Chords of superpyth: Difference between revisions
slight expansion, still far from complete |
added the tables |
||
| Line 2: | Line 2: | ||
Below are listed the [[Dyadic_chord|dyadic chords]] of 11-limit [[superpyth]] temperament. Typing the chords requires consideration of the fact that superpyth conflates [[9/8]] with [[8/7]], and [[11/10]] with [[10/9]]. If a transversal can be found which shows the chord to be essentially just, that transversal is listed along with a typing as otonal, utonal, or ambitonal. If the chord is essentially tempered, it is analyzed in terms of the transversal that employs 8/7 and 10/9. | Below are listed the [[Dyadic_chord|dyadic chords]] of 11-limit [[superpyth]] temperament. Typing the chords requires consideration of the fact that superpyth conflates [[9/8]] with [[8/7]], and [[11/10]] with [[10/9]]. If a transversal can be found which shows the chord to be essentially just, that transversal is listed along with a typing as otonal, utonal, or ambitonal. If the chord is essentially tempered, it is analyzed in terms of the transversal that employs 8/7 and 10/9. | ||
Chords essentially tempered by [[64/63]] are labeled archytas, by [[100/99]] ptolemismic, by [[176/175]] by [[245/243]] sensamagic, etc., (Todo: Complete essential tempering types | Chords essentially tempered by [[64/63]] are labeled archytas, by [[100/99]] ptolemismic, by [[176/175]] by [[245/243]] sensamagic, etc., (Todo: Complete essential tempering types) | ||
== Triads == | == Triads == | ||
{| class="wikitable" | |||
|+ | |||
|- | |||
! # | |||
! Transversal | |||
! Type | |||
|- | |||
|1 | |||
|1/1-3/2-9/8 | |||
|ambitonal | |||
|- | |||
|2 | |||
|1/1-3/2-12/7 | |||
|utonal | |||
|- | |||
|3 | |||
|1/1-8/7-12/7 | |||
|otonal | |||
|- | |||
| | |||
|1/1-3/2-9/7 | |||
| | |||
|- | |||
| | |||
|1/1-8/7-9/7 | |||
| | |||
|- | |||
| | |||
|1/1-12/7-9/7 | |||
| | |||
|- | |||
| | |||
|1/1-12/7-10/9 | |||
| | |||
|- | |||
| | |||
|1/1-9/7-10/9 | |||
| | |||
|- | |||
| | |||
|1/1-3/2-5/3 | |||
| | |||
|- | |||
| | |||
|1/1-9/7-5/3 | |||
| | |||
|- | |||
| | |||
|1/1-10/9-5/3 | |||
| | |||
|- | |||
| | |||
|1/1-3/2-5/4 | |||
| | |||
|- | |||
| | |||
|1/1-8/7-5/4 | |||
| | |||
|- | |||
| | |||
|1/1-10/9-5/4 | |||
| | |||
|- | |||
| | |||
|1/1-5/3-5/4 | |||
| | |||
|- | |||
| | |||
|1/1-8/7-10/7 | |||
| | |||
|- | |||
| | |||
|1/1-12/7-10/7 | |||
| | |||
|- | |||
| | |||
|1/1-9/7-10/7 | |||
| | |||
|- | |||
| | |||
|1/1-10/9-10/7 | |||
| | |||
|- | |||
| | |||
|1/1-5/3-10/7 | |||
| | |||
|- | |||
| | |||
|1/1-5/4-10/7 | |||
| | |||
|- | |||
| | |||
|1/1-12/7-11/9 | |||
| | |||
|- | |||
| | |||
|1/1-10/9-11/9 | |||
| | |||
|- | |||
| | |||
|1/1-10/7-11/9 | |||
| | |||
|- | |||
| | |||
|1/1-3/2-11/6 | |||
| | |||
|- | |||
| | |||
|1/1-9/7-11/6 | |||
| | |||
|- | |||
| | |||
|1/1-10/9-11/6 | |||
| | |||
|- | |||
| | |||
|1/1-5/3-11/6 | |||
| | |||
|- | |||
| | |||
|1/1-10/7-11/6 | |||
| | |||
|- | |||
| | |||
|1/1-11/9-11/6 | |||
| | |||
|- | |||
| | |||
|1/1-3/2-11/8 | |||
| | |||
|- | |||
| | |||
|1/1-8/7-11/8 | |||
| | |||
|- | |||
| | |||
|1/1-10/9-11/8 | |||
| | |||
|- | |||
| | |||
|1/1-5/3-11/8 | |||
| | |||
|- | |||
| | |||
|1/1-5/4-11/8 | |||
| | |||
|- | |||
| | |||
|1/1-11/9-11/8 | |||
| | |||
|- | |||
| | |||
|1/1-11/6-11/8 | |||
| | |||
|- | |||
| | |||
|1/1-8/7-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-12/7-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-9/7-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-10/9-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-5/4-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-10/7-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-11/9-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-11/6-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-11/8-11/7 | |||
