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 [[29edo]], [[31edo]], [[43edo]], [[50edo]], [[53edo]], [[58edo]], [[72edo]], 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 [[7/5]]-[[11/10]]-[[13/10]],

and its inversion,

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

It leads to a tetrad,

* 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 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]].

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:Essentially tempered chords]]

[[Category:Triad]]

[[Category:Tetrad]]

[[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 [[29edo]], [[31edo]], [[43edo]], [[50edo]], [[53edo]], [[58edo]], [[72edo]], 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 [[7/5]]-[[11/10]]-[[13/10]],
+and its inversion,
+* 1-[[7/5]]-[[20/11]], with steps [[7/5]]-[[13/10]]-[[11/10]].
+It leads to a tetrad,
+* 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 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]].
+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:Essentially tempered chords]]
+[[Category:Triad]]
 [[Category:Tetrad]]
+[[Category:Sinbadmic]]