Sensamagic chords: Difference between revisions
Jump to navigation
Jump to search
→top: re-categorisation (AWB) |
Cleanup and readability improvements |
||
| Line 1: | Line 1: | ||
A ''sensamagic chord'' is an [[Dyadic chord#Essentially tempered dyadic chords|essentially tempered dyadic chord]] tempered by the sensamagic comma, 245/243 | A '''sensamagic chord''' is an [[Dyadic chord #Essentially tempered dyadic chords|essentially tempered dyadic chord]] tempered by the sensamagic comma, [[245/243]]. | ||
The sensamagic triad is a sensamagic chord with three notes when reduced to the octave. | |||
Sensamagic chords number triads: 3, tetrads: 6, pentads: 2, for a total of 11. | One of the sensamagic triads in close position consists of two supermajor thirds, approximately [[9/7]], and a minor third, approximately [[6/5]], which closes at the octave because the sensamagic comma, 245/243, is tempered out: | ||
* 1-9/7-5/3 with steps of 9/7-9/7-6/5. | |||
[[File:sensamagic.jpg|alt=sensamagic.jpg|thumb|Sensamagic triad]] | |||
The other sensamagic triads are | |||
* 1-7/6-9/7, with steps of 7/6-10/9-14/9, and its inversion 1-7/6-9/5, with steps 7/6-14/9-10/9. | |||
For sensamagic tetrads there are | |||
* 1-7/6-9/7-3/2, with steps 7/6-10/9-7/6-4/3; | |||
* 1-7/6-3/2-9/5 with steps 7/6-9/7-6/5-10/9 and its inversion 1-9/7-3/2-5/3 with steps 9/7-7/6-10/9-6/5; | |||
* 1-7/6-7/5-9/5 with steps 7/6-6/5-9/7-10/9 and its inversion 1-7/6-9/7-5/3 with steps 7/6-10/9-9/7-6/5; and | |||
* 1-7/6-9/7-9/5 with steps 7/6-10/9-7/5-10/9. | |||
For pentads there are | |||
* 1-7/6-9/7-3/2-5/3 with steps 7/6-10/9-7/6-10/9-6/5 and its inversion, 1-7/6-9/7-3/2-9/5 with steps 7/6-10/9-7/6-6/5-10/9. | |||
The [[9-odd-limit]] sensamagic chords number triads: 3, tetrads: 6, pentads: 2, for a total of 11. | |||
Equal temperaments with sensamagic chords include 19, 22, 27, 41, 46, 65, 68, 87, 128, 196, 283, 324d, 411bd, 607bd and 694bd. | Equal temperaments with sensamagic chords include 19, 22, 27, 41, 46, 65, 68, 87, 128, 196, 283, 324d, 411bd, 607bd and 694bd. | ||
[[Category:9-limit]] | [[Category:9-limit]] | ||
[[Category:Chords]] | [[Category:Chords]] | ||
[[Category:Dyadic]] | [[Category:Dyadic]] | ||
[[Category:Sensamagic]] | [[Category:Sensamagic]] | ||
[[Category:Triad]] | [[Category:Triad]] | ||
Revision as of 14:30, 16 April 2021
A sensamagic chord is an essentially tempered dyadic chord tempered by the sensamagic comma, 245/243.
The sensamagic triad is a sensamagic chord with three notes when reduced to the octave.
One of the sensamagic triads in close position consists of two supermajor thirds, approximately 9/7, and a minor third, approximately 6/5, which closes at the octave because the sensamagic comma, 245/243, is tempered out:
- 1-9/7-5/3 with steps of 9/7-9/7-6/5.
The other sensamagic triads are
- 1-7/6-9/7, with steps of 7/6-10/9-14/9, and its inversion 1-7/6-9/5, with steps 7/6-14/9-10/9.
For sensamagic tetrads there are
- 1-7/6-9/7-3/2, with steps 7/6-10/9-7/6-4/3;
- 1-7/6-3/2-9/5 with steps 7/6-9/7-6/5-10/9 and its inversion 1-9/7-3/2-5/3 with steps 9/7-7/6-10/9-6/5;
- 1-7/6-7/5-9/5 with steps 7/6-6/5-9/7-10/9 and its inversion 1-7/6-9/7-5/3 with steps 7/6-10/9-9/7-6/5; and
- 1-7/6-9/7-9/5 with steps 7/6-10/9-7/5-10/9.
For pentads there are
- 1-7/6-9/7-3/2-5/3 with steps 7/6-10/9-7/6-10/9-6/5 and its inversion, 1-7/6-9/7-3/2-9/5 with steps 7/6-10/9-7/6-6/5-10/9.
The 9-odd-limit sensamagic chords number triads: 3, tetrads: 6, pentads: 2, for a total of 11.
Equal temperaments with sensamagic chords include 19, 22, 27, 41, 46, 65, 68, 87, 128, 196, 283, 324d, 411bd, 607bd and 694bd.