| | |||
|} | |||
== Tetrads == | |||
{| class="wikitable" | |||
|+ | |||
|- | |||
! # | |||
! Transversal | |||
! Type | |||
|- | |||
| | |||
|1/1-3/2-8/7-12/7 | |||
| | |||
|- | |||
| | |||
|1/1-3/2-8/7-9/7 | |||
| | |||
|- | |||
| | |||
|1/1-3/2-12/7-9/7 | |||
| | |||
|- | |||
| | |||
|1/1-8/7-12/7-9/7 | |||
| | |||
|- | |||
| | |||
|1/1-12/7-9/7-10/9 | |||
| | |||
|- | |||
| | |||
|1/1-3/2-9/7-5/3 | |||
| | |||
|- | |||
| | |||
|1/1-9/7-10/9-5/3 | |||
| | |||
|- | |||
| | |||
|1/1-3/2-8/7-5/4 | |||
| | |||
|- | |||
| | |||
|1/1-3/2-5/3-5/4 | |||
| | |||
|- | |||
| | |||
|1/1-10/9-5/3-5/4 | |||
| | |||
|- | |||
| | |||
|1/1-8/7-12/7-10/7 | |||
| | |||
|- | |||
| | |||
|1/1-8/7-9/7-10/7 | |||
| | |||
|- | |||
| | |||
|1/1-12/7-9/7-10/7 | |||
| | |||
|- | |||
| | |||
|1/1-12/7-10/9-10/7 | |||
| | |||
|- | |||
| | |||
|1/1-9/7-10/9-10/7 | |||
| | |||
|- | |||
| | |||
|1/1-9/7-5/3-10/7 | |||
| | |||
|- | |||
| | |||
|1/1-10/9-5/3-10/7 | |||
| | |||
|- | |||
| | |||
|1/1-8/7-5/4-10/7 | |||
| | |||
|- | |||
| | |||
|1/1-10/9-5/4-10/7 | |||
| | |||
|- | |||
| | |||
|1/1-5/3-5/4-10/7 | |||
| | |||
|- | |||
| | |||
|1/1-12/7-10/9-11/9 | |||
| | |||
|- | |||
| | |||
|1/1-12/7-10/7-11/9 | |||
| | |||
|- | |||
| | |||
|1/1-10/9-10/7-11/9 | |||
| | |||
|- | |||
| | |||
|1/1-3/2-9/7-11/6 | |||
| | |||
|- | |||
| | |||
|1/1-9/7-10/9-11/6 | |||
| | |||
|- | |||
| | |||
|1/1-3/2-5/3-11/6 | |||
| | |||
|- | |||
| | |||
|1/1-9/7-5/3-11/6 | |||
| | |||
|- | |||
| | |||
|1/1-10/9-5/3-11/6 | |||
| | |||
|- | |||
| | |||
|1/1-9/7-10/7-11/6 | |||
| | |||
|- | |||
| | |||
|1/1-10/9-10/7-11/6 | |||
| | |||
|- | |||
| | |||
|1/1-5/3-10/7-11/6 | |||
| | |||
|- | |||
| | |||
|1/1-10/9-11/9-11/6 | |||
| | |||
|- | |||
| | |||
|1/1-10/7-11/9-11/6 | |||
| | |||
|- | |||
| | |||
|1/1-3/2-8/7-11/8 | |||
| | |||
|- | |||
| | |||
|1/1-3/2-5/3-11/8 | |||
| | |||
|- | |||
| | |||
|1/1-10/9-5/3-11/8 | |||
| | |||
|- | |||
| | |||
|1/1-3/2-5/4-11/8 | |||
| | |||
|- | |||
| | |||
|1/1-8/7-5/4-11/8 | |||
| | |||
|- | |||
| | |||
|1/1-10/9-5/4-11/8 | |||
| | |||
|- | |||
| | |||
|1/1-5/3-5/4-11/8 | |||
| | |||
|- | |||
| | |||
|1/1-10/9-11/9-11/8 | |||
| | |||
|- | |||
| | |||
|1/1-3/2-11/6-11/8 | |||
| | |||
|- | |||
| | |||
|1/1-10/9-11/6-11/8 | |||
| | |||
|- | |||
| | |||
|1/1-5/3-11/6-11/8 | |||
| | |||
|- | |||
| | |||
|1/1-11/9-11/6-11/8 | |||
| | |||
|- | |||
| | |||
|1/1-8/7-12/7-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-8/7-9/7-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-12/7-9/7-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-12/7-10/9-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-9/7-10/9-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-8/7-5/4-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-10/9-5/4-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-8/7-10/7-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-12/7-10/7-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-9/7-10/7-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-10/9-10/7-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-5/4-10/7-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-12/7-11/9-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-10/9-11/9-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-10/7-11/9-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-9/7-11/6-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-10/9-11/6-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-10/7-11/6-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-11/9-11/6-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-8/7-11/8-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-10/9-11/8-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-5/4-11/8-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-11/9-11/8-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-11/6-11/8-11/7 | |||
