Sinbadmic chords: Difference between revisions

(9 intermediate revisions by 3 users not shown)

Line 1:

~~The~~ sinbadmic ~~tetrad~~ is a 13-limit [[~~Dyadic_chord|~~essentially tempered dyadic chord]] which is a 1001/1000 (~~sinbadmic~~) ~~tempered 1-~~11/10-13/10-10/7 ~~in one voicing, which has~~ steps of 11/10-13/11-11/10-7/5. Equal temperaments with sinbadmic ~~tetrads~~ 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.

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

The triads are of the form

* 1–[[7/5]]–[[20/13]], with steps of 7/5, [[11/10]], [[13/10]],

and its inversion,

* 1–7/5–[[20/11]], with steps of 7/5, 13/10, 11/10.

They can be extended to following palindromic tetrads:

* 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 {{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 chords]]

[[Category:Essentially tempered chords]]

[[Category:Triads]]

[[Category:Tetrads]]

[[Category:Sinbadmic]]

@@ Line 1: / Line 1: @@
-The sinbadmic tetrad is a 13-limit [[Dyadic_chord|essentially tempered dyadic chord]] which is a 1001/1000 (sinbadmic) tempered 1-11/10-13/10-10/7 in one voicing, which has steps of 11/10-13/11-11/10-7/5. Equal temperaments with sinbadmic tetrads 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.
+A '''sinbadmic chord''' is a [[13-limit]] [[essentially tempered dyadic chord]] which is tempered by [[1001/1000]] (sinbadma).
+The triads are of the form
+* 1–[[7/5]]–[[20/13]], with steps of 7/5, [[11/10]], [[13/10]],
+and its inversion,
+* 1–7/5–[[20/11]], with steps of 7/5, 13/10, 11/10.
+They can be extended to following palindromic tetrads:
+* 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 {{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 chords]]
+[[Category:Essentially tempered chords]]
+[[Category:Triads]]
+[[Category:Tetrads]]
+[[Category:Sinbadmic]]