back to list

a 7-limit 53-tone altered Pythagorean scale

🔗Danny Wier <dawier@hotmail.com>

9/3/2002 2:46:03 AM

A schismatically-altered 53-Pythagorgean ("Turkish") scale, based on the natural
third (5/4) approximating a cycle of 8 fourths (or -8 fifths), and the natural
seventh approximating a cycle of 14 fourths (or -14 fifths). The quintal schisma
is figured in every 9 fifths; the septimal schisma every 23 fifths.

This is version 1.0, a rough model. This was derived from what I call a
"balanced periodicity block"; thus the schisma every 9 fifths instead of 8. It
was done completely by hand, because I can't get Scala to do what I want it to
do, and it's more fun working it out the hard way, at least for me....

1/1 64/63 36/35 28/27 135/128
16/15 243/224 35/32 10/9 9/8
8/7 81/70 7/6 32/27 6/5
128/105 315/256 5/4 81/64 9/7
35/27 21/16 4/3 27/20 48/35
112/81 45/32 64/45 81/56 35/24
40/27 3/2 32/21 54/35 14/9
128/81 8/5 512/315 105/64 5/3
27/16 12/7 140/81 7/4 16/9
9/5 64/35 448/243 15/8 256/135
27/14 35/18 63/32 (2/1)

Both commata, syntonic (81/80) and septimal (64/63), are used, and the comma
sharp/flat is treated as an augmented seventh/diminished second. The difference
between the two commas, 5120/5103, is the schisma known as Beta 5 (according to
Scala).I'll work on a better version.~Danny~

--------------------------------------------------------------------------------

Chat with friends online, try MSN Messenger: Click Here
[http://g.msn.com/1HM1ENUS/c144??PS=47575]