reply to me

Paul Erlich wrote:

> I regret that our previous discussions were interrupted due to problems
> with the list server. I'd be happy to continue discussing those issues
> if you are so inclined. But I'd like to understand this question:

I'd be happy to continue the discussion. I remember some stuff
about 9 being a coordinate direction, a recipe for saturated chords,
and an argument about octave invariance that did reach some kind of
conclusion.

Anyway, to my question:

> Now, does anyone know of a 2-D approximation (linear
> temperament) that covers 22tet? Approximating the
> enharmonic diesis (7 0 -3)H and syntonic comma (-4 4 -1)H
> to be equal doesn't work. If it did, it would cover 12, 22,
> 34 and 46tet. It is, incidentally, significant that these
> are all even numbers.

Looking back through the archive, I see you (Paul) covered these
in March:

>> Doubly postive systems resembling 22-tet are also possible. I
>> will post some such tunings at a later date.
>
> What is the definition of "doubly positive?" Do you mean, two positive
> systems separated by exactly one-half octave? If so, I hope you don't give
> away any more of my secrets, at least until XH 17 comes out, which is, when?
> Or did someone else come up with the idea of two positive systems separated
> by exactly one-half octave before I did?

Whatever "doubly positive" means, the scales you mentioned are
the ones I thought didn't work. I wanted a 0-comma scale to
be just, preferably Pythagorean, but I can see now that there's
no problem with having tritones in there. I've had a good
look at them, but I haven't worked out the 7-limit approximation
yet. Can you help here?

Getting back to Paul's message:

> In the ancient Hindu
> sruti system, the syntonic comma (-4 4 -1) is reckoned as one sruti,
> while the interval 2048/2025 (is that a diaskhisma?) is zero srutis.
> That last interval is (11 -4 -2)H, I believe.

Thanks for using my notation. Setting (11 -4 -2)H to zero
using the method I outlined on the list before gives this
temperament. The defining matrix has a determinant of -2, which
is where the tritones come from.

As regards srutis, are these ancient or medieval in origin?
The document defining Sa- and Ma-grama on a 22 note scale seems
to me to be the earliest clearest record of 5-limit diatonic
outside of Europe. I welcome corrections on this.



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From: gbreed@cix.compulink.co.uk
Subject: Re: Nomenclature
PostedDate: 23-08-97 17:20:10
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