency ratio?
Hang on a sec, one octave up being double the requency is fine. But this is only valid in base 10 number systems. Is there something inherently more natural about base 10 rather than say, base 7 ? If humans had 6 fingers would music be different ? geoff |
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#15
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Newbe question: pitch and octave frequency ratio?
Hang on a sec, one octave up being double the requency is fine. But this is only valid in base 10 number systems. Is there something inherently more natural about base 10 rather than say, base 7 ? If humans had 6 fingers would music be different ? geoff |
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#16
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Newbe question: pitch and octave frequency ratio?
Hang on a sec, one octave up being double the requency is fine. But this is only valid in base 10 number systems. Is there something inherently more natural about base 10 rather than say, base 7 ? If humans had 6 fingers would music be different ? geoff |
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#17
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Newbe question: pitch and octave frequency ratio?
"Dick Pierce" wrote in message om... | "Richard Steinfeld" wrote in message ... | | Many harpsichordists like to couple up the mechanism so that | they're constantly playing simultaneous octaves, even one octave | above and one below, so that three pitches are sounding. | | Having built 11 harpsichords, all based on historical models, having | examined maybe 30 others from antiquity, and many dozens more modern | instruments, I must say that have NEVER EVER seen an instrument that | can be "coupled up" as you describe. | I was the leading harpsichord tuner in New York for a few years; you've heard my work. Think of your garden-variety two-manual instrument with two sets of 8' strings, one set of 4' strings, one set of 16 foot. I worked on them fairly often, especially Neuperts. Or, briefly, the high-tension aviation-age Pleyels beloved by Wanda Landowska and Rafael Puyana. In the recording world, in the typical studio situation, the emphasis is on practicality rather than historical accuracy. Although I set up instruments for people like Fernando Valente, Sylvia Kind, the NY Philharmonic, Hague Philharmonic, chamber music recordings, etc., etc., most of my bread-and-butter was with Zuckermann Harpsichords and especially Caroll Instrument Rental Service. And you wanna know what most of the recordings were that used harpsichords? They were TV commercials and top-40 records. Your mileage may vary. So, yes, I came away from all that with respect for both historical accuracy and respect for modern materials and designs. On one hand, there was the day that I struggled with an authentic Dolmetsch reproduction, an instrument that had to be adjusted with files, glue, and shims; mechanisms made with real boar's hair springs. I played with a harpsichordist who owned a Christopher Bannister instrument -- the builder shot crows in New Jersey for their authentic quills! With this type of madness, one can gain an appreciation for plastic jack guides, uniform plastic quills, aluminum mechanicals, etc.: they're reliable. When one is playing rapid repeated notes in Scarlatti, does one get better musical service from natural frayed quills that'll hang on the strings or from self-lubricating hard plastic? Will the player's artistry be better served by having to spend hours every week futzing with the harpsichord or from practicing the music? The entire world of historic performance always involves tradeoffs. I favor enlightened distinctions. As a guide, I ask myself, "If Bach came here today and heard our modern instruments, what would he have preferred? What would have been the best tools to serve his music?" | The largest common instruments, from then and now, are two manual | instruments with three sets of strings. The lower manual plays two | strings, on sounding at unisin, the other sounding at an octave, | while the upper manual plays the second unison choir. The ONLY | "coupling up" such instruments are capable of is coupling the | uppoer manual to the lower. This does not couple up or down an | octave, but rather at unison, so you have the capability of playing | the 2 unison choirs together, or adding the octave choir to the | unison. | I'd actually prefer such an instrument. I've been out of this for a long time, so things change. The larger Neuperts I recall we top manual -- 8' + 4', lower manual -- 8' + 16' For the bystander, let me explain that Neupert was (is?) the foremost manufacturer of mass-produced harpsichords. These were based upon certain historical models, but were not authentic reproductions. The firm also made custom instruments to historical configurations. These custom instruments, however, still made use of modern mechanism materials. | The occasional and, in fact, rare example of instruments based on the | large Hass model will have two more choirs on the lower manual, tuned | and octave down and two octaves up, but such instrument are, by far, | exceedingly rare exceptions to the rule. | Yes. I've never seen such an instrument (2 octaves up). I've worked on such rarities as pedal harpsichords and electonically-amplified clavichords, but not that configuration. | But, once again, there simply is no such thing in harpsichords, modern | or ancient, of "coupling up" by octaves. | I think we're splitting hairs. Yes, of course, the coupling is between the two keyboards. | It makes | the instrument louder, an advantage for a naturally quiet | instrument when playing a concerto with an orchestra. However, I | find such coupling obnoxious: to me, it ruins the musicality -- | the sound is bright, but it's also really annoying. I'd prefer a | proper Baroque situation: one string at a time or two strings in | unison (1:1). This is an authentic 18th Century configuration. | | Sorry, but you're ignoring the entire class of authentic Baroque | instruments that include the octave (4') choir. Included in that | class are most double manual instruments of the era, from France, | Flanders, Germany and England. | Now that we're talking shop, let me continue. What bugs me is the harpsichordist who just couples up the instrument and plays flat-out that way from beginning to the end of the piece -- there's no contrast in the sound. A fine artist of the time, I'd hope, would engage the 4' for occasional color or emphasis. Since the harpsichord cannot gradate the intensity of the pluck, I see one of the tools in the harpsichordist's bag of tricks being to convey the -impression- of dynamic changes through the art of phrasing, subtle (really subtle) metric changes, etc. | To | bring the ensemble into balance, just make the orchestra really | small. We lose majesty and brightness; we gain subtlety, | excitement, and warmth. Classical music becomes more like jazz. | Wow: which would you choose? | | I would choose authenticity to the original than something, uhm, | "jazzed up." :-) | I don't mean "jazzed up," but rather, let's say, playfulness, interplay, in the spirit of the music of the times. I think that figured bass was a roadmap for sensible improvisation (not Charlie Parker on the keyboard). | As these ratios become more and more complex (7:1, 23:1), we | perceive them as being increasingly dissonant, interesting, | raucous, wonderful, exciting, horrible (take your pick). | | Uh no, not exactly. There are entire sets of small whole-number | ratios that are quite consonant. You chose ratios that are, in fact | consonant. The latter example is, well, wierd in that it is so widely | separated as to be heard as two distinct tones. | | In practice, musical ratios are not as simple as I've presented | above. | | That much I'll certainly agree on. | | I've given you the general, theoretical ideal. After a | certain point in musical history, many of these ratios don't work | out quite "right." Bach wrote The Well-Tempered Clavier in an | attempt to promote a modern tuning system in which the ratios | were stretched very slightly. Our modern "equal temperament" | gives all musical keys the same characteristics as one another, | allowing a profound, innovative composer such as Bach the ability | to modulate from one key to another almost without limits. | | Please, I REALLY hope you are not equating "well-temperement" with | "equal-temperment." They are most decidely NOT the same thing, as | bach and many before and since nknew full well. | Please explain. | However, the sound of an un-tempered organ or harpsichord is | subtly and fascinatingly different. | | I should say, never, ever having heard and "untempered" keyboard | instrument. That would suggest Pythogrean intonation, something | that is physically impossible on a fretted or keyed instrument | with a finite number of freat or keys. | | I suspect you mean "just intoned" or "well-tempered" or other | tuning schemes which are not "equally tempered." Yes, such, on the | appropriate instrument playing the appropriate repertoire can be | most enjoyable. | I'm probably talking about "just intonation." | I'm going to stop dead in my | tracks right now because this subject is just so intricate. It's | worthy of a book. | | Several of which I have on the shelf beside me as we speak, from | a reprint of Pietro Aron to Barbour's eanalysis of this and other | just intonations, to Helmholtz's Sensation of Tone, discussing | aural consonance and sissonance and the role of hole-number ratios | to Fespermann Equal-Beating Temperments and many others. | | So, yes, an octave is 2:1. | | Yes, it is, but you utterly failed to answer the question as to why. | ???????????????? | Here's a moe general explanation as to why small, simple whole-number | ratios, such as 2:1 (the octave), 3:2 (the pure 5th), 4:3 (the fourth) | 5:4 (a justly intoned major third), and so on, sound pleasing. | | It has to do with the concept of "coincident partials". Except