Randomly Shifting Pitches and Phases

 
The Boy Born on Friday wrote:

OK ... listen up guys. Another related problem for you. Still wanting to recreate an 'authentic' African instrument some time soon.

It is possible that I am making this more difficult for myself than it really is, but here's the gist of what I'm after. I'll try to explain myself by first of all discussing phase.

Assume two sine waves, A and B, of equal amplitude but random phase. The experimenter can listen to each A and B alone, and also to the combined signal A + B. Clearly, since the phases are random then sometimes you will get phase additions and sometimes you will get phase cancellation. This means that sometimes A + B will be silent because of the cancellations, and sometimes A + B will be double the volume because of the phase addition of A + B. Big question here is -- what exactly is the probability that A + B will in fact be louder than A or B? If you go the Fourier route then 'loudness' is the sum of the squares of the Fourier coefficients.

Blah blah blah.

You should end up with a probability of 2/3rds that A + B is greater than unity -- i.e. louder than either A or B.

OK. Now imagine a group of say 100 singers. (African singers of course!!!).

Let the phases of these singers be random. Again, there will be variations in volume. Let's now get a second group of singers whose chops are really incredibly good and so who can COORDINATE their phases. What is the minimum number of 'deliberate singers' needed to match the volume created by those 100 random singers?

Ho Ho Ho. Aren't you all GLAD that I've been quiet for so long!!!

If you go the phase vector approach -- and I did get the idea from someone else -- then what you're really saying is that the total amplitude of the sound generated by these 100 randomly phased singers is the sum of those phase vectors. And since these phase vectors have both a direction and a length, then you're actually talking a two dimensional random walk. Since there are 100 singers, then you've basically got 100 steps of unit length. Now take 10 of those deliberate singers and match them up against 1 deliberate singer. By the law of large numbers there is now a very small degree of probability that those 10 random singers will differ from any 1 deliberate singer by any ignificant degree. Saves a lot of messing about with Fourier calculations and Parseval's theorem does that. You've basically got the N against the square root of N (in this case, the volume of 100 randomly phased singers can be matched by 10 singers if they can really listen to each other properly and so take very great care always to match their phases). 10 or thereabouts because, after all, everything is random.

So far so good.

A while ago I submitted a patch using some ideas from Roland Kuit's sample and hold workshop to create a representation of the singing that I remembered from my childhood when my mother used to carry me around on her back every morning and there was a lot of singing around. Can't remember it's precise name now but knowing me it was probably something REALLY original like "African Morning".

Now -- African singers don't always follow the Western chromatic scale when they are singing. In fact, given the opportunity they run a mile away from it but that's a whole other story. !!!!!. They also tend to use a call and response technique. So ... what you have here is that although the singers will tend to leave the octaves and fifths static and not play around with them too much, most of the other notes are up for grabs. So ... what you might have is 20 people divided up so that, at its simplest, 10 sing one part and then hand over the melody and harmonies to the other set of 10 who sing for a couple of lines and then hand it back again. Call and response. Get it?!!

Now, here we have 10 people (in this case) each of whom is individual free to bend the thirds, sevenths, seconds and sixths (usually) a little bit this way and that. The handover note is most often a third because people like to really play around with that one. The other lot never really know exactly what pitch they're going to get. And ... within each group ... nobody is ever really sure what harmonies and stuff their own side is going to come up with. They just have to listen very carefully to each other and adapt to each other.

Phew.

Now ... the chorus module that those fine people up in Clavialand have given me ... well I'm afraid that people who live in such snowy climates really have no appreciation for the finer nuances of human singing abilities. Ain't that the truth. So my beloved red box doesn't really cut it for me in trying to get this kind of note bending microtonal stuff. I want to get that bending effect as one group hold a note a little, adapt to each other, and then gradually home in on the note that they as a group really want to send scooting over to the other lot.

I hope you can see the similarity here in this kind of pitch shifting as compared to the problem I first gave you all of phase shifting.

So ... does one of you rocket scientists out there know of a method by which I can create say a 4-voice or 6 or however many I want voice patch, and kind of set up a morphing arrangement so that when I play I can create the impression of a group of people with randomly varying pitches that are slowly homing in on one central pitch? This is obviously not vibrato. In my mind there has to be a way of dedicating or morphing a knob to a voice or voices in a patch that then acts as if this is a group of voices microtonally approaching a set frequency from within a given initial range.

Phew.

I hope I've got across to you clearly enough what I'm after.

If any of you has any ideas then please let me know. As I said, I've tried choruses and vibratos and a couple of other mad things on oscillators, but can't say that I've really gotten into it cause I said to myself ... I really don't have time for this right now but maybe one of those other crazy people out there in Nord land might enjoy getting their head around this little problem. I know how some of you LOVE this kind of stuff. There's no money involved. Just the personal satisfaction of knowing how clever you are and what a fine and noble specifmen of humanity you are. Otherwise, I'll have to do it myself.

In order to help him out That Poor Guy Who Has Absolutely No Idea What Day He Was Born On (Tim Walters) wrote:

I don't have my Nord handy, so this will have to be purely verbal.

Note-on gate -> random step generator -> A-D envelope -> oscillator FM

This will make each note start at a random distance from the target pitch and drift toward the center at a rate set by the decay parameter on the envelope. Repeat as necessary for each oscillator. Obviously the oscillator FM input should be highly attenuated.

I hope that's the sort of thing you're looking for...

Friday's Child wrote:

Thanks a lot. Should work. You African or something? I'll let you know more properly next time I have earned the right to switch on my Nord and play with it a little while.

