Sinbadmic chords: Difference between revisions

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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,~~

They can be extended to following palindromic 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]].

[[Category:13-odd-limit]]

[[Category:13-odd-limit chords]]

[[Category:Essentially tempered chords]]

[[Category:Triads]]

[[Category:Tetrads]]

[[Category:Sinbadmic]]

@@ 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,
+They can be extended to following palindromic 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]].
-[[Category:13-odd-limit]]
+[[Category:13-odd-limit chords]]
 [[Category:Essentially tempered chords]]
 [[Category:Triads]]
 [[Category:Tetrads]]
 [[Category:Sinbadmic]]