Keemic chords: Difference between revisions

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A '''~~supermagic~~ chord''' is an [[11-odd-limit]] [[essentially tempered chord]] in the [[~~supermagic~~]] temperament. Since 100/99 is tempered out, [[ptolemismic chords]] are also ~~supermagic~~ chords; since 385/384 is tempered out, [[keenanismic chords]] are also ~~supermagic~~ chords. Aside from these, there are also essentially ~~supermagic~~ tempered chords.

A '''keemic chord''' is an [[11-odd-limit]] [[essentially tempered chord]] in the [[keemic]] temperament. Since [[100/99]] is [[tempering out|tempered out]], [[ptolemismic chords]] are also keemic chords; since [[385/384]] is tempered out, [[keenanismic chords]] are also keemic chords. Aside from these, there are also essentially keemic tempered chords.

The most basic of these is the '''magical seventh 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 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.

In an optimized tuning for the keemic 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]].

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* 1–12/11–6/5–3/2–7/4 with steps 12/11, 11/10, 5/4, 7/6, 8/7.

The count of ~~supermagic~~ chords is therefore tetrads: 4, and pentads: 4, for a total of 8.

The count of keemic chords is therefore tetrads: 4, and pentads: 4, for a total of 8.

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

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[[Category:Tetrads]]

[[Category:Pentads]]

[[Category:~~Supermagic~~]]

[[Category:Keemic]]

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-A '''supermagic chord''' is an [[11-odd-limit]] [[essentially tempered chord]] in the [[supermagic]] temperament. Since 100/99 is tempered out, [[ptolemismic chords]] are also supermagic chords; since 385/384 is tempered out, [[keenanismic chords]] are also supermagic chords. Aside from these, there are also essentially supermagic tempered chords.
+A '''keemic chord''' is an [[11-odd-limit]] [[essentially tempered chord]] in the [[keemic]] temperament. Since [[100/99]] is [[tempering out|tempered out]], [[ptolemismic chords]] are also keemic chords; since [[385/384]] is tempered out, [[keenanismic chords]] are also keemic chords. Aside from these, there are also essentially keemic tempered chords.
 The most basic of these is the '''magical seventh 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 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&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.
+In an optimized tuning for the keemic 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]].
@@ Line 19: / Line 19: @@
 * 1–12/11–6/5–3/2–7/4 with steps 12/11, 11/10, 5/4, 7/6, 8/7.
-The count of supermagic chords is therefore tetrads: 4, and pentads: 4, for a total of 8.
+The count of keemic chords is therefore tetrads: 4, and pentads: 4, for a total of 8.
 [[Category:11-odd-limit chords]]
@@ Line 25: / Line 25: @@
 [[Category:Tetrads]]
 [[Category:Pentads]]
-[[Category:Supermagic]]
+[[Category:Keemic]]