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. | A ''magical seventh'' is an [[11-limit]], [[essentially tempered dyadic chord]] consisting of three sharp [[6/5|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 [[Tempering out|tempered out]]. This means that in the 11-limit 4&7&15 [[Planar temperaments|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]].) 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]]. | Other temperaments that feature this chord prominently include 11-limit [[keemun]], [[superkleismic]], [[porcupine]] and [[doublewide]]. | ||
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[[Category:Magic]] | [[Category:Magic]] | ||
[[Category:Pentad]] | [[Category:Pentad]] | ||
Revision as of 07:28, 20 April 2023
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.