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Periodicity blocks

🔗Rich Holmes <rsholmes@mailbox.syr.edu>

11/14/2006 7:54:06 PM

Quick question: Is there anything in the definition of a periodicity
block that requires all intervals within the block to be larger than
the block's unison vectors?

I can't find such a requirement stated explicitly, but Erlich's
"Gentle Introduction" does seem to imply it -- a unison vector is
spoken of as "too small a distinction to keep on your instrument"; a
block containing a smaller interval would seem to be inconsistent with
that point of view.

On the other hand, way back in 1999 (the url:

/tuning/topicId_5524.html#5524?var=0&l=1

) Erlich wrote 'Bohlen's "diatonic" JI scale ... is a periodicity
block with UVs (1 2) = 245:243 and (4 -1) = 625:567'. Yet that block
contains intervals of (-2 0) = 27:25 = 133 cents, smaller than 625:567
= 169 cents.

Hence the question...

- Rich Holmes