in the | case of pure sine waves, musical tones have overtones or "partials" | that are whole number ratios of the original frequency. For example, | play the middle A note on a piano, organ or harpsichord, look at it | with a high-resolution spectrum analyzer, and not only will you find | fundamental tone at 440 Hz (or, 415 if you have it tuned, like my | harpsichords, about a semitone low), but you'll find prominent tones | at whole-number multiples of that, 2 times, 3 times, 4 times and so on, | at frequencies of 880, 1320, 1760 Hz and so on. This is true of each | and every one of the notes you play. Indeed, on some instruments, such | as the harpsichord, MOST of the energy is in these uppper partials | or harmonics. | | Now, play the octave above A440, together with A440. See what happens? | the 2nd harmonic of A440 is "coincident" with the fundamental of the | note 1 octave up (or double the frequency), at 880: | | A440 * 2 = 880 | A880 * 1 = 880 | -------------- | Difference 0 | | These two notes, assuming the instrument is tuned properly, coincide | and reinforce on another. But, let's take the upper A sightly off-tune. | Let's make it 881 instead: | | A440 * 2 = 880 Hz | A881 * 1 = 881 | -------------- | Deff: 1 Hz | | That difference will be heard in a wavering of the note at a rate of 1 | second. tune it further away, and the wavering gets faster, until about | the time when the difference is 6-10 Hz, when it stops being perceived | as a waver and starts being perceived as "fuzz" make it far enough away, | the difference tone perceived sounds quite discordant. | | Let's look at another example. As I mentioned, an interval of a pure | fifth has the ratio of 3:2. IN our example, the fifth above A is E. It | has a frequency 3:2 times that of the fundamenatl, or: | | 440 * 3/2 = 660 Hz | | Now, watch what happens. Take the THRID harmonic af the A and the SECOND | hamonic of the E: | | A440 * 3 = 1320 Hz | E660 * 2 = 1320 Hz | | Voila! coincident partials! And the same rule applies. As long as they | are close in frequency, they sound "in tune" because of the lack of | wavering. | | You can extend this to more complex rations, like, as mentioned, | 4:3 (4th), 5:4 (major 3rd), and so forth. The problem is that, | generally, the amount of energy diminshes as the harmonic number | increases and the efect of out-of-tuneness is less apparent. This | is one reason why music with strange interbvals may sound fine on | a piano, but intlerable on a harpsichord: there's FAR more energy | in these upper partials in a harpshord then a piano. | | Of ALL these intervals, those that have small whole-number ratios, | the simplest and most obvious is the unison 1:1. Next is the octave | (2:1). | | Now, the next question is, why is it called "an octave" if it's | ratio is 2:1? The word derives form the Latin for "eight." Yup. I did forget to mention that. Your explanation is great! I didn't want to go down that path since I was trying to stay somewhat within the OP's range of experience. I think that I was afraid that if I started on the "8" explanation, with white keys as a visual picture, the explanation would have gotten very far afield. So, I didn't. Good to meet you. Richard |
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#18
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Newbe question: pitch and octave frequency ratio?
"Dick Pierce" wrote in message om... | "Richard Steinfeld" wrote in message ... | | Many harpsichordists like to couple up the mechanism so that | they're constantly playing simultaneous octaves, even one octave | above and one below, so that three pitches are sounding. | | Having built 11 harpsichords, all based on historical models, having | examined maybe 30 others from antiquity, and many dozens more modern | instruments, I must say that have NEVER EVER seen an instrument that | can be "coupled up" as you describe. | I was the leading harpsichord tuner in New York for a few years; you've heard my work. Think of your garden-variety two-manual instrument with two sets of 8' strings, one set of 4' strings, one set of 16 foot. I worked on them fairly often, especially Neuperts. Or, briefly, the high-tension aviation-age Pleyels beloved by Wanda Landowska and Rafael Puyana. In the recording world, in the typical studio situation, the emphasis is on practicality rather than historical accuracy. Although I set up instruments for people like Fernando Valente, Sylvia Kind, the NY Philharmonic, Hague Philharmonic, chamber music recordings, etc., etc., most of my bread-and-butter was with Zuckermann Harpsichords and especially Caroll Instrument Rental Service. And you wanna know what most of the recordings were that used harpsichords? They were TV commercials and top-40 records. Your mileage may vary. So, yes, I came away from all that with respect for both historical accuracy and respect for modern materials and designs. On one hand, there was the day that I struggled with an authentic Dolmetsch reproduction, an instrument that had to be adjusted with files, glue, and shims; mechanisms made with real boar's hair springs. I played with a harpsichordist who owned a Christopher Bannister instrument -- the builder shot crows in New Jersey for their authentic quills! With this type of madness, one can gain an appreciation for plastic jack guides, uniform plastic quills, aluminum mechanicals, etc.: they're reliable. When one is playing rapid repeated notes in Scarlatti, does one get better musical service from natural frayed quills that'll hang on the strings or from self-lubricating hard plastic? Will the player's artistry be better served by having to spend hours every week futzing with the harpsichord or from practicing the music? The entire world of historic performance always involves tradeoffs. I favor enlightened distinctions. As a guide, I ask myself, "If Bach came here today and heard our modern instruments, what would he have preferred? What would have been the best tools to serve his music?" | The largest common instruments, from then and now, are two manual | instruments with three sets of strings. The lower manual plays two | strings, on sounding at unisin, the other sounding at an octave, | while the upper manual plays the second unison choir. The ONLY | "coupling up" such instruments are capable of is coupling the | uppoer manual to the lower. This does not couple up or down an | octave, but rather at unison, so you have the capability of playing | the 2 unison choirs together, or adding the octave choir to the | unison. | I'd actually prefer such an instrument. I've been out of this for a long time, so things change. The larger Neuperts I recall we top manual -- 8' + 4', lower manual -- 8' + 16' For the bystander, let me explain that Neupert was (is?) the foremost manufacturer of mass-produced harpsichords. These were based upon certain historical models, but were not authentic reproductions. The firm also made custom instruments to historical configurations. These custom instruments, however, still made use of modern mechanism materials. | The occasional and, in fact, rare example of instruments based on the | large Hass model will have two more choirs on the lower manual, tuned | and octave down and two octaves up, but such instrument are, by far, | exceedingly rare exceptions to the rule. | Yes. I've never seen such an instrument (2 octaves up). I've worked on such rarities as pedal harpsichords and electonically-amplified clavichords, but not that configuration. | But, once again, there simply is no such thing in harpsichords, modern | or ancient, of "coupling up" by octaves. | I think we're splitting hairs. Yes, of course, the coupling is between the two keyboards. | It makes | the instrument louder, an advantage for a naturally quiet | instrument when playing a concerto with an orchestra. However, I | find such coupling obnoxious: to me, it ruins the musicality -- | the sound is bright, but it's also really annoying. I'd prefer a | proper Baroque situation: one string at a time or two strings in | unison (1:1). This is an authentic 18th Century configuration. | | Sorry, but you're ignoring the entire class of authentic Baroque | instruments that include the octave (4') choir. Included in that | class are most double manual instruments of the era, from France, | Flanders, Germany and England. | Now that we're talking shop, let me continue. What bugs me is the harpsichordist who just couples up the instrument and plays flat-out that way from beginning to the end of the piece -- there's no contrast in the sound. A fine artist of the time, I'd hope, would engage the 4' for occasional color or emphasis. Since the harpsichord cannot gradate the intensity of the pluck, I see one of the tools in the harpsichordist's bag of tricks being to convey the -impression- of dynamic changes through the art of phrasing, subtle (really subtle) metric changes, etc. | To | bring the ensemble into balance, just make the orchestra really | small. We lose majesty and brightness; we gain subtlety, | excitement, and warmth. Classical music becomes more like jazz. | Wow: which would you choose? | | I would choose authenticity to the original than something, uhm, | "jazzed up." :-) | I don't mean "jazzed up," but rather, let's say, playfulness, interplay, in the spirit of the music of the times. I think that figured bass was a roadmap for sensible improvisation (not Charlie Parker on the keyboard). | As these ratios become more and more complex (7:1, 23:1), we | perceive them as being increasingly dissonant, interesting, | raucous, wonderful, exciting, horrible (take your pick). | | Uh no, not exactly. There are entire sets of small whole-number | ratios that are quite consonant. You chose ratios that are, in fact | consonant. The latter example is, well, wierd in that it is so widely | separated as to be heard as two distinct tones. | | In practice, musical ratios are not as simple as I've presented | above. | | That much I'll certainly agree on. | | I've given you the general, theoretical