Tuning-Math Digests messages 6677 - 6701

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Message: 6677

Date: Mon, 24 Mar 2003 09:53:44

Subject: Re: Diaschismic, Negri and Blackwood 10

From: Graham Breed

Gene Ward Smith wrote:

> I wasn't thinking of pajara, but of the 34&46 system I've been calling
> "diaschismic". My endorsement was premature; I knew diaschismic[10]
> was not only a 25/24 system, but also a 21/20 system, so I expected to
> get asses in place of regular tetrads, and I did. Trouble is, these
> are all 5-limit asses, so it's still 5-limit harmony. However, it's in
> much better tune 5-limitwise than pajara.

Sorry, I've lost the original message.  34-equal isn't consistent in the 
7-limit, so it won't define the system.  Do you mean 46&58?

2  3  5  7
0  1 -2 -8


                  Graham


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Message: 6682

Date: Tue, 25 Mar 2003 16:08:57

Subject: Re: Kleismic[8] and Hemifourths[9]

From: Carl Lumma

>Kleismic[8]
>rms error 12.274

Yeah, it's a good 'un.  But how'd you pick 8?  Once again: where
are you getting the n's????

-Carl


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Message: 6691

Date: Wed, 26 Mar 2003 00:54:51

Subject: Re: T[7] with 25/24 chroma

From: Carl Lumma

>part of "glassic" is in porcupine. you can hear the consecutive 
>triads -- major, major, minor, minor -- as the root descends stepwise 
>from "8ve" to "5th". thus part of you wants to believe it's 
>mixolydian, but melodically it's singing quite a different tune.

Oh yes, I hear that!  Great work!

-Carl


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Message: 6692

Date: Wed, 26 Mar 2003 01:03:37

Subject: Re: Kleismic[8] and Hemifourths[9]

From: Carl Lumma

>> Yeah, it's a good 'un.  But how'd you pick 8?  Once again: where
>> are you getting the n's????
>
>Now that I've sent you my maple programs, you could find them yourself.

Thanks for the tutorial.  I glanced at your stuff, but probably won't
get a chance to look at it until next week.

>Same comment, but probably worth exploring.

So, you're doing it by hand, was all I was looking for.  I wonder if
there's any way to predict the good stopping points.  I suppose they
occur when the chromatic uv is simple? .  .  .

>Pelogic[7]
>
>135/128
>[1, 9/8, 5/4, 4/3, 3/2, 8/5, 15/8]
>[5/4, 15/8, 4/3, 1, 3/2, 9/8, 8/5]
//
>Dominant sevenths[7]
>rms error 20.163 cents
//
>Hemifourths[9]
>rms error 12.690
//
>Tertiathirds[9]
>rms error 12.189 cents
//
>Hexadecimal[9]
>rms error 18.585

Ahh -- it's all coming too fast!

-Carl


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Message: 6698

Date: Sun, 30 Mar 2003 23:40:16

Subject: Re: 225/225 & 21/20 scales

From: Carl Lumma

>[4, -3, 2, -14, -8, 13] [[1, 2, 2, 3], [0, -4, 3, -2]]
>
>bad 2644.480844 comp 14.72969740 rms 12.18857055
>graham 7 scale size 9 ratio 1.285714

What's this?

-Carl


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