RE: RE: A gentle introduction to Fokker periodicity bloc ks, part 2

On Mon, 1 Nov 1999, Paul H. Erlich wrote:
>> In such cases I like to cheat a little by placing such a pitch exactly
>> on the border of the hexagon, so that both versions can be used.
>
> Nice idea, but in this case I think one has to recognize a severe difference
> in practical status between the two unison vectors involved. Your cheat,
> when used to blur the distinction between two notes separated by a syntonic
> comma, reflects the fact that musicians treat the two as just one note. But
> if you used it to try to include two notes separated by a chromatic semitone
> using this cheat, you'd be alternating between melodic minor and a different
> scale entirely.

Yes--this gets into different categories of "unisonous" intervals.
Since I am investigating how "generalized diatonic" scales embed within
ETs (I'm not really into pure JI), I distinguish between "chromatic" and
"commatic" unisons. Within the system of diatonic/heptatonic (unisons
[4 -1] and [-1 2]) scales embedded within 12TET (unisons [4 -1] and
[0 3]), the commatic intervals are the ones that vanish in the ET, while
the chromatic interval vanishes in the diatonic but _not_ the ET. If
you were considering the heptatonic scale independently of the 12TET
gamut, of course, the [4 -1] would of course still vanish, which implies
meantone.

--pH <manynote@library.wustl.edu> http://library.wustl.edu/~manynote
O
/\ "How about that? The guy can't run six balls,
-\-\-- o and they make him president."