Sensamagic chords: Difference between revisions
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A '''sensamagic chord''' is an [[essentially tempered dyadic chord]] tempered by the sensamagic comma, [[245/243]]. | 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. | 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: | ||
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. | * 1-9/7-5/3 with steps of 9/7-9/7-6/5. | ||
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The other sensamagic triads are | The other sensamagic triads are | ||
* 1-7/6-9/7, with steps | * 1-7/6-9/7, with steps 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 | For sensamagic tetrads there are the following palindromes: | ||
* 1-7/6-9/7-3/2, with steps 7/6-10/9-7/6-4/3; | * 1-7/6-9/7-3/2, with steps 7/6-10/9-7/6-4/3; | ||
* 1-7/6-9/7-9/5 with steps 7/6-10/9-7/5-10/9. | * 1-7/6-9/7-9/5 with steps 7/6-10/9-7/5-10/9. | ||
And the following inversely related pairs: | |||
* 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. | |||
For pentads there are | 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. | * 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 | The [[9-odd-limit]] sensamagic chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 1a]], meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures. | ||
Equal temperaments with sensamagic chords include {{EDOs| 19, 22, 27, 41, 46, 65, 68, 87, 128, 196, 283 }}, with 283edo giving the [[optimal patent val]]. | Equal temperaments with sensamagic chords include {{EDOs| 19, 22, 27, 41, 46, 65, 68, 87, 128, 196, 283 }}, with 283edo giving the [[optimal patent val]]. | ||
Revision as of 15:50, 26 July 2023
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 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 the following palindromes:
- 1-7/6-9/7-3/2, with steps 7/6-10/9-7/6-4/3;
- 1-7/6-9/7-9/5 with steps 7/6-10/9-7/5-10/9.
And the following inversely related pairs:
- 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.
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 are of pattern 1a, meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures.
Equal temperaments with sensamagic chords include 19, 22, 27, 41, 46, 65, 68, 87, 128, 196, 283, with 283edo giving the optimal patent val.