Keemic chords: Difference between revisions

Line 1:

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|~~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.

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|~~keemun]], [[~~Superkleismic|~~superkleismic]], [[~~Porcupine|~~porcupine]] and [[~~Jubilismic_clan~~#x-Doublewide|doublewide]].

Other temperaments that feature this chord prominently include 11-limit [[keemun]], [[superkleismic]], [[porcupine]] and [[Jubilismic clan#x-Doublewide|doublewide]].

[[Category:11-limit]]

[[Category:~~chord~~]]

[[Category:Chords]]

[[Category:~~dyadic~~]]

[[Category:Dyadic]]

[[Category:~~magic~~]]

[[Category:Magic]]

[[Category:~~pentad~~]]

[[Category:Pentad]]

[[Category:~~todo~~:~~add_links~~]]

[[Category:Todo:add links]]

@@ Line 1: / Line 1: @@
 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&amp;7&amp;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&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|104edo]].) Hence [[Magic|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 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.
-Other temperaments that feature this chord prominently include 11-limit [[Keemun|keemun]], [[Superkleismic|superkleismic]], [[Porcupine|porcupine]] and [[Jubilismic_clan#x-Doublewide|doublewide]].
+Other temperaments that feature this chord prominently include 11-limit [[keemun]], [[superkleismic]], [[porcupine]] and [[Jubilismic clan#x-Doublewide|doublewide]].
 [[Category:11-limit]]
-[[Category:chord]]
+[[Category:Chords]]
-[[Category:dyadic]]
+[[Category:Dyadic]]
-[[Category:magic]]
+[[Category:Magic]]
-[[Category:pentad]]
+[[Category:Pentad]]
-[[Category:todo:add_links]]
+[[Category:Todo:add links]]