MusicPlayerNetwork.com Forums Recording The George Massenburg Professional Recording Forum Using prime numbers for delays??

GM mentioned in another thread that he uses prime numbers for delays:
http://www.musicplayer.com/ubb/ultimatebb.php?ubb=get_topic;f=3;t=005895;p=1

Sorry, but I just don't understand how to apply this.
Could someone please elaborate on this, or point me to a reference where I can read more?

Thanks!
Mike

I don't know that there are any references on this. But it's simple.

I use prime numbers because they're indivisible by 2. Imagine if you set a delay of 8ms and hit it with a transient-kind-of event. you'd hear something like a 125Hz-based tone. So if you've got a bunch of delays and they're set, say, 8, 4, 2, 1, you're going to have a processing context that favors 125Hz and it's overtones (250Hz & etc). I use this as a worst case, and most of us don't use delays that short (although I can remember important times that I have). But even at longer delays, I get a vague sense of a "tone" even without regen. By using prime numbers you 1> are more likely to "dove-tail" several different harmonic series, and 2> are more likely to have these vague "tones" land away from musically significant harmonics. Maybe I get a sense that it sounds more "neutral".

George

George,
Ok, got it.
Thanks so much for explaining.
Mike

Mike,

Here is a set of the first Prime numbers up till "1009" for ya´ to play around with..;-)

2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349
353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809
811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953 967 971 977 983 991 997 1009

Prime numbers are a study of great interest to many people with Math as a major.. of which I´m not..never was great with numbers..

Kind regards

Peter

Thanks, Peter!
Mike

I'm a believer in prime numbers as well... maybe it goes back to my first delay line a Lexicon Primetime(circa 1979)...which I still have and use...I recall a good explaination similar to Georges in the original manual

cheers
Scott my crib

Hmmm,
Of course prime numbers are divisibe by 2.
13 divided by 2 is 6.5.

Since the audio spectrum is continuous a frequency of 125.5 Hz and its first or second order harmonics are just as capaale of engendering a "tone" as you describe as a straight 125 hertz freqeucny is.

Seems to me there is nothing sacred about whole numbers when dealing with audio frequenciues..

Some folks tune up at the standard 440hz. However, You've still got music if tuned to 440.5hz.

Based on this logic Im questioning the valididty/value of the prime number approach.
Of course, I may be missing something.

I am glad you posted those numbers. I was under the impression that a prime number was only divisible by 1 and itself.....

MW,
Yes, that's correct:
http://www.utm.edu/research/primes/

I am familiar with prime numbers from my engineering days, but I was ignorant of the musical significance. Good stuff.
Mike

Everything is divisible by 2 if you do not mind remainders and fractions..

You are right that the tones still exist. All you get from using primes is to ensure that these tones do not have harmonic octave relation to each other. So multiple fairly short delays are less likely to be simultaneously excited by a single note from an instrument that kicks out harmonically related signals. This can happen without feedback because you are effectively making a short FIR, but it is particularly important if there is any feedback around, even at very low levels.

For percussive stimulus the 'twang' will still be there using primes (unless you have a very large number of delays), it's just that it will have a greater harmonic spread, which is often useful as well at cutting down the honking effect. The twang will only actually go away when there are enough (relative) prime delays such that we can no longer distinguish the tones from each other.

For longer delays the tonal thing is less important, but still the use of primes can avoid what can otherwise sound like repeats from related delays, even when there is no feedback. Or put another way, several related delays can sound like a single one with feedback, and is therefore a much less rich effect since it lacks relational complexity - kind of wastes your processing. This is probably what GM was refering to?

However even with primes you must still watch out for difference coincidence between delays. Tonal behaviour can result from the differential timing between delays even using primes with longer delays, if they are too close to each other in absolute value, or have near relative multiples when there is feedback around. For instance using 53mS and 107mS produces a 1mS difference event between 106 and 107 if the first delay gets repeated at an audible level. This will be interpreted as a very short 1KHz event if stimulated by a very short percussive sound.

So to get the best results you need to consider the difference between the delays and the relative differences of the multiples of the delays - as well as the fundamental relationship.

O.K., well...by all means, go with your ear, instead of the logic. You'll want to remember to listen to the sonic differences that different delay sets provide.

And get back to us...please.

George

Paul's post above makes pretty good sense to me. I sort of got what George was getting at, but Paul's extended explication brought it into focus. Thanks to everybody, including Kendrix, who sort of got at the foggy misgivings I was having after having read George's initial post.

Ah that helps Paul. Got it - I think.

So, Im thinking that using prime number delays sort of mimics a room (parallel walls) with the magic realtionship between its dimensions such that resonant modes are minimized.

Is this a good metaphor for it?

George, you're right that I should just try it and listen.
I plead guilty to being too analytical at times
(pls dont get my wife on the topic ).
I'm just trying to understand.

When I get meticulous about minutia, I will go as far as to measure the return of my outboard delay unit against the original waveform. I've come to notice that even though a delay unit reads a specific number, it is not always accurate to the millisecond. But ultimately it does come down to the way my mind expects it to sound versus the way my ears hear the result. That is the true test of determining which # I use.
Dave
http://www.reitzas.com

Well, my ears have thaught me.... use modulation delays always. It will de-correlate therepetitions and you won't get notes associated.