ideal. After a | certain point in musical history, many of these ratios don't work | out quite "right." Bach wrote The Well-Tempered Clavier in an | attempt to promote a modern tuning system in which the ratios | were stretched very slightly. Our modern "equal temperament" | gives all musical keys the same characteristics as one another, | allowing a profound, innovative composer such as Bach the ability | to modulate from one key to another almost without limits. | | Please, I REALLY hope you are not equating "well-temperement" with | "equal-temperment." They are most decidely NOT the same thing, as | bach and many before and since nknew full well. | Please explain. | However, the sound of an un-tempered organ or harpsichord is | subtly and fascinatingly different. | | I should say, never, ever having heard and "untempered" keyboard | instrument. That would suggest Pythogrean intonation, something | that is physically impossible on a fretted or keyed instrument | with a finite number of freat or keys. | | I suspect you mean "just intoned" or "well-tempered" or other | tuning schemes which are not "equally tempered." Yes, such, on the | appropriate instrument playing the appropriate repertoire can be | most enjoyable. | I'm probably talking about "just intonation." | I'm going to stop dead in my | tracks right now because this subject is just so intricate. It's | worthy of a book. | | Several of which I have on the shelf beside me as we speak, from | a reprint of Pietro Aron to Barbour's eanalysis of this and other | just intonations, to Helmholtz's Sensation of Tone, discussing | aural consonance and sissonance and the role of hole-number ratios | to Fespermann Equal-Beating Temperments and many others. | | So, yes, an octave is 2:1. | | Yes, it is, but you utterly failed to answer the question as to why. | ???????????????? | Here's a moe general explanation as to why small, simple whole-number | ratios, such as 2:1 (the octave), 3:2 (the pure 5th), 4:3 (the fourth) | 5:4 (a justly intoned major third), and so on, sound pleasing. | | It has to do with the concept of "coincident partials". Except in the | case of pure sine waves, musical tones have overtones or "partials" | that are whole number ratios of the original frequency. For example, | play the middle A note on a piano, organ or harpsichord, look at it | with a high-resolution spectrum analyzer, and not only will you find | fundamental tone at 440 Hz (or, 415 if you have it tuned, like my | harpsichords, about a semitone low), but you'll find prominent tones | at whole-number multiples of that, 2 times, 3 times, 4 times and so on, | at frequencies of 880, 1320, 1760 Hz and so on. This is true of each | and every one of the notes you play. Indeed, on some instruments, such | as the harpsichord, MOST of the energy is in these uppper partials | or harmonics. | | Now, play the octave above A440, together with A440. See what happens? | the 2nd harmonic of A440 is "coincident" with the fundamental of the | note 1 octave up (or double the frequency), at 880: | | A440 * 2 = 880 | A880 * 1 = 880 | -------------- | Difference 0 | | These two notes, assuming the instrument is tuned properly, coincide | and reinforce on another. But, let's take the upper A sightly off-tune. | Let's make it 881 instead: | | A440 * 2 = 880 Hz | A881 * 1 = 881 | -------------- | Deff: 1 Hz | | That difference will be heard in a wavering of the note at a rate of 1 | second. tune it further away, and the wavering gets faster, until about | the time when the difference is 6-10 Hz, when it stops being perceived | as a waver and starts being perceived as "fuzz" make it far enough away, | the difference tone perceived sounds quite discordant. | | Let's look at another example. As I mentioned, an interval of a pure | fifth has the ratio of 3:2. IN our example, the fifth above A is E. It | has a frequency 3:2 times that of the fundamenatl, or: | | 440 * 3/2 = 660 Hz | | Now, watch what happens. Take the THRID harmonic af the A and the SECOND | hamonic of the E: | | A440 * 3 = 1320 Hz | E660 * 2 = 1320 Hz | | Voila! coincident partials! And the same rule applies. As long as they | are close in frequency, they sound "in tune" because of the lack of | wavering. | | You can extend this to more complex rations, like, as mentioned, | 4:3 (4th), 5:4 (major 3rd), and so forth. The problem is that, | generally, the amount of energy diminshes as the harmonic number | increases and the efect of out-of-tuneness is less apparent. This | is one reason why music with strange interbvals may sound fine on | a piano, but intlerable on a harpsichord: there's FAR more energy | in these upper partials in a harpshord then a piano. | | Of ALL these intervals, those that have small whole-number ratios, | the simplest and most obvious is the unison 1:1. Next is the octave | (2:1). | | Now, the next question is, why is it called "an octave" if it's | ratio is 2:1? The word derives form the Latin for "eight." Yup. I did forget to mention that. Your explanation is great! I didn't want to go down that path since I was trying to stay somewhat within the OP's range of experience. I think that I was afraid that if I started on the "8" explanation, with white keys as a visual picture, the explanation would have gotten very far afield. So, I didn't. Good to meet you. Richard |
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Newbe question: pitch and octave frequency ratio?
"Dick Pierce" wrote in message om... | "Richard Steinfeld" wrote in message ... | | Many harpsichordists like to couple up the mechanism so that | they're constantly playing simultaneous octaves, even one octave | above and one below, so that three pitches are sounding. | | Having built 11 harpsichords, all based on historical models, having | examined maybe 30 others from antiquity, and many dozens more modern | instruments, I must say that have NEVER EVER seen an instrument that | can be "coupled up" as you describe. | I was the leading harpsichord tuner in New York for a few years; you've heard my work. Think of your garden-variety two-manual instrument with two sets of 8' strings, one set of 4' strings, one set of 16 foot. I worked on them fairly often, especially Neuperts. Or, briefly, the high-tension aviation-age Pleyels beloved by Wanda Landowska and Rafael Puyana. In the recording world, in the typical studio situation, the emphasis is on practicality rather than historical accuracy. Although I set up instruments for people like Fernando Valente, Sylvia Kind, the NY Philharmonic, Hague Philharmonic, chamber music recordings, etc., etc., most of my bread-and-butter was with Zuckermann Harpsichords and especially Caroll Instrument Rental Service. And you wanna know what most of the recordings were that used harpsichords? They were TV commercials and top-40 records. Your mileage may vary. So, yes, I came away from all that with respect for both historical accuracy and respect for modern materials and designs. On one hand, there was the day that I struggled with an authentic Dolmetsch reproduction, an instrument that had to be adjusted with files, glue, and shims; mechanisms made with real boar's hair springs. I played with a harpsichordist who owned a Christopher Bannister instrument -- the builder shot crows in New Jersey for their authentic quills! With this type of madness, one can gain an appreciation for plastic jack guides, uniform plastic quills, aluminum mechanicals, etc.: they're reliable. When one is playing rapid repeated notes in Scarlatti, does one get better musical service from natural frayed quills that'll hang on the strings or from self-lubricating hard plastic? Will the player's artistry be better served by having to spend hours every week futzing with the harpsichord or from practicing the music? The entire world of historic performance always involves tradeoffs. I favor enlightened distinctions. As a guide, I ask myself, "If Bach came here today and heard our modern instruments, what would he have preferred? What would have been the best tools to serve his music?" | The largest common instruments, from then and now, are two manual | instruments with three sets of strings. The lower manual plays two | strings, on sounding at unisin, the other sounding at an octave, | while the upper manual plays the second unison choir. The ONLY | "coupling up" such instruments are capable of is coupling the | uppoer manual to the lower. This does not couple up or down an | octave, but rather at unison, so you have the capability of playing | the 2 unison choirs together, or adding the octave choir to the | unison. | I'd actually prefer such an instrument. I've been out of this for a long time, so things change. The larger Neuperts I recall we top manual -- 8' + 4', lower manual -- 8' + 16' For the bystander, let me explain that Neupert was (is?) the foremost manufacturer of mass-produced harpsichords. These were based upon certain historical models, but were not authentic reproductions. The firm also made custom instruments to historical configurations. These custom instruments, however, still made use of modern mechanism materials. | The occasional and, in fact, rare example of instruments based on the | large Hass model will have two more choirs on the lower manual, tuned | and octave down and two octaves up, but such instrument are, by far, | exceedingly rare exceptions to the rule. | Yes. I've never seen such an instrument (2 octaves up). I've worked on such rarities as pedal harpsichords and electonically-amplified clavichords, but not that configuration. | But, once again, there simply is no such thing in harpsichords, modern | or ancient, of "coupling up" by octaves. | I think we're splitting hairs. Yes, of course, the coupling is between the two keyboards. | It makes | the instrument louder, an advantage for a naturally quiet | instrument when playing a concerto with an orchestra. However, I | find such coupling obnoxious: to me, it ruins the musicality -- | the sound is bright, but it's also really annoying. I'd