| | |||
|} | |||
== Pentads == | |||
{| class="wikitable" | |||
|+ | |||
|- | |||
! # | |||
! Transversal | |||
! Type | |||
|- | |||
| | |||
|1/1-3/2-8/7-12/7-9/7 | |||
| | |||
|- | |||
| | |||
|1/1-8/7-12/7-9/7-10/7 | |||
| | |||
|- | |||
| | |||
|1/1-12/7-9/7-10/9-10/7 | |||
| | |||
|- | |||
| | |||
|1/1-9/7-10/9-5/3-10/7 | |||
| | |||
|- | |||
| | |||
|1/1-10/9-5/3-5/4-10/7 | |||
| | |||
|- | |||
| | |||
|1/1-12/7-10/9-10/7-11/9 | |||
| | |||
|- | |||
| | |||
|1/1-3/2-9/7-5/3-11/6 | |||
| | |||
|- | |||
| | |||
|1/1-9/7-10/9-5/3-11/6 | |||
| | |||
|- | |||
| | |||
|1/1-9/7-10/9-10/7-11/6 | |||
| | |||
|- | |||
| | |||
|1/1-9/7-5/3-10/7-11/6 | |||
| | |||
|- | |||
| | |||
|1/1-10/9-5/3-10/7-11/6 | |||
| | |||
|- | |||
| | |||
|1/1-10/9-10/7-11/9-11/6 | |||
| | |||
|- | |||
| | |||
|1/1-3/2-8/7-5/4-11/8 | |||
| | |||
|- | |||
| | |||
|1/1-3/2-5/3-5/4-11/8 | |||
| | |||
|- | |||
| | |||
|1/1-10/9-5/3-5/4-11/8 | |||
| | |||
|- | |||
| | |||
|1/1-3/2-5/3-11/6-11/8 | |||
| | |||
|- | |||
| | |||
|1/1-10/9-5/3-11/6-11/8 | |||
| | |||
|- | |||
| | |||
|1/1-10/9-11/9-11/6-11/8 | |||
| | |||
|- | |||
| | |||
|1/1-8/7-12/7-9/7-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-12/7-9/7-10/9-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-8/7-12/7-10/7-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-8/7-9/7-10/7-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-12/7-9/7-10/7-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-12/7-10/9-10/7-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-9/7-10/9-10/7-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-8/7-5/4-10/7-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-10/9-5/4-10/7-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-12/7-10/9-11/9-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-12/7-10/7-11/9-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-10/9-10/7-11/9-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-9/7-10/9-11/6-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-9/7-10/7-11/6-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-10/9-10/7-11/6-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-10/9-11/9-11/6-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-10/7-11/9-11/6-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-8/7-5/4-11/8-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-10/9-5/4-11/8-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-10/9-11/9-11/8-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-10/9-11/6-11/8-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-11/9-11/6-11/8-11/7 | |||
| | |||
|} | |||
== Hexads == | |||
{| class="wikitable" | |||
|+ | |||
|- | |||
! # | |||
! Transversal | |||
! Type | |||
|- | |||
| | |||
|1/1-9/7-10/9-5/3-10/7-11/6 | |||
| | |||
|- | |||
| | |||
|1/1-8/7-12/7-9/7-10/7-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-12/7-9/7-10/9-10/7-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-12/7-10/9-10/7-11/9-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-9/7-10/9-10/7-11/6-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-10/9-10/7-11/9-11/6-11/7 | |||
| | |||
|- | |||
| | |||
|1/1-10/9-11/9-11/6-11/8-11/7 | |||
| | |||
|} | |||