Topic: Line commas

1 scales

Thread (1 messages)

From: genewardsmith (2011-05-21)
Subject: Line commas

By a line comma, I mean a 7-limit comma of the form |a -b b b>, |a b -b b> or |a b b -b>. The corresponding otonal tetrad will be of thr form [2b 0 0], [0 2b 0] or [0 0 2b], and the simplest comma pump will simply march along a line of the tetrad lattice, as for instance [0,0,0],[1,0,0],[2,0,0] etc.

A nice example is |11 -10 -10 10>. A comma pump is provided by [0 0 0], [0 0 -1], ..., [0 0 -20]. In spite of the variation in interval sizes, the scale one obtains by merging the pump has a certain regularity:

! line40.scl
|11 -10 -10 10> tempered line scale in 2080et tuning
40
!
8.65385
26.53846
102.11538
120.00000
128.65385
146.53846
222.11538
240.00000
248.65385
266.53846
342.11538
360.00000
368.65385
386.53846
462.11538
480.00000
488.65385
506.53846
582.11538
600.00000
608.65385
626.53846
702.11538
720.00000
728.65385
746.53846
822.11538
840.00000
848.65385
866.53846
942.11538
960.00000
968.65385
986.53846
1062.11538
1080.00000
1088.65385
1106.53846
1182.11538
1200.00000