Sinbadmic chords: Difference between revisions

Revision as of 10:51, 23 August 2023

A sinbadmic chord is a 13-limit essentially tempered dyadic chord which is tempered by 1001/1000 (sinbadma).

The triads are of the form

and its inversion,

It leads to following tetrads:

Equal temperaments with sinbadmic chords include 29, 31, 43, 50, 53, 58, 72, 87, 103, 111, 130, 183, 190, 198, 270, 571, 590, 643, 860, 1130, 1431 and 1701, with 1701edo giving the optimal patent val.

The name is derived from the sinbadma (1001/1000), a comma that is reminiscent of the tales of 1001 Nights.

@@ Line 2: / Line 2: @@
 The triads are of the form
-* 1-[[7/5]]-[[20/13]], with steps [[7/5]]-[[11/10]]-[[13/10]],
+* 1-[[7/5]]-[[20/13]], with steps of [[7/5]]-[[11/10]]-[[13/10]],
 and its inversion,
-* 1-[[7/5]]-[[20/11]], with steps [[7/5]]-[[13/10]]-[[11/10]].
+* 1-[[7/5]]-[[20/11]], with steps of [[7/5]]-[[13/10]]-[[11/10]].
-It leads to a tetrad,
+It leads to following tetrads:
-* 1-[[11/10]]-[[13/10]]-[[10/7]] in one voicing, which has steps of [[11/10]]-[[13/11]]-[[11/10]]-[[7/5]].
+* 1-[[11/10]]-[[13/10]]-[[10/7]] with steps of [[11/10]]-[[13/11]]-[[11/10]]-[[7/5]];
+* 1-[[11/10]]-[[10/7]]-[[11/7]] with steps of [[11/10]]-[[13/10]]-[[11/10]]-[[14/11]];
+* 1-[[13/10]]-[[10/7]]-[[13/7]] with steps of [[13/10]]-[[11/10]]-[[13/10]]-[[14/13]].
-Equal temperaments with sinbadmic chords include {{EDOs| 29, 31, 43, 50, 53, 58, 72, 87, 103, 111, 130, 183, 190, 198, 270, 571, 590, 643, 860, 1130, 1431 and 1701 }}, with [[1701edo]] giving the [[optimal patent val]].
+Equal temperaments with sinbadmic chords include {{Optimal ET sequence| 29, 31, 43, 50, 53, 58, 72, 87, 103, 111, 130, 183, 190, 198, 270, 571, 590, 643, 860, 1130, 1431 and 1701 }}, with [[1701edo]] giving the [[optimal patent val]].
 The name is derived from the ''sinbadma'' (1001/1000), a [[comma]] that is reminiscent of the [[Wikipedia: One Thousand and One Nights|tales of 1001 Nights]].