Fwd: [tuning] Re:75/64 (was: A new diminished seventh chord)

A strange consonant quasi minor-major seventh chord arises from the
scale given below.

11:13:16:20

This doesn't exist in the SCALA chords archive.

Any suggestions for names?

Oz.

Begin forwarded message:

> From: Ozan Yarman <ozanyarman@...>
> Date: November 18, 2009 10:02:35 PM GMT+02:00
> To: tuning@yahoogroups.com
> Subject: Re: [tuning] Re:75/64 (was: A new diminished seventh chord)
>
> An interesting scale from the differentials of 75/64:
>
> Original > Differential > Normalized
> 75/64 > 11/64 > 88/64 (11/8)
> 88/64 > 13/64 > 13/8
> 13/8 > 5/8 > 5/4
> 1/4 > 2/1
>
> Ascending order:
>
> 75/64
> 5/4
> 11/8
> 13/8
> 2/1
>
> Oz.
>
> ✩ ✩ ✩
> www.ozanyarman.com
>
> On Nov 16, 2009, at 2:25 AM, Jacques Dudon wrote:
>
>>
>>
>> Lovely theme Monz !
>>
>> May I disgress here by adding why 75/64 is a very special minor
>> third for me ?
>> (besides being in 5-limit !)
>> On the contrary to 7/6, 75/64 's differential tone is a neutral
>> fourth (11/64) which transposed to the same octave,
>> introduces a 88/75 interval that repeats pretty much the same
>> interval (they differ by a schisma of 5632/5625).
>> This is a fractal property that is illustrated in a infinity of
>> recurrent sequences such as 35:41:48:56, 99:116:136:160,
>> 169:198:232:272, ...
>> and so on where x^2 = 8(x - 1) - that is called "Isrep" in my
>> terminology, and has 4 - 2^(1/2) = 1,171572875254 as solution.
>>
>> One of those sequences is 64:75:88:104:128:192 (differentials 11
>> > 13 > 16 > 24) and if it may be seen more rapidly degenerating
>> than other series, it does it in unique way, since the spiral
>> crosses the octave (128) of the first tone.
>> 128 - 104 = 24 then introduces a new tone, but extends luckily the
>> diminished seventh chord (if ever you still want to hear it that
>> way) to a 64:75:88:96:104 (n-1) class -c (differentially
>> coherent) pentatonic scale :
>>
>> isrep_75
>>
>> 1/1
>> 75/64
>> 11/8
>> 3/2
>> 13/8
>> 2/1
>>
>> No idea if the 13/8 and 11/8 quartertones here, in combination to
>> 75/64, would be of any interest in maqam music (or extrapolations),
>> may be Ozan knows ?
>> However it has some ethiopian accents, and other charms.
>>
>> - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
>> Jacques
>>
>>
>>
>>
>>
>>
>