The long DIVA thread

[Urs]

(btw if anyone can enlighten me as to where my thinking was wrong that whole debate, I'd be genuinely interested in hearing it. I still haven't heard a sensible explanation. Via PM's would be fine.)

I haven't followed all of it. Basically I think that because of the single master oscillator being devided down, each note has a common denominator with each other. Thus at some point they coincide in having a phase reset. I'm with you when you say it doesn't happen very often. IMHO opinion it doesn't matter if you have twelve or one master osc.

Depending on the implementation the octaves will however be in perfect sync. It depends though. The DCOs of a Juno 60 for instance also stem from a master oscillator and yet there's a slight detune between octaves. Which, if you look at the maths, is easily explained.

The other thing is overtones. A note 1 octave above another note naturally shares 50% of the harmonics of the lower note. In a divide down situation these would be in perfect sync too.

Was that what it was about...?

[hakey]

Was that what it was about...?

Yep, what you've said is pretty much how I understood things. And, yes to the theoretical possibility of a long cycle phase reset (though I guess that rather depends upon the absolutely accuracy of the whole top division + divide down process - and even then, would any timbrel effect be noticeable?).

What we never quite got to the bottom of was Brok's insistence that (apologies, this will be slightly convoluted, readers with narcoleptic tendencies might want to stop here ) not only would all notes of 'n' octave interval be in phase, including their harmonics (as you pointed out, and I agree, and which I argue would be possible to reproduce with my patented free-running, phase-locked samples), *but also* that for other intervals that shared harmonics those shared harmonics would be phase synced/locked as well.

Now my thinking is that the top octave must be divided according to something like equal temperament, therefore even for intervals close to perfect (eg the fifth), being close will not be good enough. Only truly *perfect* intervals (of integer freq ratio) share (low order) harmonics so, excepting octave intervals, Brok's harmonic phase locking just doesn't occur.

And that was all as a result of my wider speculative argument that it is within the realm of the possible to emulate the characteristics of a divide down oscillator synth using accurately looped free-running samples (where all notes of octave interval are phase locked). I still think this is the case. Not that I'm for one minute suggesting it's a worthwhile strategy, just that it's possible.

(this all mixed in with several pages of *ahem* hissy fits, drama and the like, admittedly from all sides )

[Urs]

Yeah, dunno. Howard and I discussed that a bit. We didn't know either.

[hakey]

Yeah, dunno. Howard and I discussed that a bit. We didn't know either.

You mean the alleged harmonic phase lock?

Well you just can't have perfect intervals with equal temperament (and it would be obvious if a synth were tuned some other way - just intonation, for example, would only sound right in one key).

Maybe one of the intervals in a divide down synth might be perfect, say all C to G intervals. But you can't have all fifth intervals (G/D, F/C, A/E, etc) perfect - for one thing adding 2 cents for every one of the twelve possible fifth intervals would make an octave 1224 cents! Without perfect intervals the harmonics are not at exactly the same frequency, so you lose any idea of harmonic phase sync.

(BTW I remember my Virus had a clever algorithm which tuned everything to just intonation on the fly - that might be quite interesting with phase locked oscillators + a nice ensemble/phaser on top.)

[Urs]

Yeah, of course. Like tonewheel organs I guess string ensembles are slightly off off equal temperament.

[News From The Sky]

That brings up an idea... Diva could have a paraphonic mode... as long as the routing stays simple, it would be doable. Hehe, if only for a bit of Poly 800 vibe.

<cough> Solina <cough>

I like this idea!

Also, I hope you're planning on including the Solina ensemble effect (in both Diva and eventually Lush). As I recall it's basically multivoice chorus with phase-offset LFOs - having a 2-8 voice chorus with an LFO Offset parameter should cover it and go well beyond...

Urs, you mentioned an alternate Berlin Modular member in place of Lush - are you ready to tell us what that is?

[pj geerlings]

Something from my dark past ...

