Spin Semiconductor

AN-0001 gives this formula for finding pitch shift coefficients:

For pitch shifting up:
C = 2^14 * (2^N-1)
N = Desired amount of pitch shift in octaves

But I'm having trouble finding how we're supposed to express the target interval "in octaves". For example, to do an upward perfect fifth, the ratio is 1:1.498 or so, or in just intonation 3/2. However, putting 1.498 or 1.5 into that formula for N doesn't work. 2/3 also doesn't work.

I tried a few other possible things, such as: we know an octave is 16384, so divide by 12 to find one semitone and multiply by 7 to find a fifth. I know that this doesn't take into consideration the non-linear math of pitches, so it doesn't surprise me that it doesn't work.

So, how do we find N?

If I remember correctly, it is:

N=((2^(1/12))^S)/2

Read as: The 12th root of 2 raised to the Sth power divided by 2

S is the number of semitones

Absolutely working,
for the 5th. the number is for wldr 5486,01617072184

djmalan wrote:Absolutely working,
for the 5th. the number is for wldr 5486,01617072184

Not exactly. That's the number for 5 semitones, but a perfect fifth is 7 semitones. 5 semitones is a fourth (blame the dastardly inventors of the diatonic scale).

Thanks for that formula Frank. Will have to make a little spreadsheet to do this for me. Then I'll have to work out how translate the SOF statement of the pot-controlled ramp speed directly into the interval. Darn math, I hate it.

D'oh: don't know how I missed this thread. Sorry to make you answer this twice, Frank.

Not a problem (actually forgot about that thread). I like answering and helping, just have not been able to as much lately. And if someone like Sean answers, I'll back off and read his posts and try to pick up a few new things myself.

Sorry , this is it 8164.26314754755
And I have list includes all formulas for every somitone as an (open office format like exel)ods. if you want ,I did it last summer and check with tuner.

Oops, if djmalan is correct my equation is wrong and should be:

N=((2^(1/12))^S) - 1

So let me summarize:

;For pitch shifting up:
;C = 2^14 * (2^N-1)
;where
;N=((2^(1/12))^S) - 1
;N = Desired amount of pitch shift in octaves
;S is the number of semitones

Is it OK?

How does this look for pitch shifting down?

See page 8 of http://www.spinsemi.com/Products/appnot ... N-0001.pdf It has the equations for calculating C for up and down.

I'm having a pretty hard time with this.

Question #1

I'm starting by just putting the values into Excel to see how they all come out.

Using this calculation for # of octaves for a given # of semitones:

Octaves = POWER(2, (Semitones/12))/2
or equivalently,
Octaves = POWER(2, (Semitones/12) - 1)

The value comes out correctly, 1 octave for 12 semitones and 2 octaves for 24 semitones. However it gives 0 semitones = 0.5 octaves which is certainly wrong.

If instead I use:

Octaves =POWER(2, (Semitones/12)) - 1,

Then 0 semitones = 0 octaves and 12 semitones = 1 octave, however 24 semitones comes out at 3 octaves.

If I use:

Octaves = semitones/12, then all 3 are correct, however this isn't right either!

djmalan if you are still there I would appreciate some insight, as you said you worked it all out and checked it with a tuner!

Question #2
AN-001 shows that the correct WLDR value for +1 octave is 16384, and +2 octaves is 32767. However, it seems like the real correct value for +2 octaves should be 32768, however we are limited by the # of available bits to 32767. So we use 32767 instead of 32768, which is "good enough for rock and roll or possibly avant garde" music?

This is all a bit odd since we are working with powers. The simple answer is:

#octaves = #semitones/12

But semitones are not evenly distributed in the octave, they follow a power curve so to calculate the the frequency multiplier:

=POWER(POWER(2,1/12),A1)

Where A1 is the cell in a spreadsheet that is the number of semitones of desired shift.

And yes, we are limited to 32767 on the coefficient so it is just short of 2 octaves up.

Ultimately I'm trying to come up with a way to allow the user to enter semitones and cents to get accurate, repeatable pitch shifts. So, just for my own sanity, what is the parameter for WLDR for a positive pitch shift of one semitone?

Muchas gracias,

DL

I think there might be some confusion here, you can't get 2 octaves up, WLDR of 32767 = about 19 semitones.

I use this which seems to be close enough for jazz, rock and roll is more forgiving

For up shifts:

WLDR=16,384*(2^(1/12*semitones)-1) so for one semitone up
you get 16384*(2^(1/12*1)-1) = 974.24 divide that by 32768 to get the decimal value for writing directly to rmpX_rate.

For down shifts:

WLDR = (-16384*(1-(1/2^(1/12*semitones))))*-1

Hi Slacker, thank you for coming to my emotional rescue (C)(P). You are my knight in shining armor. That reference simply is an indication of my age (cough).

Ah, so 32767 is NOT 2 octaves but only 12 + 7 = 19? That's an interesting development. Anyway thanks for your example. All I'm trying to do is come up with the proper math for my little program. I think that other than the nice sounding intervals, that very small shifts for the barberpole flange type of effect are probably the most useful application of this effect.

[Edit: Well, don't I feel silly now. I re-read the AN-0001 and I don't think that it is claimed anywhere that 32767 gives two octaves of pitch shift. Pardon me!]

Here's my table with all semitones calculated:
Anyway, per this calculation, 19 semitones is in fact very close to two "octaves", which I may need some assistance in absorbing. Nevertheless it does allow me to proceed!

Cheers,

DL

Your WLDR numbers look right but your octaves figures probably aren't what you want, looks like you've divided the WLDR value by 16384?
The Octaves figure you want is Semitones/12 that then give 19/12 = 1.58333 or 1 and 7/12 which is an octave and a fifth up.