Supersaw!

[Music Engineer]

using only 1 HP filter after the mixed sawtooths is not going to work IMO

assuming your filter to be a pure linear implementation (that is, without any internal saturation) and assuming further that all filters use the same parameters (cutoff, resonance), the result of filtering the sum of the sawtooths is the same as filtering each saw and then summing the filtered results. this property is known as superposition principle of LTI systems.

interesting thread btw.

doing some experiments myself, i found that the initial phases of the individual saws is of critical importance, especially when the detuning is low. i tend to reduce the detuning all the way down to zero and then adjust the phases by trial and error in order to minimize the comb-filter effect. another thing that may be worth investigating is to adjust the phases of the individual harmonics as well. probably not what roland was doing, though.

[aciddose]

you don't need to worry about phase (it can be set to random values) if you use a power law for the pitch distribution.

[Music Engineer]

you don't need to worry about phase (it can be set to random values) if you use a power law for the pitch distribution.

i've seen your power law earlier in this thread. i did not yet try it yet, but thanks for posting it. i will probably try it at some stage. currently i use a combination of exponential detuning (in semitones) and absolute offset in Hz. the nice thing about the absolute offset is that it tends to produce less detuning in the high registers. i've read about this in some kurzweil manual.

[aciddose]

you can accomplish the same effect by scaling the detuning values generated using what i posted by 1 - (key / 128) ^ 2 or something like that. you just need to subtract 1 first to center them about 0, then shape, then add 1.

[Music Engineer]

you can accomplish the same effect by scaling the detuning values generated using what i posted by 1 - (key / 128) ^ 2 or something like that. you just need to subtract 1 first to center them about 0, then shape, then add 1.

hmm...you say, you can make a power-of-power law equivalent to an exponential-plus-offset law by this? i may have to think about that more carefully but my gut feeling actually tells me that an exponential function is fundamentally different from a power function. but that aside, your subtraction of the mean made me think about what the perceived pitch of a mix of sawtooths would actually be. subtraction of the mean assumes that perceived pitch is the arithmetic mean i guess? is that psychoacoustically validated? perhaps a geometric mean could also be used? dunno really.

[Music Engineer]

ahh wait - you were talking about the "less detuning in the high registers" part, right? not about the pitch distribution function. in this case - yes. actually, that would be the already mentioned keyscaling of the detuning. something like that

[aciddose]

the arithmetic mean of scaling factor (v) = perceived mean.

the output values are scaling values of course, so 1.0 would be no change, 0.0 is negative infinity, etc.

you couldn't actually increase the detune with a linear scale:

hz = main_hz * ((v - 1) * fraction + 1)

you can however decrease it. the result would be non-linear i think, but for the purpose it's used (just to make smaller detunes at higher freqs) it should be just fine.

just try xhip, clear the preset and select ramp wave for osc1, then adjust the pulsewidth control (repurposed to unison detune depth). you'll hear the power law with distribution = 0.5 applied there.

http://xhip.presetexchange.com/xhip
http://xhip.presetexchange.com/temp/xhip.dll (actually i'd recommend this working-version, it's less stable and messed up, but for this purpose works ok. only difference is dc correction and amplitude correction, but you don't mind that i hope, do you?)

[Music Engineer]

the arithmetic mean of scaling factor (v) = perceived mean.

is this just an assumption or is it backed up by psychoacoustic listening experiments?

just try xhip, clear the preset and select ramp wave for osc1, then adjust the pulsewidth control (repurposed to unison detune depth). you'll hear the power law with distribution = 0.5 applied there.

did it. sounds good to me. certainly less flangy than some other stuff i tried. is there already a highpass built in or is it just seven straight saws? from an oscilloscope view, i'd guess the latter?

[aciddose]

it's sixteen actually, you can configure that in the "stable" version, but the gui control is not there in the "working" version. it's raw, then goes through a single master hpf. again, possible to disable in the "stable", control missing in "working".

not only is it "less" flangy, it's as far as i'm aware the least possible flange - the detuning values should have maximal LCD values. i'm guessing it isn't perfect though because i can sometimes hear two waves phase by the reset - but i guess that's impossible to avoid right? the time would be near infinite for more than two to line up, but for two it's got to be a finite amount related to the detune depth.

yeah - so it actually may be maximal lowest common denominator.

forgot about this:

"is this just an assumption or is it backed up by psychoacoustic listening experiments?"

i've never read anything on it, but if you listen it seems to stay in tune. any other method of "centering" the pitch doesn't work. so it's likely to be the best method. it's certainly the most obvious and simplest method.

