reply to Carl Lumma

>1. 13/12 - 4/3 - 5/3

Can't you reduce this to 13/4 - 4 - 5?

>I will say that my conclusions supported my long-standing belief that
>octave-invariance is out the window when you go above the 7-limit.

Although I basically agree with you, I wouldn't say it goes out the
window at a particular limit. Octave invariance is never complete no
matter how low the limit, and achieving consonance at higher limits
requires that more and more attention be paid to register. At the
7-limit, it is certainly true that 7:5 is more consonant than 10:7 and
chords that include the former are perceived as more stable than those
that include the latter. Even in 22-tET where these intervals are both
represented by a half-octave, chords where the half-octave represents a
7:5 tend to sound a good deal more stable than those where the
half-octave represents a 10:7. In most contexts, 7:6 is quite a bit more
consonant than 12:7. Even in 12-tET, a minor sixth alone can be heard as
a dissonance, in sharp contrast to a major third. Triadic harmony will
tend to clarify the meaning of the minor sixth to the point where it can
no longer be considered dissonant. At any limit, the choice of bass note
is extremely important in determining the stability of a chord.

On Thu, 11 Feb 1999, Paul H. Erlich wrote:

> >1. 13/12 - 4/3 - 5/3
>
> Can't you reduce this to 13/4 - 4 - 5?

I think in reality it's 4/5 - 1 - 5/4

(remember small integers? small integers good.)

-Bram