prefer a | proper Baroque situation: one string at a time or two strings in | unison (1:1). This is an authentic 18th Century configuration. | | Sorry, but you're ignoring the entire class of authentic Baroque | instruments that include the octave (4') choir. Included in that | class are most double manual instruments of the era, from France, | Flanders, Germany and England. | Now that we're talking shop, let me continue. What bugs me is the harpsichordist who just couples up the instrument and plays flat-out that way from beginning to the end of the piece -- there's no contrast in the sound. A fine artist of the time, I'd hope, would engage the 4' for occasional color or emphasis. Since the harpsichord cannot gradate the intensity of the pluck, I see one of the tools in the harpsichordist's bag of tricks being to convey the -impression- of dynamic changes through the art of phrasing, subtle (really subtle) metric changes, etc. | To | bring the ensemble into balance, just make the orchestra really | small. We lose majesty and brightness; we gain subtlety, | excitement, and warmth. Classical music becomes more like jazz. | Wow: which would you choose? | | I would choose authenticity to the original than something, uhm, | "jazzed up." :-) | I don't mean "jazzed up," but rather, let's say, playfulness, interplay, in the spirit of the music of the times. I think that figured bass was a roadmap for sensible improvisation (not Charlie Parker on the keyboard). | As these ratios become more and more complex (7:1, 23:1), we | perceive them as being increasingly dissonant, interesting, | raucous, wonderful, exciting, horrible (take your pick). | | Uh no, not exactly. There are entire sets of small whole-number | ratios that are quite consonant. You chose ratios that are, in fact | consonant. The latter example is, well, wierd in that it is so widely | separated as to be heard as two distinct tones. | | In practice, musical ratios are not as simple as I've presented | above. | | That much I'll certainly agree on. | | I've given you the general, theoretical ideal. After a | certain point in musical history, many of these ratios don't work | out quite "right." Bach wrote The Well-Tempered Clavier in an | attempt to promote a modern tuning system in which the ratios | were stretched very slightly. Our modern "equal temperament" | gives all musical keys the same characteristics as one another, | allowing a profound, innovative composer such as Bach the ability | to modulate from one key to another almost without limits. | | Please, I REALLY hope you are not equating "well-temperement" with | "equal-temperment." They are most decidely NOT the same thing, as | bach and many before and since nknew full well. | Please explain. | However, the sound of an un-tempered organ or harpsichord is | subtly and fascinatingly different. | | I should say, never, ever having heard and "untempered" keyboard | instrument. That would suggest Pythogrean intonation, something | that is physically impossible on a fretted or keyed instrument | with a finite number of freat or keys. | | I suspect you mean "just intoned" or "well-tempered" or other | tuning schemes which are not "equally tempered." Yes, such, on the | appropriate instrument playing the appropriate repertoire can be | most enjoyable. | I'm probably talking about "just intonation." | I'm going to stop dead in my | tracks right now because this subject is just so intricate. It's | worthy of a book. | | Several of which I have on the shelf beside me as we speak, from | a reprint of Pietro Aron to Barbour's eanalysis of this and other | just intonations, to Helmholtz's Sensation of Tone, discussing | aural consonance and sissonance and the role of hole-number ratios | to Fespermann Equal-Beating Temperments and many others. | | So, yes, an octave is 2:1. | | Yes, it is, but you utterly failed to answer the question as to why. | ???????????????? | Here's a moe general explanation as to why small, simple whole-number | ratios, such as 2:1 (the octave), 3:2 (the pure 5th), 4:3 (the fourth) | 5:4 (a justly intoned major third), and so on, sound pleasing. | | It has to do with the concept of "coincident partials". Except in the | case of pure sine waves, musical tones have overtones or "partials" | that are whole number ratios of the original frequency. For example, | play the middle A note on a piano, organ or harpsichord, look at it | with a high-resolution spectrum analyzer, and not only will you find | fundamental tone at 440 Hz (or, 415 if you have it tuned, like my | harpsichords, about a semitone low), but you'll find prominent tones | at whole-number multiples of that, 2 times, 3 times, 4 times and so on, | at frequencies of 880, 1320, 1760 Hz and so on. This is true of each | and every one of the notes you play. Indeed, on some instruments, such | as the harpsichord, MOST of the energy is in these uppper partials | or harmonics. | | Now, play the octave above A440, together with A440. See what happens? | the 2nd harmonic of A440 is "coincident" with the fundamental of the | note 1 octave up (or double the frequency), at 880: | | A440 * 2 = 880 | A880 * 1 = 880 | -------------- | Difference 0 | | These two notes, assuming the instrument is tuned properly, coincide | and reinforce on another. But, let's take the upper A sightly off-tune. | Let's make it 881 instead: | | A440 * 2 = 880 Hz | A881 * 1 = 881 | -------------- | Deff: 1 Hz | | That difference will be heard in a wavering of the note at a rate of 1 | second. tune it further away, and the wavering gets faster, until about | the time when the difference is 6-10 Hz, when it stops being perceived | as a waver and starts being perceived as "fuzz" make it far enough away, | the difference tone perceived sounds quite discordant. | | Let's look at another example. As I mentioned, an interval of a pure | fifth has the ratio of 3:2. IN our example, the fifth above A is E. It | has a frequency 3:2 times that of the fundamenatl, or: | | 440 * 3/2 = 660 Hz | | Now, watch what happens. Take the THRID harmonic af the A and the SECOND | hamonic of the E: | | A440 * 3 = 1320 Hz | E660 * 2 = 1320 Hz | | Voila! coincident partials! And the same rule applies. As long as they | are close in frequency, they sound "in tune" because of the lack of | wavering. | | You can extend this to more complex rations, like, as mentioned, | 4:3 (4th), 5:4 (major 3rd), and so forth. The problem is that, | generally, the amount of energy diminshes as the harmonic number | increases and the efect of out-of-tuneness is less apparent. This | is one reason why music with strange interbvals may sound fine on | a piano, but intlerable on a harpsichord: there's FAR more energy | in these upper partials in a harpshord then a piano. | | Of ALL these intervals, those that have small whole-number ratios, | the simplest and most obvious is the unison 1:1. Next is the octave | (2:1). | | Now, the next question is, why is it called "an octave" if it's | ratio is 2:1? The word derives form the Latin for "eight." Yup. I did forget to mention that. Your explanation is great! I didn't want to go down that path since I was trying to stay somewhat within the OP's range of experience. I think that I was afraid that if I started on the "8" explanation, with white keys as a visual picture, the explanation would have gotten very far afield. So, I didn't. Good to meet you. Richard |
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Newbe question: pitch and octave frequency ratio?
"Richard Steinfeld" wrote in message ... "Geoff Wood" -nospam wrote in message ... | ras wrote: | I understand that a octave have 12 'intervals' as well as how you do | the math (twelfth root of 2) but not why an octave: "is itself a | frequency ratio of 2:1". | | Any help will be most appreciated, thanks | Mike | | And octave below A 440 is 220, and an octave higher is 880. The octave | above and below those is 110 and 1660Hz.. Well--1760Hz--but who's counting. Norm Strong |
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Newbe question: pitch and octave frequency ratio?
"Richard Steinfeld" wrote in message ... "Geoff Wood" -nospam wrote in message ... | ras wrote: | I understand that a octave have 12 'intervals' as well as how you do | the math (twelfth root of 2) but not why an octave: "is itself a | frequency ratio of 2:1". | | Any help will be most appreciated, thanks | Mike | | And octave below A 440 is 220, and an octave higher is 880. The octave | above and below those is 110 and 1660Hz.. Well--1760Hz--but who's counting. Norm Strong |
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Newbe question: pitch and octave frequency ratio?
"Richard Steinfeld" wrote in message ... "Geoff Wood" -nospam wrote in message ... | ras wrote: | I understand that a octave have 12 'intervals' as well as how you do | the math (twelfth root of 2) but not why an octave: "is itself a | frequency ratio of 2:1". | | Any help will be most appreciated, thanks | Mike | | And octave below A 440 is 220, and an octave higher is 880. The octave | above and below those is 110 and 1660Hz.. Well--1760Hz--but who's counting. Norm Strong |
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Newbe question: pitch and octave frequency ratio?
"Geoff Wood" -nospam wrote in message ... Hang on a sec, one octave up being double the requency is fine. But this is only valid in base 10 number systems. Is there something inherently more natural about base 10 rather than say, base 7 ? It's valid in any base numbering system. Nature doesn't care what numbering system we humans use to measure it. Computers use base 2, but synthesizers like Microsoft GS Wavetable SW Synth work just fine. If humans had 6 fingers would music be different ? Musical instruments would certainly be different. Music would be different because of that. Music theory would probaby be about the same, because the physics of sound would be the same. geoff |
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Newbe question: pitch and octave frequency ratio?