Loco,
Could you please elaborate on that? Sorry, I am not clear on what you are saying.
Thanks,
Mike

Modulation changes the delay time over time and usually has at least two parameters. The rate determines how fast the delay time changes. Depth is the degree of the timing differences. Other parameters might include the shape of the modulation, sine, square, or trinagle.

So if yo set up a delay of 11ms with modulation, it could actually be changing over time between 9ms and 13ms. The rate would be the speed that the changes occour (2 times per second vs 100 times per second), and the depth would be how far the changes extend (is the spread 4ms or 10ms). In short delay times we call it chorus and flanging. In longer delay times we perceive it as detuning of the vocal.

There are examples of this in nature, too. The doppler effect is one, where a sound that is moving away from you seems to go down in pitch, or a leslie speaker that changes sound depending on how fast it is spinning.

Steve

Thanks. Very helpful explanation.

What is the argument to "always use modulation delays"?

My most frequent application is to use a relatively long delay on electric guitar, just at the level where you don't noticeably hear it, to gain a reverb effect w/o the tails, etc., that come along with reverb. I am just trying to learn how to best do this.

Thanks,
Mike

Yep. That's why I prefer to use an Echoplex. Or any sort of tape delay.

Good one, Loco.

George

Uh................is this an inside joke, or for real?

Someone please elaborate on this concept a little more. Sorry for my lack of knowledge. I'm just trying to learn.
Thanks,
Mike

Mike, no it's not a joke, and I think Extreme Mixing explained it pretty well. Did you understand George's first post and Paul's subsequent one? How the delays stacked on top of each other create tones? Well, if each of the delays happen at slightly different times and/or pitches than the others (which is what modulation delay does), that won't happen. It also won't happen if you use an actual tape delay because tape mechanisms aren't completely precise, there are very slight modulations in the timing and pitch. In fact, that's what modulating delays initially were emulating - "flanging" refers to the trick of putting your finger on the flange of a tape reel while it's turning to alter the pitch and time.

On a related side note... I never consciously used prime numbers to get my delay times, but my ears have always told me to land on them. Interestingly enough, I had an old Ampex 1/4" deck from the 60's in here for awhile. The distance between the record and playback heads was about 1.6 inches, which at 15 ips would equate to a delay of 107 ms - the classic slapback. And a prime number. Happy coincidence? When using digital delays, if I want a great slapback on a vocal I set it to 107 and put a bit of modulation on it... try it, then try using 106 or 108 while listening in real time. It just doesn't sound as good.

For a longer delay on something like a guitar, first try to get the delay in time to the performance - like on the quarter or half note of the beat. Then gradually tweak the delay length forward and backward a millisecond at a time while you listen. You'll land on a "sweet spot" at some point that will sound best to you. And chances are good that that point will be a prime number. But a slight bit of modulation helps things sound more natural too, if your delay unit has that (and most of them do).

Great stuff, Lee. Thaks so much for taking the time to explain that in detail. That gives me enough info to test it out for myself. Super.
Mike

Just a simple heads-up to anyone using PT...

The DigiRack delays come standard with a modulation feature.

I usually set mine to 1.25hz, with about 25% depth.

Adjust to taste.

At first I thought you'd simply substituted one set of harmonics for another set, GM. But Paul Frindle's explanation, while a bit confusing, gave me the key. Maybe this will help others understand.

2 4 6 8 10... any even number can be divided by 2, which increases the chance that two delays will be harmonically related.

1 3 5 7 11, primes are especially resistant to convergent harmonics because each one can be halved and never quite match any others' harmonics. They'll always be fractionally different from one another, whereas the even numbers can easily match up at multiple frequencies.

Am I making any sense?

I still believe the factor of two argument is not the key to this.
After internalizing Pauls helpful post Im thinking of this along the lines that a carefully chosen set of delays that mimics a room that minimizes resonances is the what you are aiming for.

Note that prime numbers are often involved in the RATIO of the room dimenstions required to achieve this.

However, multiply the ratios by 2 (double the room size / double the delay times) and you maintain that same room resonance behavior.

So, if this logic applies, then the factor of 2 argument is not the key- its the relationship between the resulting resonances /
(tones) that is key.
Some non-prime number (and some even number delays) can fulfill this condition.

I beleive this is consitent with Pauls post.

Interesting footnote (that may or may not relate to this thread)- I remember an interview with Roger Nichols a few years ago where he responded to a question about Equalization - he said the first frequency to look at is 125 hz - most likely with ~cut~ in mind......

I think you're confusing the two concepts as different when in fact, they are two parts of the same concept. The room dimensions and lack of annoying resonances when those dimensional ratios are prime numbers occur because any division of multiple prime numbers by 2 can never encourage the same resonances. (Unless two or more of those dimensions are identical. IE, a room that's a cube or a room where the floor/ceiling area or wall area is a square. Obviously, that creates room modes that are coincident in two or three dimensions.)

So long as you use ratios that are prime, you'll always have resonances from height that are different than width that are different from length. No resonant spikes of energy.

Paul?

Sheeesh. Wrong. And wrong-headed as well, I think.

George