Hi all.

I was doing some extremely complicated MIDI pitch bend programming,
stuff much too intricate to actually play, and I ran across this
problem.

Given that most quality sequencers have a possilbe pitch bend range of
-8192 to +8191, I was trying to figure out what numbers correspond to
various musical intervals (major 3, perfect 5, etc).

This of course will vary depending on the pitch bend range of the
recieveing instrument.

Given a pitch bend range of +/- 12 (an octave), bending down we (in
theory) get this:

Interval bend value semitones

m2 -0683 1
M2 -1365 2
m3 -2048 3
M3 -2731 4
P4 -3413 5
aug 4 -4096 6
P5 -4779 7
m6 -5461 8
M6 -6144 9
m7 -6827 10
M7 -8426 11
8va -8192 12

....now this is based on purely straight division, and rounding each
value to the nearest whole number.

Unfortunately, some of my results ended up in flat or sharp notes, some
as much as 50 cents.

So I conclude that my sound module does not respond in a linear fashion
to incoming pitch wheel data. The module in question is a Proteus.

So -

1.
Do ALL sound modules respond with the same non-linear pitch bend curve?

2.
If so, has anyone devised a chart more accurate than mine, based on
this non-linear curve?

3.
Has anyone devised charts for sound modules set to other pitch bend
ranges besides a full octave? I imagine separate charts would be
needed for bend ranges of a Major 3 through an Octave.

4.
IF, in fact, the curve is universal, great. If not, do all modules by
any given manufacturer use the same curve, resulting in a need for a
different set of charts for each company's synths, or does it get even
more complicted: different boxes by the same company using different
curves?

Any input is appriciated.

James T.
Tydirium Multimedia

On Fri, 19 Sep 2003 16:48:48 GMT, jt wrote:

Hi all.

I was doing some extremely complicated MIDI pitch bend programming,
stuff much too intricate to actually play, and I ran across this
problem.

Given that most quality sequencers have a possilbe pitch bend range of
-8192 to +8191, I was trying to figure out what numbers correspond to
various musical intervals (major 3, perfect 5, etc).

This of course will vary depending on the pitch bend range of the
recieveing instrument.

Given a pitch bend range of +/- 12 (an octave), bending down we (in
theory) get this:

Interval bend value semitones

m2 -0683 1
M2 -1365 2
m3 -2048 3
M3 -2731 4
P4 -3413 5
aug 4 -4096 6
P5 -4779 7
m6 -5461 8
M6 -6144 9
m7 -6827 10
M7 -8426 11
8va -8192 12

...now this is based on purely straight division, and rounding each
value to the nearest whole number.

Unfortunately, some of my results ended up in flat or sharp notes, some
as much as 50 cents.

So I conclude that my sound module does not respond in a linear fashion
to incoming pitch wheel data. The module in question is a Proteus.

So -

1.
Do ALL sound modules respond with the same non-linear pitch bend curve?

The most common curve is linear by cents (that is, a non-linear
curve proportionate to the standard scale. If you used linear
division, the notes you're selecting using whole numbers as ratios
should be right on the equal temperament scale.

However, not all modules use the same curve. It is *not* defined in
the GM spec, and of course non-GM modules can do whatever they want
anyway.

If you want to get perfect intervals, you need to convert the
interval into cents, then apply it as a ratio compared to the full
scale.

For example, a perfect fifth is a very simple linear ratio -- 3:2.
1.5 times the root note. But on the equal temperament scale, it works
out to 1.4983. So, you're not going to get it selecting it that way.
You need to figure out how many cents each interval is, not the linear
ratios. If I didn't mess my math up, that is 9 cents flat. You'd
need to use 709.511 cents.

Which yields -4844 as the pitch bend interval to use to generate it,
not -4779.


2.
If so, has anyone devised a chart more accurate than mine, based on
this non-linear curve?

For the linear by cents scale, I'm sure of it. No links handy, but
people who do microtuning likely have pitch bend settings to handle
that kind of thing.

Another way to do it, for synths which support microtuning, is to
retune the scale to make the root interval perfect.

3.
Has anyone devised charts for sound modules set to other pitch bend
ranges besides a full octave? I imagine separate charts would be
needed for bend ranges of a Major 3 through an Octave.