"Geoff Wood" -nospam wrote in message ... Hang on a sec, one octave up being double the requency is fine. But this is only valid in base 10 number systems. Is there something inherently more natural about base 10 rather than say, base 7 ? It's valid in any base numbering system. Nature doesn't care what numbering system we humans use to measure it. Computers use base 2, but synthesizers like Microsoft GS Wavetable SW Synth work just fine. If humans had 6 fingers would music be different ? Musical instruments would certainly be different. Music would be different because of that. Music theory would probaby be about the same, because the physics of sound would be the same. geoff |
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Newbe question: pitch and octave frequency ratio?
"Geoff Wood" -nospam wrote in message ... Hang on a sec, one octave up being double the requency is fine. But this is only valid in base 10 number systems. Is there something inherently more natural about base 10 rather than say, base 7 ? It's valid in any base numbering system. Nature doesn't care what numbering system we humans use to measure it. Computers use base 2, but synthesizers like Microsoft GS Wavetable SW Synth work just fine. If humans had 6 fingers would music be different ? Musical instruments would certainly be different. Music would be different because of that. Music theory would probaby be about the same, because the physics of sound would be the same. geoff |
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Newbe question: pitch and octave frequency ratio?
"Geoff Wood" -nospam wrote in message ... | | Hang on a sec, one octave up being double the requency is fine. But this is | only valid in base 10 number systems. Is there something inherently more | natural about base 10 rather than say, base 7 ? | | If humans had 6 fingers would music be different ? | | Think of what Theloneus Monk would have turned out with two more fingers. Crazy, man. Richard |
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Newbe question: pitch and octave frequency ratio?
"Geoff Wood" -nospam wrote in message ... | | Hang on a sec, one octave up being double the requency is fine. But this is | only valid in base 10 number systems. Is there something inherently more | natural about base 10 rather than say, base 7 ? | | If humans had 6 fingers would music be different ? | | Think of what Theloneus Monk would have turned out with two more fingers. Crazy, man. Richard |
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Newbe question: pitch and octave frequency ratio?
"Geoff Wood" -nospam wrote in message ... | | Hang on a sec, one octave up being double the requency is fine. But this is | only valid in base 10 number systems. Is there something inherently more | natural about base 10 rather than say, base 7 ? | | If humans had 6 fingers would music be different ? | | Think of what Theloneus Monk would have turned out with two more fingers. Crazy, man. Richard |
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Newbe question: pitch and octave frequency ratio?
"Richard Steinfeld" wrote in message ...
I was the leading harpsichord tuner in New York for a few years; you've heard my work. Think of your garden-variety two-manual instrument with two sets of 8' strings, one set of 4' strings, one set of 16 foot. I worked on them fairly often, especially Neuperts. Or, briefly, the high-tension aviation-age Pleyels beloved by Wanda Landowska and Rafael Puyana. If you're primary work was on Neuperts and Pleyels then, no, I have not heard your work. Neuperts and Pleyels are NOT "garden variety two-manual instruments." Harpsichords with the disposition of 16'+8' on the lower manual and 8'+4' on the upper manual are NOT "garden variety two-manual instruments." They are in fact, very unusual in the harpsichord world for a variety of reasons. Neither are based on any real historical artifacts, most especially the Pleyel, which is a piano in every respect but the action. Event the Neupert so-called "Bach" model is a ******* child, built into a heavy case, strung heavily, with a disposition that has no historical precendent whatsoever and is, in fact, based on a single instrument of dubious lineage, article 316 from the Staatliche Sammlung fur Musikinstrumente at the Scloss Charlottenburg in Berlin. Hubbard (Three Centuries of Harpsichord Making, Harvard University Press 1967) pretty thoroughly demolishes the case that the dispostion of this instrument is original, pointing our numerous and obvious modifications happening long after the instrument left the hands of the maker, and, likely, long after Bach and any other person had left this earth. That being said, I am not at all surprised by your disdain for the sound of such instruments "coupled up." They are , at best, bad caricatures of harpsichords at unison pitch with their innappropriate scaling, excessively heavy stringing and construction, thick, over-braced piano-style soundboards, their complex but ineffectual mechanical contrivances and all the rest. Now, add the 4' and 16', and they go from lousy to intolerably awful. These instruments should suffer the fate that befell the instruments in the Palace of Versais in the early 19th century: they should be broken down for firewood (that woudln't work with a Pleyel: these ARE pianos, complete with enormous cast-iron frames and behemoth piano cases). In the recording world, in the typical studio situation, the emphasis is on practicality rather than historical accuracy. Although I set up instruments for people like Fernando Valente, Sylvia Kind, the NY Philharmonic, Hague Philharmonic, chamber music recordings, etc., etc., most of my bread-and-butter was with Zuckermann Harpsichords and especially Caroll Instrument Rental Service. And you wanna know what most of the recordings were that used harpsichords? They were TV commercials and top-40 records. Your mileage may vary. My friend, I would suggest that the recording world of the likes of the NY Phiharmonic a generation ago was FAR from representative of the state of the harpsichord world. At least in the Boston area and elsewhere, there was a far higher level of enlightenment and appreciation of the true art and history of harpsichord. We're talking about performers and scholars like Ralph Kirkpatrick, Kenneth Gilbert, Leonhardt, Gibbons and many others who shunned the technically marvelous but musically disasterous heavy-weight plucking-pianos like Neupert and Pleyel, prefering instead far more historically accurate and appropriate, FAR better sounding examples from Hubbard, Dowd and many others. As an example of the absurdity of instruments like the Pleyel, Italian 2x8' instruments, a common continuo instrument, weigh less than the bench for an instrument like a Pleyel, and had case walls that were thinner than the soundboard of such an instrument, and soundboards that were thinner still. Such instruments, being of such lightweight construction and having the commensurate light stringing with no over-spun wire, were brighter, far louder, more responsive, blended better and more cohesive then the musical ******* children of some misguided industrial-mechanical program from Neupert and Pleyel. The largest instrument I now have, a two-manual 2x8', 1x4' based on the 1750 Taskin weighs all of 96 pounds, and ALL the strings on the instrument weigh less than a single bass string on a Pleyel. Coupling the 4' on that instrument results in a cohesive, full, articulate sound, nothing like the disjointed, schizophrenic buzz and ruslte of a Neupert. Now, to be fair, more contemporary Neuperts have migrated more towards what is now the real mainstream of harpsichord practice, but they did so quite reluctantly, dragged kicking and screaming into musical propriety by a market that simply refused to buy any more of their crap. With this type of madness, one can gain an appreciation for plastic jack guides, uniform plastic quills, aluminum mechanicals, etc.: they're reliable. When one is playing rapid repeated notes in Scarlatti, does one get better musical service from natural frayed quills that'll hang on the strings or from self-lubricating hard plastic? Will the player's artistry be better served by having to spend hours every week futzing with the harpsichord or from practicing the music? And interesting veiwpoint, as the most problematic harpsichord I EVER worked on was a Neupert Bach model: save on older Zuckerman kit that had a wrestplank glue joint fail, I have NEVER encountered an instrument until the Neupert that had such abysmal reliability. Their fancy-dancy aluminum jacks were useless. And your comment is interesting in light of my own and many other's experience with instruments from the likes of Hubbard and Dowd and others. I have NONE of the problems you speak, and do NOT spend hours per week, nor have I ever, "futzing" with the instrument. The entire world of historic performance always involves tradeoffs. I favor enlightened distinctions. As a guide, I ask myself, "If Bach came here today and heard our modern instruments, what would he have preferred? What would have been the best tools to serve his music?" He'd probably scoff at the Pleyel, show bemusement at Landowska's style, and find a good madern reproduction to be VERY reliable. | The largest common instruments, from then and now, are two manual | instruments with three sets of strings. The lower manual plays two | strings, on sounding at unisin, the other sounding at an octave, | while the upper manual plays the second unison choir. The ONLY | "coupling up" such instruments are capable of is coupling the | uppoer manual to the lower. This does not couple up or down an | octave, but rather at unison, so you have the capability of playing | the 2 unison choirs together, or adding the octave choir to the | unison. | I'd actually prefer such an instrument. I've been out of this for a long time, so things change. The larger Neuperts I recall we top manual -- 8' + 4', lower manual -- 8' + 16' For the bystander, let me explain that Neupert was (is?) the foremost manufacturer of mass-produced harpsichords. No, they were NOT the "foremost," they were only the largest. They might be considered the MacDonalds of harpsichords. This, in many eyes, is