Jacobin chords: Difference between revisions

Revision as of 03:10, 8 June 2023

Jacobin chords are essentially tempered dyadic chords tempered by the jacobin comma, 6656/6655.

Since the temperament is very complex, even the simplest jacobin chords are 55-odd-limit. There are

For tetrads, there are

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-Jacobin chords are [[essentially tempered dyadic chord]]s tempered by the jacobin comma, [[6656/6655]].
+'''Jacobin chords''' are [[essentially tempered dyadic chord]]s tempered by the jacobin comma, [[6656/6655]].
-There are seven chords in total involving this comma. The notation assumes each interval is the interval from the chord and not from the tonic. There are 5 triads:
+Since the temperament is very complex, even the simplest jacobin chords are 55-odd-limit. There are
+* 1-11/8-16/11 with steps 11/8-55/52-11/8;
+* 1-64/55-11/8 with steps 64/55-13/11-16/11, and its inverse
+* 1-13/11-11/8 with steps 13/11-64/55-16/11.
-* 1/1 - 55/52 - 11/8 - 11/8
+For tetrads, there are
-* 1/1 - 64/55 - 13/11 - 16/11
+* 1-11/8-16/11-104/55 with steps 11/8-55/52-13/10-55/52;
-* 1/1 - 13/10 - 16/11 - 128/121
+* 1-13/11-11/8-104/55 with steps 13/11-64/55-11/8-55/52, and its inverse
-* 1/1 - 13/11 - 8/5 - 128/121
+* 1-64/55-11/8-16/11 with steps 64/55-13/11-55/52-11/8;
-* 1/1 - 5/4 - 11/8 - 121/104
+* 1-64/55-11/8-104/55 with steps 64/55-13/11-11/8-55/52, and its inverse
+* 1-13/11-11/8-16/11 with steps 13/11-64/55-55/52-11/8.
-And 2 tetrads which both span two octaves:
-* 20/13 - 11/8 - 11/8 - 11/8 across 4/1
-* 13/11 - 8/5 - 16/11 - 16/11 across 4/1
+[[Category:55-odd-limit]]
 [[Category:Jacobin]]
 [[Category:Essentially tempered chords]]
 [[Category:Triads]]
 [[Category:Tetrads]]