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Pentatonic 5-limit Fokker blocks

🔗Gene Ward Smith <gwsmith@svpal.org>

9/23/2005 3:46:09 PM

I decided to do a survey of all of these derivable from 16/15, 27/25
and 81/80; not all of these turned out to be known. In the list
below, five scales each for each pair, the first listed is self-
inverse, and the other two successive pairs are inverse to each
other.

16/15 & 81/80

1. Pythagorean pentatonic (hexany16 and chin_5)

2. Korea_5; "the Delightful" according to Lou Harrison

3. Inverse korea_5, unlisted

4. Listed as tranh and prime_5. What you might call the standard 5-
limit pentatonic, it's also the 5-limit 5-et dwarf.

5. Inverse prime_5. Unlisted! Just as in the 7-limit Zarlino (the 7-
et dwarf) gets all the press and Redfield is relatively ignored,
this one isn't even listed in the Scala directory. However, it and
its inverse show up three times in this survey, under each of the
pairs.

16/15 & 27/25

1. Harrison_min and pipedum_5

2. Unlisted; 6/5 4/3 8/5 5/3 2 with intervals 6/5 6/5 10/9 6/5 25/24
6/5

3. Inverse of the previous: 6/5 5/4 3/2 5/3 2 with intervals 6/5 6/5
25/24 6/5 10/9 6/5

4&5 same as 4&5 for 16/15 and 81/80 and also 27/25 and 81/80

27/25 & 81/80

1. Pipedum5a

2. Unlisted: 10/9 27/20 3/2 5/3 2

3. Unlisted; inverse of previous 10/9 27/20 3/2 9/5 2

4&5 same as previous 4&5