NOT a virtue. And Neupert had, decades ago, lost its market supremecy, simply trampled into the dust by their own refusal to adapt to what the market wanted. Instead, they tried to continue with selling the crap they did: silly caricatures of harpsichords, not harpsichords. These were based upon certain historical models, Now, they were not, as Hubbard quite soundly demonstrated nearly 40 years ago. but were not authentic reproductions. The firm also made custom instruments to historical configurations. These custom instruments, however, still made use of modern mechanism materials. And, until Huepert really changed their tune in the late 1970's they were dismal failures in a market increasingly dominated by more knowledgeable performers. | Sorry, but you're ignoring the entire class of authentic Baroque | instruments that include the octave (4') choir. Included in that | class are most double manual instruments of the era, from France, | Flanders, Germany and England. | Now that we're talking shop, let me continue. What bugs me is the harpsichordist who just couples up the instrument and plays flat-out that way from beginning to the end of the piece -- there's no contrast in the sound. A fine artist of the time, I'd hope, would engage the 4' for occasional color or emphasis. Since the harpsichord cannot gradate the intensity of the pluck, I see one of the tools in the harpsichordist's bag of tricks being to convey the -impression- of dynamic changes through the art of phrasing, subtle (really subtle) metric changes, etc. This engaging and disengaging of stops is almost entirely a modern artifact resulting from the incorporation of stop-changing pedals, something which NEVER existed on historical instruments. You will find, however, historical precedent in mirroring or echoing sections on two keyboards, for example, playing the lower keyboard coupled gives 2x8, or 2x8+2x4, while the upper manual gives simply 1x8. | | Please, I REALLY hope you are not equating "well-temperement" with | "equal-temperment." They are most decidely NOT the same thing, as | bach and many before and since nknew full well. | Please explain. It's very simple: "equal temperement" is one thing," "well temperment" is something else altogether. Equal temperment simply treats every half step identically, all having a ratio of 2^(1/12). Period. End of discussion. It's mathematically "perfect" as far as evenly dividing the octave geometrically across 12 intervals. It results in nearly pure 5ths, and awful sounding 3rds, but ALL fifths are nearly pure, and ALL 3rds are equally awful. It allows free transposition to any key, with the assurance that things will be equally mediocre-sounding no matter how far you transpose. There is exactly one and only one variety of equal temperement. There are a number of well-temperments, but, in general, they sacrifice a little bit on the purity of the fifths and gain an enormous advantage in better consonance of the thirds. They do NOT allow free and arbitrary transpositions, all keys do NOT have identical intervals, and all half- steps are NOT the same. But unlike true just intonations, all keys are plausible, and distant modulations are not disasterous. A more rigorous explanation can be found in texts ranging anywhere from Mersenne, Aron, Werkmeister, Kirnberger and other older sources through Helmholtz (The Sensation of Tone) through to more modern texts like Barbour and Fespermann. |
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Newbe question: pitch and octave frequency ratio?
"Richard Steinfeld" wrote in message ...
I was the leading harpsichord tuner in New York for a few years; you've heard my work. Think of your garden-variety two-manual instrument with two sets of 8' strings, one set of 4' strings, one set of 16 foot. I worked on them fairly often, especially Neuperts. Or, briefly, the high-tension aviation-age Pleyels beloved by Wanda Landowska and Rafael Puyana. If you're primary work was on Neuperts and Pleyels then, no, I have not heard your work. Neuperts and Pleyels are NOT "garden variety two-manual instruments." Harpsichords with the disposition of 16'+8' on the lower manual and 8'+4' on the upper manual are NOT "garden variety two-manual instruments." They are in fact, very unusual in the harpsichord world for a variety of reasons. Neither are based on any real historical artifacts, most especially the Pleyel, which is a piano in every respect but the action. Event the Neupert so-called "Bach" model is a ******* child, built into a heavy case, strung heavily, with a disposition that has no historical precendent whatsoever and is, in fact, based on a single instrument of dubious lineage, article 316 from the Staatliche Sammlung fur Musikinstrumente at the Scloss Charlottenburg in Berlin. Hubbard (Three Centuries of Harpsichord Making, Harvard University Press 1967) pretty thoroughly demolishes the case that the dispostion of this instrument is original, pointing our numerous and obvious modifications happening long after the instrument left the hands of the maker, and, likely, long after Bach and any other person had left this earth. That being said, I am not at all surprised by your disdain for the sound of such instruments "coupled up." They are , at best, bad caricatures of harpsichords at unison pitch with their innappropriate scaling, excessively heavy stringing and construction, thick, over-braced piano-style soundboards, their complex but ineffectual mechanical contrivances and all the rest. Now, add the 4' and 16', and they go from lousy to intolerably awful. These instruments should suffer the fate that befell the instruments in the Palace of Versais in the early 19th century: they should be broken down for firewood (that woudln't work with a Pleyel: these ARE pianos, complete with enormous cast-iron frames and behemoth piano cases). In the recording world, in the typical studio situation, the emphasis is on practicality rather than historical accuracy. Although I set up instruments for people like Fernando Valente, Sylvia Kind, the NY Philharmonic, Hague Philharmonic, chamber music recordings, etc., etc., most of my bread-and-butter was with Zuckermann Harpsichords and especially Caroll Instrument Rental Service. And you wanna know what most of the recordings were that used harpsichords? They were TV commercials and top-40 records. Your mileage may vary. My friend, I would suggest that the recording world of the likes of the NY Phiharmonic a generation ago was FAR from representative of the state of the harpsichord world. At least in the Boston area and elsewhere, there was a far higher level of enlightenment and appreciation of the true art and history of harpsichord. We're talking about performers and scholars like Ralph Kirkpatrick, Kenneth Gilbert, Leonhardt, Gibbons and many others who shunned the technically marvelous but musically disasterous heavy-weight plucking-pianos like Neupert and Pleyel, prefering instead far more historically accurate and appropriate, FAR better sounding examples from Hubbard, Dowd and many others. As an example of the absurdity of instruments like the Pleyel, Italian 2x8' instruments, a common continuo instrument, weigh less than the bench for an instrument like a Pleyel, and had case walls that were thinner than the soundboard of such an instrument, and soundboards that were thinner still. Such instruments, being of such lightweight construction and having the commensurate light stringing with no over-spun wire, were brighter, far louder, more responsive, blended better and more cohesive then the musical ******* children of some misguided industrial-mechanical program from Neupert and Pleyel. The largest instrument I now have, a two-manual 2x8', 1x4' based on the 1750 Taskin weighs all of 96 pounds, and ALL the strings on the instrument weigh less than a single bass string on a Pleyel. Coupling the 4' on that instrument results in a cohesive, full, articulate sound, nothing like the disjointed, schizophrenic buzz and ruslte of a Neupert. Now, to be fair, more contemporary Neuperts have migrated more towards what is now the real mainstream of harpsichord practice, but they did so quite reluctantly, dragged kicking and screaming into musical propriety by a market that simply refused to buy any more of their crap. With this type of madness, one can gain an appreciation for plastic jack guides, uniform plastic quills, aluminum mechanicals, etc.: they're reliable. When one is playing rapid repeated notes in Scarlatti, does one get better musical service from natural frayed quills that'll hang on the strings or from self-lubricating hard plastic? Will the player's artistry be better served by having to spend hours every week futzing with the harpsichord or from practicing the music? And interesting veiwpoint, as the most problematic harpsichord I EVER worked on was a Neupert Bach model: save on older Zuckerman kit that had a wrestplank glue joint fail, I have NEVER encountered an instrument until the Neupert that had such abysmal reliability. Their fancy-dancy aluminum jacks were useless. And your comment is interesting in light of my own and many other's experience with instruments from the likes of Hubbard and Dowd and others. I have NONE of the problems you speak, and do NOT spend hours per week, nor have I ever, "futzing" with the instrument. The entire world of historic performance always involves tradeoffs. I favor enlightened distinctions. As a guide, I ask myself, "If Bach came here today and heard our modern instruments, what would he have preferred? What would have been the best tools to serve his music?" He'd probably scoff at the Pleyel, show bemusement at Landowska's style, and find a good madern reproduction to be VERY reliable. | The largest common instruments, from then and now, are two manual | instruments with three sets of strings. The lower manual plays two | strings, on sounding at unisin, the other sounding at an octave, | while the upper manual plays the second unison choir. The ONLY | "coupling up" such instruments are capable of is coupling the | uppoer manual to the lower. This does not couple up or down an | octave, but rather at unison, so you have the capability of playing | the 2 unison choirs together, or adding the