[Music Engineer]

it's sixteen actually, you can configure that in the "stable" version, but the gui control is not there in the "working" version. it's raw, then goes through a single master hpf. again, possible to disable in the "stable", control missing in "working".
.

i see. when switching to single saw, i can see the slight bent in the saw that comes from the highpass. i guess, just a DC blocker - with very low cutoff?

not only is it "less" flangy, it's as far as i'm aware the least possible flange - the detuning values should have maximal LCD values.

now this is interesting. you mentioned that you have found some math that explains this lowest common denominator property? i'd be interested in reading up more on this. can you point me to some paper or article or something?

i'm guessing it isn't perfect though because i can sometimes hear two waves phase by the reset - but i guess that's impossible to avoid right?

i think so.

i've never read anything on it, but if you listen it seems to stay in tune.

true.

[aciddose]

now this is interesting. you mentioned that you have found some math that explains this lowest common denominator property? i'd be interested in reading up more on this. can you point me to some paper or article or something?

so would i... that's just my recollection of how i came up with this method. i'm not sure if i came to the conclusion myself or if i read it somewhere.

http://en.wikipedia.org/wiki/Least_common_multiple

it doesn't appear to say that here..

http://en.wikipedia.org/wiki/Chebyshev_function

not here either.

it seems to be headed in a similar direction though.. i'm not certain.

i did this about four or five years ago and since then i hadn't really looked at or cared about the code. it "just worked". when i did write it, i didn't bother to comment it or take notes and i didn't even note to myself what i was doing or why. the original code was more complex and used variable names like "b" or "qz" (yikes) and i found that the same result could be had by using pow(distribution, factor) as i posted earlier.

anyway, i'm not certain it's maximal LCD (or according to wikipedia we should be calling it LCM) it just seems to be pretty close based upon the results. it's just my vague recollection of "why" i did it that way that says "it might have something to do with what i read somewhere about a power or a power" and nothing more than that.

i might have just typed it in at random

it definitely isn't something to do with primes - well not definitely, but unlikely. otherwise i'd have invented a ridiculously obvious way to calculate prime fractions. that's pretty unlikely. (what, zero possibility?)

[Music Engineer]

OK, so to sum up (just for the record and to see if i have understood this thing right), it is desirable to have the period-lengths of the individual saws to have the maximum least common multiple in order to have them phase-aligned as rarely as possible which should result in minimum "flanginess". the power law might achieve this goal, but we currently have no formal proof for that.

[djsubject]

re-listened and 1 still sounds the best to me!!
its stronger than 2, i love it!!

Agree, #1 sounds better.

well, thats helped me to trust my ears a bit more

looking forward to seeing in what form this experiment will reach us,

Subz

[antto]

i could write an app to run 7 saws for a _very_ long time and count how often lots of saws cross each other
this is pretty easy actually

some time ago, i was also thinkering about the "detune weights" (distribution sounds better)
it was for a "fat saw" oscillator and to be honest, it was a supersaw but i didn't know it had a name
what i came up with was an algorithm for "positioning" 1 stereo osc of an odd-number of sawtooths in a specific way, i was chasing some symetry, i can't remember what it was
it was like so: 5 saws for the left channel, 5 for the right
the distribution was such that: no two saws have the same coefficient, and for each channel - there were saws with positive and negative signs
it was weird, i think my idea was that at the end when you sum each channel's coefficients they are each equal to 0 or something similar
but i have no idea if they would cross each other too often or not .. hm..

[aciddose]

OK, so to sum up (just for the record and to see if i have understood this thing right), it is desirable to have the period-lengths of the individual saws to have the maximum least common multiple in order to have them phase-aligned as rarely as possible which should result in minimum "flanginess". the power law might achieve this goal, but we currently have no formal proof for that.

definitely. i've never been able to test (or listen to) any better method but no i don't specifically know of any formal mathematical proof for this property. i'm pretty certain it can't be exactly the maximal LCM because if it were, then those would be fractions of primes, right? (being no LCM in that case)