Sinbadmic chords: Difference between revisions
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The triads are of the form | The triads are of the form | ||
* | * 1–[[7/5]]–[[20/13]], with steps of 7/5, [[11/10]], [[13/10]], | ||
and its inversion, | 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 {{ | 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]]. | 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:Essentially tempered chords]] | ||
[[Category:Triads]] | [[Category:Triads]] | ||
[[Category:Tetrads]] | [[Category:Tetrads]] | ||
[[Category:Sinbadmic]] | [[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.