Actually, although not in such detail (!) -- i.e. no step by step instructions like what you did which is kind of what I like -- someone else contacted me privately and ALSO suggested an FM osc. I must be getting old.

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Took your tour. Didn't try any funny stuff. I promise. Heard Gilgamesh. Just curious. You got anything anywhere I could listen to of you butchering that poor little kalimba? What did it ever do to you? Hope that 8-year old girl didn't get too upset.

Oh yes ... you know that bit I said about no payment being available? I was lying. You get to be called 'bwana' for about 15 seconds. Hope that makes you feel good. Andy Warhol should like that one. OK. Your 15 seconds are up.

My but I'm getting chatty again. Very bad sign.

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Seriously though, thanks for the suggestion. I'll definitely try it out and I do think it's the way to go. I also feel that if I incorporate it into the patch that Kees van der Maarel very kindly sent me and use Jan Punter's calculations, or something close to them, I'll get pretty close to what I want. (See Interesting Threads: Tunings - red)

OK. It's back to work for me.

While I'm away ... I suggest you all start practising hitting your delete buttons. Way things are going looks like it's going to be a very bad year for you really serious types on this list. God alone know what kind of ridiculous stuff I'll be sending once I DO have a bit more time!!

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Had a 10 minute break so tried out your idea. The four voices in the attached patch are exaggerating the effect somewhat -- but it looks like what you suggested will work! So simple. I seem to have made the whole thing way more complicated in my mind than it actually was.

Thanks very much!! Just hope everything else I want to try out is just as simple!!

Oh yes ......... Anyone happen to have done those microtonal calculations for an anhemitonic equi-heptatonic? Thought not. Ah well.

Tim Walters wrote:

> The four voices in the attached patch are exaggerating the effect somewhat-- but it looks like what you suggested will work!

It might actually sound better to use the pitch input on the oscillators rather than the FM input. Or it might not. Turning down the modulation knob will de-exaggerate it a bit in either case. Another thing you might try is using N random generators, dividing each by N, and adding them together. This will make large deviations less likely than small ones, giving you an increasingly bell-shaped distribution for larger N.

> Oh yes ......... Anyone happen to have done those microtonal calculations for an anhemitonic equi-heptatonic?

I actually have an idea for this, but I don't want to say anything until I try it (it'll have to be Friday night, the next time I'm in my studio).

Just to make sure I understand it, is what you want to divide the octave into seven equal parts?

By the way, I actually do know that I was born on Saturday--I looked it up when I was a kid, hoping that it was a Friday since my birthday is on a 13th.

Friday's Child wrote:

> It might actually sound better to use the pitch input on the oscillators rather than the FM input. Or it might not.

Tried that. Makes it sound interestingly different, actually, rather than 'better' per se. I accidentally sent in one of my earlier experimentations. Had a couple of slightly better later ones. But ... didn't think it worth doing a resend since they were all only rough sketches anyway -- and there is always a severe danger of me clogging up people's Inboxes with irrelevant twaddle. Can't have that!

> Another thing you might try is using N random generators, dividing each by N, and adding them together. This will make large deviations less likely than small ones, giving you an increasingly bell-shaped distribution for larger N.

Good idea. Really don't think I would ever have thought of that one by myself. Thanks.

> > Oh yes ......... Anyone happen to have done those microtonal calculations for an anhemitonic equi-heptatonic?

> I actually have an idea for this, but I don't want to say anything until I try it (it'll have to be Friday night, the next time I'm in my studio).

Oh goodeeeeeeee!!!

I now have an army in training of LOVE mercenaries who will be with you fairly shorter to bombard you with pleasurable thoughts and all around feelings of good will. (They deal strictly and only in the more spiritual and esoteric forms of pleasure I might add. That's the kind of person I am.)

 >Just to make sure I understand it, is what you want to divide the octave into seven equal parts?

Well ... I would pretty much like to be able to divide the octave into any number of parts that I want. For example, many koras, donso ngonis and other kinds of stringy instruments can be tuned and retuned by the performer for the occasion and to get the effect they want -- for that particular song or performance. However, the more xylophony, more closely defined structure-type instruments tend to be tuned by the manufacturers to enhance what they feel are the best properties of that particular instrument. (So people wanting different effects would have to buy different balaphons). So -- I would kind of like to be able to build a kora and tell people that they are free to tune it how they want from piece to piece (for the occasion); and on other occasions I would kind of like to be able to fix it myself so that I have created an instrument and then just kind of hand it over so that they have about as much choice as the average balaphon player.

So ... a bit of both.

> By the way, I actually do know that I was born on Saturday--I looked it up when I was a kid, hoping that it was a Friday since my birthday is on a 13th.

Weird guy, aren't you? Thought so. The fact that you know what day you were born on makes you an honorary African. Welcome to the club. Now, if you had been born where I was your given day-name would be 'Kwame' (means "boy born on Saturday". Pronounced 'Kami' with a short-i)

See I'm giving away LOTS of prizes. Bet the rest of you are getting jealous and wish you'd got there first. OK. It's back to work for me.

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 Just to clarify:

 > Tim said: Just to make sure I understand it, is what you want to divide the octave into seven equal parts?

I would like to be able to divide the octave into 7 parts -- but whose precise sizes and intervals can be determined both by me; and also by the performer; at will.

Thus, some traditional tunings have the fifth pretty much at the point suggested by the harmonic series while the intervals absorb and have greater variations; and there are other tunings with much more equal divisions of their intervals so that the fifth is no more 'right' or 'wrong' than any other interval.

I would basically like a system like that gives me that kind of flexibility for my 7 notes.