Re: locally concordant tetrads

Paul H. Erlich wrote:

> Going from lowest
> (most concordant) up the list:
>
> First there were a bunch of chords which were really triads with the lower
> note doubled an octave higher.
>
> The next most concordant tetrad was:
> 0 498 886 1384�
> or 9:12:15:20 or 1/1:4/3:5/3:20/9. It is an open-voiced JI minor seventh
> chord in third inversion, or an open-voiced JI major added sixth chord in
> second inversion.

Sound familiar, fellow guitarists? I learned that tetrad at age 7 on the ukulele as, "My dog has fleas." But, of course, it's also the (approximate) standard tuning of the lowest four strings on the guitar. How did ye olde guitar and ukulele players know how to do that without a supercomputer? Tee hee.

Paul, I _love_ the graphic you posted for triads (enttriad.jpg). I just can't quit staring at it!

--
David J. Finnamore
Nashville, TN, USA
http://members.xoom.com/dfinn.1
--

Keenan Pepper wrote...

>This would tend to judge the entropy of the chord as a whole, not a
>particular voicing of the chord. This seemed to ba a problem in the local
>minima of the tetrad graph; some chords didn't make it or got bumped down
>simply beacause they didn't have a voicing open enough. Octave equivalence
>just makes sence.

I disagree. For dyads octave equivalence can be handy, maybe even roughly
insightful up to the 9-limit. For triads and higher-ads, it gets messy
very quickly. Observe how much "voicing" can contribute to a characteristic
sound, even for 5-limit triadic music (let alone jazz!). Get into
higher-limit JI, and many chords will run into different harmonic-series
representations as you invert them. Take the 7-limit utonal tetrad. In
"1st" (Partchian) inversion, (1/1 7/6 7/5 7/4), it doesn't really
approximate any harmonic chord that I know of, but the intervals are all
consonant, and we have a characteristic minor sound. But in 2nd inversion,
the chord clearly (IMO) approximates a 10:12:15:17 tetrad.

-Carl