Right, you'd need different conversions for each different pitch
bend range you could select.

4.
IF, in fact, the curve is universal, great. If not, do all modules by
any given manufacturer use the same curve, resulting in a need for a
different set of charts for each company's synths, or does it get even
more complicted: different boxes by the same company using different
curves?

There are a few standards. The most common is the linear by cents
method, which is non-linear in pitch but linear compared to the
standard scale (makes tuning to the equal temperament scale very easy,
as your numbers should work out for).

If your synth doesn't use that, you'll need to find out what it is.


--
*-__Jeffery Jones__________| *Starfire* |____________________-*
** Muskego WI Access Channel 14/25 http://www.execpc.com/~jeffsj/mach7/
*Starfire Design Studio* http://www.starfiredesign.com/

"Jeffery S. Jones" wrote in message
...
On Fri, 19 Sep 2003 16:48:48 GMT, jt wrote:


If you want to get perfect intervals, you need to convert the
interval into cents, then apply it as a ratio compared to the full
scale.

For example, a perfect fifth is a very simple linear ratio -- 3:2.
1.5 times the root note. But on the equal temperament scale, it works
out to 1.4983. So, you're not going to get it selecting it that way.
You need to figure out how many cents each interval is, not the linear
ratios. If I didn't mess my math up, that is 9 cents flat. You'd
need to use 709.511 cents.
Cut......

You did the math wrong. The value in cents is 1200log2(f2/f1) where f2 and
f1 are the frequencies as a ratio. That equates to 3986.3137*log10(f2/f1).
For a perfect fifth, f2/f1=1.5.
cents = 3986.31*log(1.5) = 701.95 cents and a chromatic 5th is 2^(7/12) =
1.498307 times,
cents = 3.986.31*log(1.498307) = 700 cents. Therefore a perfect fifth is
1.95 cents sharper than a chromatic fifth.
Bob

"Jeffery S. Jones" wrote in message
...
On Fri, 19 Sep 2003 16:48:48 GMT, jt wrote:


If you want to get perfect intervals, you need to convert the
interval into cents, then apply it as a ratio compared to the full
scale.

For example, a perfect fifth is a very simple linear ratio -- 3:2.
1.5 times the root note. But on the equal temperament scale, it works
out to 1.4983. So, you're not going to get it selecting it that way.
You need to figure out how many cents each interval is, not the linear
ratios. If I didn't mess my math up, that is 9 cents flat. You'd
need to use 709.511 cents.
Cut......

You did the math wrong. The value in cents is 1200log2(f2/f1) where f2 and
f1 are the frequencies as a ratio. That equates to 3986.3137*log10(f2/f1).
For a perfect fifth, f2/f1=1.5.
cents = 3986.31*log(1.5) = 701.95 cents and a chromatic 5th is 2^(7/12) =
1.498307 times,
cents = 3.986.31*log(1.498307) = 700 cents. Therefore a perfect fifth is
1.95 cents sharper than a chromatic fifth.
Bob

In article , Dr. Bob
wrote:

"Jeffery S. Jones" wrote in message
...
On Fri, 19 Sep 2003 16:48:48 GMT, jt wrote:


If you want to get perfect intervals, you need to convert the
interval into cents, then apply it as a ratio compared to the full
scale.

For example, a perfect fifth is a very simple linear ratio -- 3:2.
1.5 times the root note. But on the equal temperament scale, it works
out to 1.4983. So, you're not going to get it selecting it that way.
You need to figure out how many cents each interval is, not the linear
ratios. If I didn't mess my math up, that is 9 cents flat. You'd
need to use 709.511 cents.
Cut......

You did the math wrong. The value in cents is 1200log2(f2/f1) where f2 and
f1 are the frequencies as a ratio. That equates to 3986.3137*log10(f2/f1).
For a perfect fifth, f2/f1=1.5.
cents = 3986.31*log(1.5) = 701.95 cents and a chromatic 5th is 2^(7/12) =
1.498307 times,
cents = 3.986.31*log(1.498307) = 700 cents. Therefore a perfect fifth is
1.95 cents sharper than a chromatic fifth.
Bob


Wow, thanks for all the help guys, but this math is just a touch over
my head.

You'd think that with MIDI being 20 years old already, there'd be a
simple chart showing all of this stuff floating around!

JT