octave choir to the | unison. | I'd actually prefer such an instrument. I've been out of this for a long time, so things change. The larger Neuperts I recall we top manual -- 8' + 4', lower manual -- 8' + 16' For the bystander, let me explain that Neupert was (is?) the foremost manufacturer of mass-produced harpsichords. No, they were NOT the "foremost," they were only the largest. They might be considered the MacDonalds of harpsichords. This, in many eyes, is NOT a virtue. And Neupert had, decades ago, lost its market supremecy, simply trampled into the dust by their own refusal to adapt to what the market wanted. Instead, they tried to continue with selling the crap they did: silly caricatures of harpsichords, not harpsichords. These were based upon certain historical models, Now, they were not, as Hubbard quite soundly demonstrated nearly 40 years ago. but were not authentic reproductions. The firm also made custom instruments to historical configurations. These custom instruments, however, still made use of modern mechanism materials. And, until Huepert really changed their tune in the late 1970's they were dismal failures in a market increasingly dominated by more knowledgeable performers. | Sorry, but you're ignoring the entire class of authentic Baroque | instruments that include the octave (4') choir. Included in that | class are most double manual instruments of the era, from France, | Flanders, Germany and England. | Now that we're talking shop, let me continue. What bugs me is the harpsichordist who just couples up the instrument and plays flat-out that way from beginning to the end of the piece -- there's no contrast in the sound. A fine artist of the time, I'd hope, would engage the 4' for occasional color or emphasis. Since the harpsichord cannot gradate the intensity of the pluck, I see one of the tools in the harpsichordist's bag of tricks being to convey the -impression- of dynamic changes through the art of phrasing, subtle (really subtle) metric changes, etc. This engaging and disengaging of stops is almost entirely a modern artifact resulting from the incorporation of stop-changing pedals, something which NEVER existed on historical instruments. You will find, however, historical precedent in mirroring or echoing sections on two keyboards, for example, playing the lower keyboard coupled gives 2x8, or 2x8+2x4, while the upper manual gives simply 1x8. | | Please, I REALLY hope you are not equating "well-temperement" with | "equal-temperment." They are most decidely NOT the same thing, as | bach and many before and since nknew full well. | Please explain. It's very simple: "equal temperement" is one thing," "well temperment" is something else altogether. Equal temperment simply treats every half step identically, all having a ratio of 2^(1/12). Period. End of discussion. It's mathematically "perfect" as far as evenly dividing the octave geometrically across 12 intervals. It results in nearly pure 5ths, and awful sounding 3rds, but ALL fifths are nearly pure, and ALL 3rds are equally awful. It allows free transposition to any key, with the assurance that things will be equally mediocre-sounding no matter how far you transpose. There is exactly one and only one variety of equal temperement. There are a number of well-temperments, but, in general, they sacrifice a little bit on the purity of the fifths and gain an enormous advantage in better consonance of the thirds. They do NOT allow free and arbitrary transpositions, all keys do NOT have identical intervals, and all half- steps are NOT the same. But unlike true just intonations, all keys are plausible, and distant modulations are not disasterous. A more rigorous explanation can be found in texts ranging anywhere from Mersenne, Aron, Werkmeister, Kirnberger and other older sources through Helmholtz (The Sensation of Tone) through to more modern texts like Barbour and Fespermann. |
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#31
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Newbe question: pitch and octave frequency ratio?
"Richard Steinfeld" wrote in message ...
I was the leading harpsichord tuner in New York for a few years; you've heard my work. Think of your garden-variety two-manual instrument with two sets of 8' strings, one set of 4' strings, one set of 16 foot. I worked on them fairly often, especially Neuperts. Or, briefly, the high-tension aviation-age Pleyels beloved by Wanda Landowska and Rafael Puyana. If you're primary work was on Neuperts and Pleyels then, no, I have not heard your work. Neuperts and Pleyels are NOT "garden variety two-manual instruments." Harpsichords with the disposition of 16'+8' on the lower manual and 8'+4' on the upper manual are NOT "garden variety two-manual instruments." They are in fact, very unusual in the harpsichord world for a variety of reasons. Neither are based on any real historical artifacts, most especially the Pleyel, which is a piano in every respect but the action. Event the Neupert so-called "Bach" model is a ******* child, built into a heavy case, strung heavily, with a disposition that has no historical precendent whatsoever and is, in fact, based on a single instrument of dubious lineage, article 316 from the Staatliche Sammlung fur Musikinstrumente at the Scloss Charlottenburg in Berlin. Hubbard (Three Centuries of Harpsichord Making, Harvard University Press 1967) pretty thoroughly demolishes the case that the dispostion of this instrument is original, pointing our numerous and obvious modifications happening long after the instrument left the hands of the maker, and, likely, long after Bach and any other person had left this earth. That being said, I am not at all surprised by your disdain for the sound of such instruments "coupled up." They are , at best, bad caricatures of harpsichords at unison pitch with their innappropriate scaling, excessively heavy stringing and construction, thick, over-braced piano-style soundboards, their complex but ineffectual mechanical contrivances and all the rest. Now, add the 4' and 16', and they go from lousy to intolerably awful. These instruments should suffer the fate that befell the instruments in the Palace of Versais in the early 19th century: they should be broken down for firewood (that woudln't work with a Pleyel: these ARE pianos, complete with enormous cast-iron frames and behemoth piano cases). In the recording world, in the typical studio situation, the emphasis is on practicality rather than historical accuracy. Although I set up instruments for people like Fernando Valente, Sylvia Kind, the NY Philharmonic, Hague Philharmonic, chamber music recordings, etc., etc., most of my bread-and-butter was with Zuckermann Harpsichords and especially Caroll Instrument Rental Service. And you wanna know what most of the recordings were that used harpsichords? They were TV commercials and top-40 records. Your mileage may vary. My friend, I would suggest that the recording world of the likes of the NY Phiharmonic a generation ago was FAR from representative of the state of the harpsichord world. At least in the Boston area and elsewhere, there was a far higher level of enlightenment and appreciation of the true art and history of harpsichord. We're talking about performers and scholars like Ralph Kirkpatrick, Kenneth Gilbert, Leonhardt, Gibbons and many others who shunned the technically marvelous but musically disasterous heavy-weight plucking-pianos like Neupert and Pleyel, prefering instead far more historically accurate and appropriate, FAR better sounding examples from Hubbard, Dowd and many others. As an example of the absurdity of instruments like the Pleyel, Italian 2x8' instruments, a common continuo instrument, weigh less than the bench for an instrument like a Pleyel, and had case walls that were thinner than the soundboard of such an instrument, and soundboards that were thinner still. Such instruments, being of such lightweight construction and having the commensurate light stringing with no over-spun wire, were brighter, far louder, more responsive, blended better and more cohesive then the musical ******* children of some misguided industrial-mechanical program from Neupert and Pleyel. The largest instrument I now have, a two-manual 2x8', 1x4' based on the 1750 Taskin weighs all of 96 pounds, and ALL the strings on the instrument weigh less than a single bass string on a Pleyel. Coupling the 4' on that instrument results in a cohesive, full, articulate sound, nothing like the disjointed, schizophrenic buzz and ruslte of a Neupert. Now, to be fair, more contemporary Neuperts have migrated more towards what is now the real mainstream of harpsichord practice, but they did so quite reluctantly, dragged kicking and screaming into musical propriety by a market that simply refused to buy any more of their crap. With this type of madness, one can gain an appreciation for plastic jack guides, uniform plastic quills, aluminum mechanicals, etc.: they're reliable. When one is playing rapid repeated notes in Scarlatti, does one get better musical service from natural frayed quills that'll hang on the strings or from self-lubricating hard plastic? Will the player's artistry be better served by having to spend hours every week futzing with the harpsichord or from practicing the music? And interesting veiwpoint, as the most problematic harpsichord I EVER worked on was a Neupert Bach model: save on older Zuckerman kit that had a wrestplank glue joint fail, I have NEVER encountered an instrument until the Neupert that had such abysmal reliability. Their fancy-dancy aluminum jacks were useless. And your comment is interesting in light of my own and many other's experience with instruments from the likes of Hubbard and Dowd and others. I have NONE of the problems you speak, and do NOT spend hours per week, nor have I ever, "futzing" with the instrument. The entire world of historic performance always involves tradeoffs. I favor enlightened distinctions. As a guide, I ask myself, "If Bach came here today and heard our modern instruments, what would he have preferred? What would have been the best tools to serve his music?" He'd probably scoff at the Pleyel, show bemusement at Landowska's style, and find a good madern reproduction to be VERY reliable. | The