septimal intervals

Graham Breed said:

> To state my own opinion, which is the only one I trust, a just 4:6:7
> chord is more consonant than a major triad in 12 equal. Extending
> consonance to the 7-limit means just that -- no further.

In the more usual timbres at least, the 7:6 interval beats too much to
be consonant, affected as it is by the unison. The 7:5 is obscured by
the fifth and fourth. There is a slightly stronger case for the 7:4, but
note that the first partial of the lower tone beats with the fundamental
of the upper tone (8:7).

The 7:4 forms dissonant intervals with the consonances of the senario,
whereas 8:5 does not (at least not with 6:5 & 4:3).

This is a vast subject however, which can scarcely be treated here on
the scale it deserves.

I quite agree that the dissonance or consonance of the septimals proves
nothing regarding the undecimal intervals.


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From: Gregg Gibson
Subject: 22-tone equal, reply to Ehrlich
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Gregg Gibson wrote:
>Bill Alves (quoted by Paul Ehrlich) made a very interesting comment to
>the effect that the four chromatic modal genera (scales) comprising 28
>modes, that I have discovered and posted:

Just to set the record straight, I think it was Paul who made this comment
-- sometimes the quotes in these posts are hard to follow.

>Gamelan scales
>by the way can be very satisfactorily reproduced in 19-tone equal.
>
If by this you mean that reasonable gamelan scales can be found in 19TET,
then I agree. If you mean that gamelan tuners always intuitively aim at
some subset of 19TET, then I disagree. (One writer suggested that this was
the case with respect to 9TET, but I take great exception to his
reasoning.)


^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
^ Bill Alves email: alves@hmc.edu ^
^ Harvey Mudd College URL: http://www2.hmc.edu/~alves/ ^
^ 301 E. Twelfth St. (909)607-4170 (office) ^
^ Claremont CA 91711 USA (909)607-7600 (fax) ^
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^


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