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 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.

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 ~~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 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]].

[[Category:11-odd-limit]]

[[Category:11-odd-limit chords]]

[[Category:Essentially tempered chords]]

[[Category:~~Pentads~~]]

[[Category:Tetrads]]

[[Category:Supermagic]]

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-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&amp;7&amp;15 [[Planar temperaments|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|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 4&amp;7&amp;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&amp;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 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&amp;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]].
-[[Category:11-odd-limit]]
+[[Category:11-odd-limit chords]]
 [[Category:Essentially tempered chords]]
-[[Category:Pentads]]
+[[Category:Tetrads]]
 [[Category:Supermagic]]