19edo: Difference between revisions

Line 18:

=== As an approximation of other temperaments ===

The most salient characteristic of 19-et is that, having an almost just minor third and perfect fifths and major thirds about seven cents narrow, it serves as a good tuning for [[Meantone family|meantone]] temperament. It is also suitable for [[Regular Temperaments#magic|magic/muggles]] temperament, because five of its major thirds are equivalent to one of its ''twelfths.'' For all of these there are more optimal tunings: the fifth of 19-et is flatter than the usual for meantone, and a more accurate approximation is [[31edo|31 equal temperament]]. Similarly, the generating interval of magic temperament is a major third, and again 19-et's is flatter; [[41edo|41 equal temperament]] more closely matches it. It does make for a good tuning for muggles, which in 19et is the same as magic. 19edo's 7-step supermajor third can be used for [[sensi]], whose generator is a very sharp major third, two of which make an approximate 5/3 minor sixth, though [[46edo]] ~~is a~~ better sensi ~~tuning~~.

The most salient characteristic of 19-et is that, having an almost just minor third and perfect fifths and major thirds about seven cents narrow, it serves as a good tuning for [[Meantone family|meantone]] temperament. It is also suitable for [[Regular Temperaments#magic|magic/muggles]] temperament, because five of its major thirds are equivalent to one of its ''twelfths.'' For all of these there are more optimal tunings: the fifth of 19-et is flatter than the usual for meantone, and a more accurate approximation is [[31edo|31 equal temperament]]. Similarly, the generating interval of magic temperament is a major third, and again 19-et's is flatter; [[41edo|41 equal temperament]] more closely matches it. It does make for a good tuning for muggles, which in 19et is the same as magic. 19edo's 7-step supermajor third can be used for [[sensi]], whose generator is a very sharp major third, two of which make an approximate 5/3 minor sixth, though [[27edo]] and [[46edo]] are better sensi tunings.

However, for all of these 19-et has the practical advantage of requiring fewer pitches, which makes physical realizations of it easier to build. (Many 19-et instruments have been built.) 19-et is in fact the second equal temperament, after 12-et which is able to deal with [[Harmonic Limit|5-limit]] music in a tolerable manner, and is the fifth (after 12) [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta integral edo]]. It is less successful with [[7-limit]] (but still better than 12-et), as it eliminates the distinction between a septimal minor third ([[7/6]]), and a septimal whole tone ([[8/7]]). 19-EDO also has the advantage of being excellent for negri, keemun, godzilla, magic/muggles and triton/liese, and fairly decent for sensi. Keemun and Negri are of particular note for being very simple 7-limit temperaments, with their MOS scales in 19-EDO offering a great abundance of septimal tetrads. The [[Graham complexity]] of a 7-limit tetrad is 6 for keemun, 7 for negri, 8 for godzilla, 10 for meantone, 11 for triton, 12 for magic/muggles and 13 for sensi.

@@ Line 18: / Line 18: @@
 === As an approximation of other temperaments ===
-The most salient characteristic of 19-et is that, having an almost just minor third and perfect fifths and major thirds about seven cents narrow, it serves as a good tuning for [[Meantone family|meantone]] temperament. It is also suitable for [[Regular Temperaments#magic|magic/muggles]] temperament, because five of its major thirds are equivalent to one of its ''twelfths.'' For all of these there are more optimal tunings: the fifth of 19-et is flatter than the usual for meantone, and a more accurate approximation is [[31edo|31 equal temperament]]. Similarly, the generating interval of magic temperament is a major third, and again 19-et's is flatter; [[41edo|41 equal temperament]] more closely matches it. It does make for a good tuning for muggles, which in 19et is the same as magic. 19edo's 7-step supermajor third can be used for [[sensi]], whose generator is a very sharp major third, two of which make an approximate 5/3 minor sixth, though [[46edo]] is a better sensi tuning.
+The most salient characteristic of 19-et is that, having an almost just minor third and perfect fifths and major thirds about seven cents narrow, it serves as a good tuning for [[Meantone family|meantone]] temperament. It is also suitable for [[Regular Temperaments#magic|magic/muggles]] temperament, because five of its major thirds are equivalent to one of its ''twelfths.'' For all of these there are more optimal tunings: the fifth of 19-et is flatter than the usual for meantone, and a more accurate approximation is [[31edo|31 equal temperament]]. Similarly, the generating interval of magic temperament is a major third, and again 19-et's is flatter; [[41edo|41 equal temperament]] more closely matches it. It does make for a good tuning for muggles, which in 19et is the same as magic. 19edo's 7-step supermajor third can be used for [[sensi]], whose generator is a very sharp major third, two of which make an approximate 5/3 minor sixth, though [[27edo]] and [[46edo]] are better sensi tunings.
 However, for all of these 19-et has the practical advantage of requiring fewer pitches, which makes physical realizations of it easier to build. (Many 19-et instruments have been built.) 19-et is in fact the second equal temperament, after 12-et which is able to deal with [[Harmonic Limit|5-limit]] music in a tolerable manner, and is the fifth (after 12) [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta integral edo]]. It is less successful with [[7-limit]] (but still better than 12-et), as it eliminates the distinction between a septimal minor third ([[7/6]]), and a septimal whole tone ([[8/7]]). 19-EDO also has the advantage of being excellent for negri, keemun, godzilla, magic/muggles and triton/liese, and fairly decent for sensi. Keemun and Negri are of particular note for being very simple 7-limit temperaments, with their MOS scales in 19-EDO offering a great abundance of septimal tetrads. The [[Graham complexity]] of a 7-limit tetrad is 6 for keemun, 7 for negri, 8 for godzilla, 10 for meantone, 11 for triton, 12 for magic/muggles and 13 for sensi.