largest common instruments, from then and now, are two manual | instruments with three sets of strings. The lower manual plays two | strings, on sounding at unisin, the other sounding at an octave, | while the upper manual plays the second unison choir. The ONLY | "coupling up" such instruments are capable of is coupling the | uppoer manual to the lower. This does not couple up or down an | octave, but rather at unison, so you have the capability of playing | the 2 unison choirs together, or adding the octave choir to the | unison. | I'd actually prefer such an instrument. I've been out of this for a long time, so things change. The larger Neuperts I recall we top manual -- 8' + 4', lower manual -- 8' + 16' For the bystander, let me explain that Neupert was (is?) the foremost manufacturer of mass-produced harpsichords. No, they were NOT the "foremost," they were only the largest. They might be considered the MacDonalds of harpsichords. This, in many eyes, is NOT a virtue. And Neupert had, decades ago, lost its market supremecy, simply trampled into the dust by their own refusal to adapt to what the market wanted. Instead, they tried to continue with selling the crap they did: silly caricatures of harpsichords, not harpsichords. These were based upon certain historical models, Now, they were not, as Hubbard quite soundly demonstrated nearly 40 years ago. but were not authentic reproductions. The firm also made custom instruments to historical configurations. These custom instruments, however, still made use of modern mechanism materials. And, until Huepert really changed their tune in the late 1970's they were dismal failures in a market increasingly dominated by more knowledgeable performers. | Sorry, but you're ignoring the entire class of authentic Baroque | instruments that include the octave (4') choir. Included in that | class are most double manual instruments of the era, from France, | Flanders, Germany and England. | Now that we're talking shop, let me continue. What bugs me is the harpsichordist who just couples up the instrument and plays flat-out that way from beginning to the end of the piece -- there's no contrast in the sound. A fine artist of the time, I'd hope, would engage the 4' for occasional color or emphasis. Since the harpsichord cannot gradate the intensity of the pluck, I see one of the tools in the harpsichordist's bag of tricks being to convey the -impression- of dynamic changes through the art of phrasing, subtle (really subtle) metric changes, etc. This engaging and disengaging of stops is almost entirely a modern artifact resulting from the incorporation of stop-changing pedals, something which NEVER existed on historical instruments. You will find, however, historical precedent in mirroring or echoing sections on two keyboards, for example, playing the lower keyboard coupled gives 2x8, or 2x8+2x4, while the upper manual gives simply 1x8. | | Please, I REALLY hope you are not equating "well-temperement" with | "equal-temperment." They are most decidely NOT the same thing, as | bach and many before and since nknew full well. | Please explain. It's very simple: "equal temperement" is one thing," "well temperment" is something else altogether. Equal temperment simply treats every half step identically, all having a ratio of 2^(1/12). Period. End of discussion. It's mathematically "perfect" as far as evenly dividing the octave geometrically across 12 intervals. It results in nearly pure 5ths, and awful sounding 3rds, but ALL fifths are nearly pure, and ALL 3rds are equally awful. It allows free transposition to any key, with the assurance that things will be equally mediocre-sounding no matter how far you transpose. There is exactly one and only one variety of equal temperement. There are a number of well-temperments, but, in general, they sacrifice a little bit on the purity of the fifths and gain an enormous advantage in better consonance of the thirds. They do NOT allow free and arbitrary transpositions, all keys do NOT have identical intervals, and all half- steps are NOT the same. But unlike true just intonations, all keys are plausible, and distant modulations are not disasterous. A more rigorous explanation can be found in texts ranging anywhere from Mersenne, Aron, Werkmeister, Kirnberger and other older sources through Helmholtz (The Sensation of Tone) through to more modern texts like Barbour and Fespermann. |
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Newbe question: pitch and octave frequency ratio?
"Dick Pierce" wrote ...
These instruments should suffer the fate that befell the instruments in the Palace of Versais in the early 19th century: they should be broken down for firewood (that woudln't work with a Pleyel: these ARE pianos, complete with enormous cast-iron frames and behemoth piano cases). Or those plexiglass and aluminum(?) things I saw in a couple of pop groups in the 70s. There are a number of well-temperments, but, in general, they sacrifice a little bit on the purity of the fifths and gain an enormous advantage in better consonance of the thirds. A friend of mine just sent me a CD he engineered of the new Pasi dual-temperment organ at St. Cecilia's in Omaha... http://www.tcvomaha.com/ArchivedIssu...19Feature7.htm http://www.pasiorgans.com/opus14.html |
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#33
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Newbe question: pitch and octave frequency ratio?
"Dick Pierce" wrote ...
These instruments should suffer the fate that befell the instruments in the Palace of Versais in the early 19th century: they should be broken down for firewood (that woudln't work with a Pleyel: these ARE pianos, complete with enormous cast-iron frames and behemoth piano cases). Or those plexiglass and aluminum(?) things I saw in a couple of pop groups in the 70s. There are a number of well-temperments, but, in general, they sacrifice a little bit on the purity of the fifths and gain an enormous advantage in better consonance of the thirds. A friend of mine just sent me a CD he engineered of the new Pasi dual-temperment organ at St. Cecilia's in Omaha... http://www.tcvomaha.com/ArchivedIssu...19Feature7.htm http://www.pasiorgans.com/opus14.html |
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#34
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Newbe question: pitch and octave frequency ratio?
"Dick Pierce" wrote ...
These instruments should suffer the fate that befell the instruments in the Palace of Versais in the early 19th century: they should be broken down for firewood (that woudln't work with a Pleyel: these ARE pianos, complete with enormous cast-iron frames and behemoth piano cases). Or those plexiglass and aluminum(?) things I saw in a couple of pop groups in the 70s. There are a number of well-temperments, but, in general, they sacrifice a little bit on the purity of the fifths and gain an enormous advantage in better consonance of the thirds. A friend of mine just sent me a CD he engineered of the new Pasi dual-temperment organ at St. Cecilia's in Omaha... http://www.tcvomaha.com/ArchivedIssu...19Feature7.htm http://www.pasiorgans.com/opus14.html |
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Newbe question: pitch and octave frequency ratio?
Dick Pierce wrote:
snip Richard, I've been following this thread a bit and found it very interesting. I must admit that I learned quite a bit from your broad knowledge. Just out of curiosity: Do you happen to know what type of harpsichord Keith Jarret plays "Bach: The Goldberg Variations, ECM" on and how it is tempered? How do you like his play? It sure is completely different from Glenn Gould's on piano... Cheers, Franco |
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Newbe question: pitch and octave frequency ratio?
Dick Pierce wrote:
snip Richard, I've been following this thread a bit and found it very interesting. I must admit that I learned quite a bit from your broad knowledge. Just out of curiosity: Do you happen to know what type of harpsichord Keith Jarret plays "Bach: The Goldberg Variations, ECM" on and how it is tempered? How do you like his play? It sure is completely different from Glenn Gould's on piano... Cheers, Franco |
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Newbe question: pitch and octave frequency ratio?
Dick Pierce wrote:
snip Richard, I've been following this thread a bit and found it very interesting. I must admit that I learned quite a bit from your broad knowledge. Just out of curiosity: Do you happen to know what type of harpsichord Keith Jarret plays "Bach: The Goldberg Variations, ECM" on and how it is tempered? How do you like his play? It sure is completely different from Glenn Gould's on piano... Cheers, Franco |
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Newbe question: pitch and octave frequency ratio?
On Thu, 1 Jul 2004 08:16:34 +1200, "Geoff Wood"
-nospam wrote: Hang on a sec, one octave up being double the requency is fine. But this is only valid in base 10 number systems. Is there something inherently more natural about base 10 rather than say, base 7 ? If humans had 6 fingers would music be different ? Double is double, however you represent the numbers. |
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Newbe question: pitch and octave frequency ratio?
On Thu, 1 Jul 2004 08:16:34 +1200, "Geoff Wood"
-nospam wrote: Hang on a sec, one octave up being double the requency is fine. But this is only valid in base 10 number systems. Is there something inherently more natural about base 10 rather than say, base 7 ? If humans had 6 fingers would music be different ? Double is double, however you represent the numbers. |
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#40
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Newbe question: pitch and octave frequency ratio?
On Thu, 1 Jul 2004 08:16:34 +1200, "Geoff Wood"
-nospam wrote: Hang on a sec, one octave up being double the requency is fine. But this is only valid in base 10 number systems. Is there something inherently more natural about base 10 rather than say, base 7 ? If humans had 6 fingers would music be different ? Double is double, however you represent the numbers. |
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