Keemic chords: Difference between revisions
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A '''magical seventh''' is an [[11-limit]] [[essentially tempered dyadic chord]] consisting of three sharp [[6/5|minor thirds]] and | A '''magical seventh''' is an [[11-limit]] [[essentially tempered dyadic chord]] consisting of three sharp [[6/5|classical minor thirds]] and a [[8/7|septimal whole tone]], 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 [[supermagic]] [[planar temperament]] tempering these out, the chord is the tempering of | ||
* 1–6/5–16/11–7/4, with steps 6/5, 6/5, 6/5, 8/7. | |||
In an optimized tuning for the | In an optimized tuning for the supermagic 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 does not 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]]. | ||
[[Category:11-odd-limit]] | [[Category:11-odd-limit chords]] | ||
[[Category:Essentially tempered chords]] | [[Category:Essentially tempered chords]] | ||
[[Category: | [[Category:Tetrads]] | ||
[[Category:Supermagic]] | [[Category:Supermagic]] | ||
Revision as of 13:11, 17 October 2024
A magical seventh is an 11-limit essentially tempered dyadic chord consisting of three sharp classical minor thirds and a septimal whole tone, 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 supermagic planar temperament tempering these out, the chord is the tempering of
- 1–6/5–16/11–7/4, with steps 6/5, 6/5, 6/5, 8/7.
In an optimized tuning for the supermagic 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 does not appear that often.
Other temperaments that feature this chord prominently include 11-limit keemun, superkleismic, porcupine and doublewide.