Harmonics into Semitones

[werzel]

OK, I did a double test using MPS and Sytrus (which has the pitch multiplier).
I played a note that had only the fundamental active in both and checked the frequency using MAnalyser.
I then moved the multiplier up to x2 and checked the second harmonic of MPS against it. They were identical.
My calculations were gleaned from a chart on the Harmonic Series wikipedia page. I didn't get caught up in frequency values because they would vary depending on your fundamental (lower the fundamental and the distance between the lower harmonics is greater than if you raise the fundamental).
I also didn't get into the frequencies because there may be a bit of number shaving in the algorithms to lean things more towards the equal temperament scaling of notes, but I'm not sure.
C3 = 261 Hz
C4= 523.8 Hz
G4= 785.2 Hz
C5= 1046 Hz
E5= 1308 Hz
G5 = 1570 Hz
Bb= 1831 Hz
etc.

Always assume that the programmers are correct and I am wrong....it'll get you further!

[jmg8]

What is the result then? Is it possible to set the pitch of the sines to match a harmonic series and then have that sound right for any note?

[drewfx]

Something is wrong.

Adding 19.02 st is the same as multiplying the frequency by 3. It's the twelfth root of 2 raised to the power of 19.02 = 3 (almost exactly).

Can you measure the pertinent frequencies to see what you're getting? I don't have the synths, but I get the expected results with MOsc.

[werzel]

Harmonics occur as a ratio of the fundamental. Would a math module be needed to insure that the relationship of each osc that is acting as the harmonic keep that ratio no matter what note is used as the fundamental?
If n= fundamental
nx2= first harm
nx3= second
etc.

I don't know how to accomplish that other than using a synth that already has that algorithm figured in where I can select the harmonics individually. I'm fascinated by it, but the last time that I tried to create a harmonic series synth I used 32 identical synths and had each one play a single harmonic....so it wasn't very economical.
Perhaps Vojtek will have some input once he gets tired of coding and takes a forum break!

[dmbaer]

What is the result then? Is it possible to set the pitch of the sines to match a harmonic series and then have that sound right for any note?

Try this, then (now that I understand what you're trying to achieve).

I assume you've got multiple "tone generators" in your preset, one for each partial - if not, ignore this suggestion.

Use a basic oscillator, go into Advanced mode, and set the desired partial to fully on and the rest to fully off. This should get you sine waves at exactly-placed frequencies in relation to the fundamental frequency. Don't mess with any frequency adjustments. Just leave them at the default.

[jmg8]

What is the result then? Is it possible to set the pitch of the sines to match a harmonic series and then have that sound right for any note?

Try this, then (now that I understand what you're trying to achieve).

I assume you've got multiple "tone generators" in your preset, one for each partial - if not, ignore this suggestion.

Use a basic oscillator, go into Advanced mode, and set the desired partial to fully on and the rest to fully off. This should get you sine waves at exactly-placed frequencies in relation to the fundamental frequency. Don't mess with any frequency adjustments. Just leave them at the default.

By advanced mode, you mean harmonic mode right?
That will not work, as the level of each harmonic is not per voice modulatable. That is the reason I am trying to mimic the harmonic OSC using individual OSCs, so I get per voice control over each harmonic.

[jmg8]

Something is wrong.

Adding 19.02 st is the same as multiplying the frequency by 3. It's the twelfth root of 2 raised to the power of 19.02 = 3 (almost exactly).

Can you measure the pertinent frequencies to see what you're getting? I don't have the synths, but I get the expected results with MOsc.

What note are you using? Try C3.
Now compare the 2nd harmonic (3rd bar on the harmonic OSC) to 19.02st. Surely you don't get the same pitch right?

[jmg8]

Harmonics occur as a ratio of the fundamental. Would a math module be needed to insure that the relationship of each osc that is acting as the harmonic keep that ratio no matter what note is used as the fundamental?
If n= fundamental
nx2= first harm
nx3= second
etc.

I don't know how to accomplish that other than using a synth that already has that algorithm figured in where I can select the harmonics individually. I'm fascinated by it, but the last time that I tried to create a harmonic series synth I used 32 identical synths and had each one play a single harmonic....so it wasn't very economical.
Perhaps Vojtek will have some input once he gets tired of coding and takes a forum break!

Yes, this is the same conclusion I came to (with your help)
It is not possible to achieve using OSCs.
Some sort of multiplier is needed, because the difference between each harmonic (in semitones) changes depending on the note (frequency)

[Whywhy]

I think what dmbaer want to said, it's:
If you want 16 osc's for make 16 harmonics, take 16 osc's in additive mode, first osc, first harmonics, second osc, second harmonics...It make sense to me. But perhaps you want to archive some things else....or, in the osc advanced tab, if I remember correctly, you can select 8 harmonics for any kind of waves, I will try it tomorrow morning.
Your osc project could be a nice additive oscillator , fm just one harmonics with another, per voices...can't wait to try it !

[drewfx]

Something is wrong.

Adding 19.02 st is the same as multiplying the frequency by 3. It's the twelfth root of 2 raised to the power of 19.02 = 3 (almost exactly).

Can you measure the pertinent frequencies to see what you're getting? I don't have the synths, but I get the expected results with MOsc.

