What is this numeric progression?

I have been working with Paul's extreme stretch and I wanted to generate a series of base frequencies that do not share harmonics. I succeeded far greater than I imagined.

If you that the following series of fundamentals 25, 75, 125, ... 275 And calculate the harmocis for each 25, 50, 100, ... 51200 you will find no harmonics are shared.

This works with 12, 36, ... 132 and 1, 3, 7, ... And by inspection to 47.

The formula to generate the fundamentals is the same in each case

Twice the starting number is added to get the next higher fundamental.

I can't wait to hear this. I wonder what the implication is for harmony that does not share harmonics between chord members.

Who else has found this relationship and what is it called?

Chris
*

On Thu, Apr 12, 2012 at 2:50 PM, <chrisvaisvil@...> wrote:
>
> I have been working with Paul's extreme stretch and I wanted to generate a
> series of base frequencies that do not share harmonics. I succeeded far
> greater than I imagined.
>
> If you that the following series of fundamentals 25, 75, 125, ... 275 And
> calculate the harmocis for each 25, 50, 100, ... 51200 you will find no
> harmonics are shared.

You must be making a mistake here - 75 is itself a harmonic of 25 :)

-Mike

--- In tuning@yahoogroups.com, chrisvaisvil@... wrote:
>
> I have been working with Paul's extreme stretch and I wanted to generate a series of base frequencies that do not share harmonics. I succeeded far greater than I imagined.
>
> If you that the following series of fundamentals 25, 75, 125, ... 275 And calculate the harmocis for each 25, 50, 100, ... 51200 you will find no harmonics are shared.

I don't understand this. 75 is the third harmonic of 25. 25*3 = 75. Therefore these do share harmonics.

Also, the fifth harmonic of 75 (375) is equal to the third harmonic of 125.

> This works with 12, 36, ... 132 and 1, 3, 7, ... And by inspection to 47.
>
> The formula to generate the fundamentals is the same in each case
>
> Twice the starting number is added to get the next higher fundamental.
>
> I can't wait to hear this. I wonder what the implication is for harmony that does not share harmonics between chord members.
>
> Who else has found this relationship and what is it called?

Keenan

Obviously I made a grand blunder.

My apologies

Chris
*

-----Original Message-----
From: "Keenan Pepper" <keenanpepper@gmail.com>
Sender: tuning@yahoogroups.com
Date: Thu, 12 Apr 2012 20:02:35
To: <tuning@yahoogroups.com>
Reply-To: tuning@yahoogroups.com
Subject: [tuning] Re: What is this numeric progression?

--- In tuning@yahoogroups.com, chrisvaisvil@... wrote:
>
> I have been working with Paul's extreme stretch and I wanted to generate a series of base frequencies that do not share harmonics. I succeeded far greater than I imagined.
>
> If you that the following series of fundamentals 25, 75, 125, ... 275 And calculate the harmocis for each 25, 50, 100, ... 51200 you will find no harmonics are shared.

I don't understand this. 75 is the third harmonic of 25. 25*3 = 75. Therefore these do share harmonics.

Also, the fifth harmonic of 75 (375) is equal to the third harmonic of 125.

> This works with 12, 36, ... 132 and 1, 3, 7, ... And by inspection to 47.
>
> The formula to generate the fundamentals is the same in each case
>
> Twice the starting number is added to get the next higher fundamental.
>
> I can't wait to hear this. I wonder what the implication is for harmony that does not share harmonics between chord members.
>
> Who else has found this relationship and what is it called?

Keenan

> Obviously I made a grand blunder.

If you're going to make blunders, make them grand! :)

It looks like you are trying create a scale (or a set of frequencies to use
as base frequencies in Extreme Stretch, which sounds like it amounts to the
same thing) that avoids tones that are based on harmonics of some other
tone in the scale. That's a lot harder than it looks; I tried it a while
back, in an attempt to think about "atonality" outside of the 12-EDO model,
and I couldn't do it. Not to say that someone smarter couldn't do better,
but the naive attempts I made always had pretty nice JI approximations
buried in them somewhere, and more abundantly than I would have thought.

Igs even wrote a piece of music, "Anxiously Orbiting In Andromeda," using
John O'Sullivan's "worst scale", which was his attempt to make something
similar. It's on _Transcendissonance_, and he discusses the scale in his
liner notes. Maybe you use it for your experiment: Here it is, in cents:

0
102
217.6
291.3
351
466.6
524.7
659.8
742.3
849.1
993.2
1135.9
1200

I note that neither John nor Igs consider 351 cents to be just, even though
it's a very good 11/9 -- an interval I like a lot.

Regards,
Jake

Aye - grand it was! I keep getting my head confused into thinking the
harmonic series is a*2=b. b*2=c, c*2=d, and so on.

I think it comes from the fact that an octave is 2f - but 2 octaves is not
4f but actually 3f.

I did try John's (and Micheal's) "bad" tunings - but not on an album
http://micro.soonlabel.com/bad/

The object was to avoid having doubling up frequencies in the harmonic
series to avoid accenting high frequencies in PES. So, you do have that
right. I can't say I thought of using John's scale as a basis for PES -
however, since the harmonic series crowds in together higher up its some
what futile isn't it. I mean - the worst case I can think of is C and F# -
and if their series coincides at some point then it just isn't going to
happen out side of a trivial example (C and F# 6 octaves above and
discounting anything about human hearing).

Chris

On Thu, Apr 12, 2012 at 4:55 PM, Jake Freivald <jdfreivald@...> wrote:

> **
>
>
> > Obviously I made a grand blunder.
>
> If you're going to make blunders, make them grand! :)
>
> It looks like you are trying create a scale (or a set of frequencies to
> use as base frequencies in Extreme Stretch, which sounds like it amounts to
> the same thing) that avoids tones that are based on harmonics of some other
> tone in the scale. That's a lot harder than it looks; I tried it a while
> back, in an attempt to think about "atonality" outside of the 12-EDO model,
> and I couldn't do it. Not to say that someone smarter couldn't do better,
> but the naive attempts I made always had pretty nice JI approximations
> buried in them somewhere, and more abundantly than I would have thought.
>
> Igs even wrote a piece of music, "Anxiously Orbiting In Andromeda," using
> John O'Sullivan's "worst scale", which was his attempt to make something
> similar. It's on _Transcendissonance_, and he discusses the scale in his
> liner notes. Maybe you use it for your experiment: Here it is, in cents:
>
>

http://cote.cc/blog/alternative-scale-tuning-in-logic-pro-9

Charles Lucy
lucy@...

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