Topic: Breedpump scale

1 scales

Thread (1 messages)

From: Gene Ward Smith (2004-09-06)
Subject: Breedpump scale

I checked for comma pumps of minimal length for 2401/2400, consisting
of tetrads and such that each tetrad shares an interval with ajoining
ones in the chord sequence. This produced 244 distinct scales of
sixteen notes. One of these scales is distinguished by the fact that
it contains the maximal number--three--of both subminor and supermajor
tetrads. While there are no complete pentads all of these subminor and
supermajor tetrads are a useful addition to the eight 7-limit tetrads
of the pump circle. Below I give the scale in the no-threes tuning,
where 3 is approximated by 2401/800. While this is an entirely
acceptable tuning, especially if you believe that slightly sharp
fifths are melodically superior, one can of course tune so as to make
the harmony even closer to just.

! breedpump.scl
Comma pump in breed (2401/2400 planar)
16
! four major and minor tetrads, three supermajor and subminor tetrads
!
50/49
16807/16000
343/320
400/343
20000/16807
49/40
5/4
7/5
10/7
2401/1600
49/32
80/49
4000/2401
7/4
25/14
2
! comma pump [[1, 1, -2]->[1, 1, -1]->[0, 1, -1]->[0, 0, -1]
! ->[0, 0, 0]->[0, -1, 0],[0, -1, 1]->[0, -2, 1]->[-1, -2, 1]