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]]

Latest revision as of 14:13, 19 March 2025

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,

  • 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 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.

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