Keemic chords: Difference between revisions
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A ''magical seventh'' is an 11-limit essentially tempered dyadic chord consisting of three sharp minor thirds and an 8/7, in other words a 6/5-6/5-6/5-8/7 chord, which closes at the octave since both 100/99 and 385/384 (and therefore 875/864) are tempered out. This means that in the 11-limit 4&7&15 planar temperament tempering these out, the chord is the tempering of 1-6/5-16/11-7/4. | |||
In an optimized tuning for the 4&7&15 temperament, the marvel comma 225/224 shrinks in size and may reverse direction, and adding it to the list of commas does little tuning damage; this results in 11-limit magic temperament, which has the same optimal patent val ([[104edo]].) Hence [[magic]] (19&22) temperament is practically the most accurate temperament that include this chord. Magic, however, does give it a Graham complexity of 12, so it doesn't appear that often. | In an optimized tuning for the 4&7&15 temperament, the marvel comma 225/224 shrinks in size and may reverse direction, and adding it to the list of commas does little tuning damage; this results in 11-limit magic temperament, which has the same optimal patent val ([[104edo|104edo]].) Hence [[Magic|magic]] (19&22) temperament is practically the most accurate temperament that include this chord. Magic, however, does give it a Graham complexity of 12, so it doesn't appear that often. | ||
Other temperaments that feature this chord prominently include 11-limit [[Keemun|keemun]], [[Superkleismic|superkleismic]], [[Porcupine|porcupine]] and [[ | Other temperaments that feature this chord prominently include 11-limit [[Keemun|keemun]], [[Superkleismic|superkleismic]], [[Porcupine|porcupine]] and [[Jubilismic_clan#x-Doublewide|doublewide]]. | ||
[[Category:11-limit]] | |||
[[Category:chord]] | |||
[[Category:dyadic]] | |||
[[Category:magic]] | |||
[[Category:pentad]] | |||
[[Category:todo:add_links]] | |||
Revision as of 00:00, 17 July 2018
A magical seventh is an 11-limit essentially tempered dyadic chord consisting of three sharp minor thirds and an 8/7, in other words a 6/5-6/5-6/5-8/7 chord, which closes at the octave since both 100/99 and 385/384 (and therefore 875/864) are tempered out. This means that in the 11-limit 4&7&15 planar temperament tempering these out, the chord is the tempering of 1-6/5-16/11-7/4.
In an optimized tuning for the 4&7&15 temperament, the marvel comma 225/224 shrinks in size and may reverse direction, and adding it to the list of commas does little tuning damage; this results in 11-limit magic temperament, which has the same optimal patent val (104edo.) Hence magic (19&22) temperament is practically the most accurate temperament that include this chord. Magic, however, does give it a Graham complexity of 12, so it doesn't appear that often.
Other temperaments that feature this chord prominently include 11-limit keemun, superkleismic, porcupine and doublewide.