Topic: Octone again

1 scales

Thread (1 messages)

From: Gene Ward Smith (2005-05-26)
Subject: Octone again

If you take the octone to be

1-15/14-60/49-5/4-10/7-3/2-12/7-7/4

then while it isn't Tenney reduced, it has other desireable properties.
It is the union of a justly-tuned otonal tetrad with a utonal tetrad,
and the 2401/2400 approximations have been reduced to an approximate
10/7 relationship from 60/49 to 7/4. Moreover, it is epimorphic and
(by a margin of 2401/2400) a constant structure. If we have 49/40 in
place of 60/49, it falls right on the boundry of being epimorphic and
CS. This strikes me as a rather curious musical example and one worth
keeping in mind.

Here's the replacement octone:

! octone.scl
octone around 60/49-7/4 interval
8
!
15/14
60/49
5/4
10/7
3/2
12/7
7/4
2

Here is the octone in 612, which is very close to the minimax tuning.
In this case, we get that the scale is proper. For 60/49, it was
strictly proper, epimorphic and CS. For 49/40, it was improper and
permutation epimorphic. 

! octo.scl
octone in 612 equal
8
!
119.60784
350.98039
386.27451
617.64706
701.96078
933.33333
968.62745
1200.0000