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Morphing from mean to reverse-mean

🔗Robert C Valentine <BVAL@IIL.INTEL.COM>

8/27/2000 2:35:10 AM

Some composition thoughts...

I was thinking about a piece that would start in a reverse
meantone, xengothic tuning (not necessarilly a xen gothic
style, I was more thinking that thirds would be treated as
consonances BUT, due to the tuning be somewhat strident). At
the end of the piece, the same passage is played, however the
tuning has been 'morphed' to a normal meantone, so that the
thirds are now consonant.

Something like a Crab Canon would be a nice fit here, as
the begininng section would emphasise the thirds and sixths
resolving to fourths and fifths, while the ending could
emphasise the fourths and fifths (now a bit unpure) resolving
to consonant thirds and sixths.

Whether such a strong formal plan as 'crab cannon' was used, it
looks like an ABA' form is a natural, with the emphasis mentioned
above. The middle section (in the center of the morph), will be
alot like 12tet, since the flats and sharps have to reverse their
orientation and would cross (become synonymous) here.

Using gigantic temperments may be a good strategy for for
approaching the morph in discreet steps. Whether the final
composition morphs discretely or continuously...

for instance, in 310tet, the following diatonic systems are
some of those available. [L and s stepsizes, then cents
values for a few important intervals]

L s M2 M3 P5
58 10 225 449 712
56 15 217 434 708
54 20 209 418 705
52 25 201 403 701
50 30 194 387 697
48 35 186 372 693
46 40 178 356 689

323tet is interesting, providing the morph from 17 to 19 tet,
however, going to 646tet gives an even better morph from 17
to better than 31.

M2 M3 P5
212 424 706 this is 17
208 416 704
204 409 702
201 401 700
197 394 698
193 386 697 L=104 s=63 [105,63 is 31tet]
189 379 695 this is 19

Bob Valentine