What note are you using? Try C3.
Now compare the 2nd harmonic (3rd bar on the harmonic OSC) to 19.02st. Surely you don't get the same pitch right?

With either C3 or C4, the measured frequency of the 3rd harmonic bar (G) in harmonics mode is always equal to normal mode with pitch set to +19.02, which does in fact equal 3 times the measured C frequency as expected.

And it has to work - otherwise it wouldn't be 12 tone equal temperament.

[Whywhy]

I have made a test this morning, and it works with the oscillators additive engine but not with the advanced oscillator harmonics.
I have set up 18 oscillators and 18 volume modules, -6db per news harmonics. -i m not sure if -6 is right... normally no, it's not linear-
First osc, first harmonics, second osc ,second harmonics...
Jmg8, it's that or I misunderstood?
Ps:
A lot of crazy things are possibles, per voices, if you add some transform per harmonics,some fm or some filters, drives, per 6 harmonics modular block.

[jmg8]

Something is wrong.

Adding 19.02 st is the same as multiplying the frequency by 3. It's the twelfth root of 2 raised to the power of 19.02 = 3 (almost exactly).

Can you measure the pertinent frequencies to see what you're getting? I don't have the synths, but I get the expected results with MOsc.

What note are you using? Try C3.
Now compare the 2nd harmonic (3rd bar on the harmonic OSC) to 19.02st. Surely you don't get the same pitch right?

With either C3 or C4, the measured frequency of the 3rd harmonic bar (G) in harmonics mode is always equal to normal mode with pitch set to +19.02, which does in fact equal 3 times the measured C frequency as expected.

And it has to work - otherwise it wouldn't be 12 tone equal temperament.

Wow, you are right! I am really glad about this.
There must have been some offset with a modulation I had set up or some other mistake. Because now every time I test it, it is exactly 19.02.
This is good news, thanks.

So last thing is this. Please would someone give me the semitones for the first 16 harmonics.
My maths is very bad and I cant work it out on my own. Werzel started it off (thanks) but stopped at around 12 harmonics and I need to know the last few, please.

[Whywhy]

Thanks for everyone taking the time to try and explain this to me.
To be clear the reason I am asking is that, I am making my own harmonic OSC in MSF so I can experiment with per voice modulation for each harmonic individually. Here is a crude mock-up.

MSF Harmonic OSC.jpg

So to start with I am making this with 16 OSCs all set to sine. I needed to know at what pitch to set each OSC to make the harmonic series. In this scenario, I will not know the frequency, as I can not know what note someone will press when playing with the synth. So I needed a way to offset each OSC by semitones (and cents)
I believe Werzel came up with the correct solution for me here, thanks

So I will start to experiment with it and hopefully, it will work as expected.
My only worry is this: Will the difference in semitones change depending on which note I input, or will they always stay the same difference apart?

A question, how have you do the "macro" ?with multiparameter and edit page?- I refer to that:
attachment=0]MSF Harmonic OSC.jpg[/attachment]
It's look good!

[werzel]

OK jmg8, here is a complete list of the first 32 harmonics. Double check yourself as you get into serious upper harmonics as some of them use the same semitone jump but then have -/+ cent values to keep the ratios accurate. I did 32 just in case you were tempted to come back and ask for more, higher than that is going to be a pain. (I changed the display method so you knew where I/ we left off.)

Fundamental
Harmonic 2 [+12 semitones]
Harmonic 3 [+19 semitones, plus 2 cents]
Harmonic 4 [+24 semitones]
Harmonic 5 [+28 semitones, minus 14 cents]
Harmonic 6 [+32 semitones, plus 2 cents]
Harmonic 7 [+36 semitones, minus 31 cents]
Harmonic 8 [+36 semitones]
Harmonic 9 [+38 semitones, plus 4 cents]
Harmonic 10 [+40 semitones, minus 14 cents]
Harmonic 11 [+42 semitones, minus 49 cents]
Harmonic 12 [+43 semitones, plus 2 cents]
Harmonic 13 [+44 semitones, +41 cents]
Harmonic 14 [+46 semitones, -31 cents]
Harmonic 15 [+47 semitones, -12 cents]
Harmonic 16 [+48 semitones]
Harmonic 17 [+49 semitones, +5 cents]
Harmonic 18 [+50 semitones, +4 cents]
Harmonic 19 [+51 semitones, -2 cents]
Harmonic 20 [+52 semitones, -14 cents]
Harmonic 21 [+53 semitones, -29 cents]
Harmonic 22 [+54 semitones, -49 cents]
Harmonic 23 [+54 semitones, +28 cents]
Harmonic 24 [+55 semitones, +2 cents]
Harmonic 25 [+56 semitones, -27 cents]
Harmonic 26 [+56 semitones, +41 cents]
Harmonic 27 [+57 semitones, +6 cents]
Harmonic 28 [+58 semitones, -31 cents]
Harmonic 29 [+58 semitones, +30 cents]
Harmonic 30 [+59 semitones, -12 cents]
Harmonic 31 [+59 semitones, +45 cents]
Harmonic 32 [+60 semitones]

[werzel]

If you are looking to drive yourself completely crazy, you can change all of the + signs to - and - signs to + (including the semitones) to get the undertone series, where the undertones are below the fundamental tone.
When you write the harmonic series and the undertone series out musically, they are mirror images of one another.