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.  
* 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
* 1–7/6–9/7, with steps 7/6, 10/9, 14/9, and its inversion
* 1-7/6-9/5, with steps 7/6-14/9-10/9.
* 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;  
* 1–7/6–9/7–3/2, 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:  
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  
* 1–7/6–3/2–9/5 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;  
* 1–9/7–3/2–5/3 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  
* 1–7/6–7/5–9/5 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.  
* 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,  
* 1–7/6–9/7–3/2–5/3 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.  
* 1–7/6–9/7–3/2–9/5 with steps 7/6, 10/9, 7/6, 6/5, 10/9.  


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 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]]