Topic: The Tripentatonic scale

1 scales

Thread (1 messages)

From: Gene Ward Smith (2003-09-25)
Subject: The Tripentatonic scale

I was considering how to put three copies of the meantone pentatonic
scale together in a reasonable way, and concluded that the supermajor
seconds temperament was the way to go. This divides a meantone fifth
into three parts to get a supermajor second of around 8/7, which is
the  generator. Hence it has 81/80 and (3/2)/(8/7)^3 = 1029/1024 as
commas.

Tripentatonic has three copies of pentatonic in it, and is
pseudo-Myhill; adding another note gives us a 16-note supermajor
seconds MOS. If we use 6/31 for the generator, tripentatonic is

[0, 1, 5, 6, 7, 11, 12, 13, 18, 19, 20, 24, 25, 26, 30]

Adding a 14 gives us the MOS.

Here is Tripentatonic in Scala format:

! tripenta.scl
6/31 generator supermajor seconds tripentatonic scale
15
!
38.709677
193.548387
232.258065
270.967742
425.806452
464.516129
503.225806
696.774194
735.483871
774.193548
929.032258
967.741935
1006.451613
1161.290323
1200.000000