Sinbadmic chords: Difference between revisions

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~~The~~ '''sinbadmic ~~tetrad~~''' is a [[13-limit]] 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 ~~name is derived from~~ the ~~''sinbadma'' (~~[[~~1001~~/~~1000~~]]~~), a~~ [[~~comma~~]] ~~that is reminiscent~~ of ~~the~~ [~~https:~~//~~en.wikipedia.org/wiki/One_Thousand_and_One_Nights tales of 1001 Nights~~]

The triads are of the form

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

[[Category:~~Tetrad~~]]

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]]

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-The '''sinbadmic tetrad''' is a [[13-limit]] 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 name is derived from the ''sinbadma'' ([[1001/1000]]), a [[comma]] that is reminiscent of the [https://en.wikipedia.org/wiki/One_Thousand_and_One_Nights tales of 1001 Nights]
+The triads are of the form
+* 1–[[7/5]]–[[20/13]], with steps of 7/5, [[11/10]], [[13/10]],
-[[Category:Tetrad]]
+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]]