Sensamagic chords: Difference between revisions
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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: | 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. | ||
[[File:sensamagic.jpg|alt=sensamagic.jpg|thumb|Sensamagic triad]] | [[File:sensamagic.jpg|alt=sensamagic.jpg|thumb|Sensamagic triad]] | ||
The other sensamagic triads are | 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: | 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: | 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. | ||
Equal | [[Equal temperament]]s with sensamagic chords include {{EDOs| 19, 22, 27, 41, 46, 65, 68, 87, 128, 196, 283 }}, with 283edo giving the [[optimal patent val]]. | ||
== See also == | == See also == | ||
* [[Undecimal sensamagic chords]] | * [[Undecimal sensamagic chords]] | ||
[[Category:9-odd-limit]] | [[Category:9-odd-limit chords]] | ||
[[Category:Essentially tempered chords]] | [[Category:Essentially tempered chords]] | ||
[[Category:Triads]] | [[Category:Triads]] | ||