Re: [tuning] Replies to Dan and David on locally concordant tetrads

"Paul H. Erlich" schrieb:
>
> Dan Stearns wrote (off-list),
>
> ...
> David Finnamore wrote,
...
>
> >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.
>
> Unfortunately, if you do tune the lowest (highest in pitch) four strings on
> the guitar exactly like that, and tune the other two in successive 4:3
> fourths, your lowest string will be a comma off from your highest string.
> ...

I have a question, guys - a guitar string further on:
If I compare the harmonic on the 4th fret on the G-String with the
harmonic on the 5th fret of the B-String,what kind of Komma do I hear?
Sorry, as a teacher I�m too lazy. Could anybody explain?
Thank you
Harald K�gler

Hi Paul,

One of the more interesting results of this are the instances of
subtle tempering that you point out, what I'm not clear on is how much
this is a part of the process... in other words if you were to set the
larger limit of the adjacent notes to something on the order of say
1350�, would the most concordant stack of 1:2s have slightly tempered
octaves; and would that result be equally "valid" (as the stack of
fourths result is)? If the results did not give an unusually, or
undesirably tempered stack of 1:2s, then might this also be a good
model for an adaptive retuning model for other common
stack-of-an-interval chords, such as the stack of minor and major
thirds, and the stack of fifths?

> (2) If you _do_ play the notes of the tetrad only two at a time, and
choose all pairs with equal frequency/probability, you have a good
measure of the
expected harmonic entropy of the resulting music.

Is there some way to combine this sort of a "harmonic entropy of the
resulting music" model with some melodic analogue to the work that's
been done dealing with optimizing given scales to best accommodate a
given array of vertical sonorities. In other words some paradigm that
attempts to generalize 'melodic diatonicity' (i.e., some attempt to
codify what might be the "best" melodic 2, 3, 4, 5, 6, 7, 8, 9, 10,
11, etc., note scales). I know
that MOS, propriety, and tetrachordality attempt to deal with melodic
stability in a sense, but I'm thinking of something more like the
harmonic entropy measure for dyads with it's peaks and valleys, and
what your presently gearing up to do when you write, "for sets of
considerably more than four notes (i.e., scales rather than
chords)"... something on the order of a synergistic melodic entropy I
suppose is what I'm imagining here... anyway, keep up the good work.

Dan