Code: Select all

      ---- Hammond Gears -----    ------ MK50240 --------
      gear               error    div               error
      ratio              cents                      cents
   C# 71/82  0.6297118  -0.684    451   0.6297118  -0.684
   D  67/73  0.6674969   0.200    426   0.6666667  -1.955
   Eb 35/36  0.7070707  -0.088    402   0.7064677  -1.565
   E  69/67  0.7489824  -0.396    379   0.7493404   0.432
   F  12/11  0.7933884  -0.681    358   0.7932961  -0.882
   F# 37/32  0.8409091   0.026    338   0.8402367  -1.359
   G  49/40  0.8909091   0.020    319   0.8902821  -1.199
   G# 48/37  0.9434889  -0.707    301   0.9435216  -0.647
   A  11/8   1.0000000   0.000    284   1.0000000   0.000
   Bb 67/46  1.0592885  -0.285    268   1.0597015   0.390
   B  54/35  1.1220779  -0.593    253   1.1225296   0.104
   C  85/52  1.1888112  -0.576    239   1.1882845  -1.344

[hakey]

@ pj - Interesting - I see the MK50240 is a top octave frequency divider. At a quick glance I can't see a perfect fifth or fourth interval and it is more or less in agreement with equal temperament (a max 1.5 cent deviation isn't far off).

I get the feeling you might know a bit more than you're letting on. Can you shed any light on this notion of harmonic phase lock between (non perfect) intervals other than octaves?

[pj geerlings]

@ pj - Interesting - I see the MK50240 is a top octave frequency divider. At a quick glance I can't see a perfect fifth or fourth interval and it is more or less in agreement with equal temperament (a max 1.5 cent deviation isn't far off).

Check out the "D" it's more like 2 cents off - but in a string ensemble the chorus mucks with the tuning way more than that so it isn't too big a deal...
A just intonation perfect fifth is 2 cents off of equal tempered and that's the closest a just interval comes to it's equal tempered interval

I get the feeling you might know a bit more than you're letting on. Can you shed any light on this notion of harmonic phase lock between (non perfect) intervals other than octaves?

It is a design configuration question
- in a tone-wheel organ all "common" frequencies were from the same generator and the harmonic series was forsaken in favor of the equal tempered equivalent (except for the 7th harmonic which is so far off from equal that there was no drawbar for it at all)
- in a divider-based instrument the best you can expect is that the octaves of each note will tend to reinforce.

peace y'all
pj

[hakey]

Check out the "D" it's more like 2 cents off

You're right! And it's ratio is 0.6666667? If that's a rounding of 0.66 recurring (=2:3) then perhaps the interval D to A is in this case a perfect fifth?

in a divider-based instrument the best you can expect is that the octaves of each note will tend to reinforce.

Yep, that's what I was thinking.

Cheers!

[pj geerlings]

Check out the "D" it's more like 2 cents off

You're right! And it's ratio is 0.6666667? If that's a rounding of 0.66 recurring (=2:3) then perhaps the interval D to A is in this case a perfect fifth?

in a divider-based instrument the best you can expect is that the octaves of each note will tend to reinforce.

Yep, that's what I was thinking.

Cheers!

look at the dividers for the D and A :

D = 426 = 2 * 3 * 71
A = 284 = 2 * 2 * 71

note that they can be reduced to exactly 3:2

[hakey]

D = 426 = 2 * 3 * 71
A = 284 = 2 * 2 * 71

note that they can be reduced to exactly 3:2

Indeed! Any ideas of how accurate the division process is? Is it, for want of a better word, perfect?

[pj geerlings]

D = 426 = 2 * 3 * 71
A = 284 = 2 * 2 * 71

note that they can be reduced to exactly 3:2

Indeed! Any ideas of how accurate the division process is? Is it, for want of a better word, perfect?

it's exact but not significant because the "perfect" D / A relationship given above is in the minority - nearly all of the other intervals generated by the MK50240 are in no way perfect ...

[hakey]

nearly all of the other intervals generated by the MK50240 are in no way perfect ...

Yep - I see that (and I understand why it wouldn't even be possible to tune every fifth interval to be perfect, every fourth etc...).

[Howard]

Yeah, of course. Like tonewheel organs I guess string ensembles are slightly off off equal temperament.

They're equal temperament.

Without perfect intervals the harmonics are not at exactly the same frequency, so you lose any idea of harmonic phase sync

Yes.