Re: RE: the unknown comma

from muenda@hotmail.com

I was wondering about the comma that occurs between the two tritones
45/32 and 64/45, which equals 2048/2025. is this a well known or used comma?

This is the diaschisma of about 19.55 cents. It's equal to the octave-reduced
enharmonic pitch four perfect fifths plus two major thirds away. Don't if it's
"used" as such, but it sure is there. :)

>from muenda@hotmail.com

>I was wondering about the comma that occurs between the two tritones
>45/32 and 64/45, which equals 2048/2025. is this a well known or used comma?
>

> [muenda qwa sahure, TD 303.8]
>
> I was wondering about the comma that occurs between the two
> tritones 45/32 and 64/45, which equals 2048/2025. is this a
> well known or used comma?

In Helmholtz's _On the Sensations of Tone_, appendix XX,
section D, on page 453 of the Dover reprint edition,
Alexander Ellis, in his 'Table of Intervals not exceeding
one Octave', calls this interval by the name of 'Diaskhisma'.

It has an interval size of ~19.55 cents, and certainly appears,
whether purposely or inadvertently, in a great deal of 5-limit
JI music. Of course, it would also frequently be implied in
differently-tuned music which implies 5-limit JI.

-monz

Joseph L. Monzo Philadelphia monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
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The diaschisma is "used" by Graham Breed in defining a bunch of scales -- see
http://www.cix.co.uk/~gbreed/diaschis.htm. He may have come up with this idea
after discussing 22-tone tunings with me. Several years ago, we discussed my
interpretation of ancient Indian tuning, which came up again a few days ago. It
seems that although 5/3 and 27/16, a syntonic comma apart, were considered
sruti #s 16 and 17, respectively, 16/15 and 135/128, a diaschisma apart were
both considered sruti # 2. Graham describes regular temperaments which
consistently distinguish the syntonic comma but not the diaschisma, and so
could serve as a model for ancient Indian tuning.