19edo: Difference between revisions

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== Theory ==

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

19edo's most salient characteristic is that, having an almost just minor third and perfect fifths and major thirds about seven cents flat, it serves as a good tuning for [[meantone]]. It is ~~also suitable for [[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 ~~19edo is flatter than the usual for meantone, and~~ [[~~31edo~~]] ~~is more optimal. Similarly, the generating interval of magic temperament is a major third~~, and ~~again 19edo's is flatter; [[41edo]] more closely matches it. It does make for a good tuning for muggles, but in 19edo it 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 major sixth, though [[46edo]] is~~ a ~~better sensi tuning~~.

19edo can be understood as having distinct sharps and flats, rather than sharps and flats being enhamronic, and differs from 17edo in that its minor second is two steps while its chromatic semitone is one, better reflecting melodic intuition. In terms of temperament, its most salient characteristic is that, having an almost just minor third and perfect fifths and major thirds about seven cents flat, it serves as a good tuning for [[meantone]]. In fact, it is nearly identical to the "enharmonic" scale of [[1/3-comma meantone]], and can be considered a closed form thereof.

However, for all of these 19edo has the practical advantage of requiring fewer pitches, which makes it easier to implement in physical instruments, and many 19edo instruments have been built. 19edo is ~~in fact~~ the ~~second~~ edo~~, after [[12edo]]~~ which is able to approximate [[5-limit~~]] intervals~~ and ~~chords with tolerable accuracy~~ (~~unless you count [[~~15edo]])~~, and is the fifth [[zeta integral edo]], after 12edo~~. It is less successful in the [[7-limit]] (but still better than 12edo), as it conflates the septimal subminor third ([[7/6]]) with the septimal whole tone ([[8/7]]). 19edo 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 scale]]s in 19edo 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~~.

However, one drawback is that it does not have a good approximation to the seventh harmonic, being too flat for septimal meantone (like [[31edo]]) and too sharp for flattone (like [[45edo]]). It is also suitable for [[magic]] temperament, because five of its major thirds are equivalent to one of its twelfths. It is also flat of the best tuning range for magic (like [[41edo]]), meaning it supports the alternative extension called "muggles", a kind of "flattone" for magic, which converges with septimal magic at 19edo.

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 major sixth, though [[46edo]] is a better sensi tuning.

However, for all of these 19edo has the practical advantage of requiring fewer pitches, which makes it easier to implement in physical instruments, and many 19edo instruments have been built.

19edo is the third edo which is able to accurately approximate the 5-limit after 12edo and 15edo (that is, assuming 15edo's error of 18 cents on 3/2 is acceptable). It is less successful in the [[7-limit]] (but still better than 12edo), as it conflates the septimal subminor third ([[7/6]]) with the septimal whole tone ([[8/7]]), which is called semaphore temperament.

19edo 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 scale]]s in 19edo offering a great abundance of septimal tetrads.

=== As a means of extending harmony ===

Because 19edo's 5-limit chords are more ~~blended and consonant~~ than those of 12edo, it can be a much better candidate for using alternate forms of harmony such as quartal, secundal, and poly chords. [[William Lynch]] suggests the use of seventh chords of various types to be the fundamental sonorities with a triad deemed as incomplete. Higher extensions involving the 7th harmonic as well as other non-diatonic chord extensions which tend to clash in 12edo blend much better in 19edo.

Because 19edo's 5-limit chords are more concordant than those of 12edo, it can be a much better candidate for using alternate forms of harmony such as quartal, secundal, and poly chords. [[William Lynch]] suggests the use of seventh chords of various types to be the fundamental sonorities with a triad deemed as incomplete. Higher extensions involving the 7th harmonic as well as other non-diatonic chord extensions which tend to clash in 12edo blend much better in 19edo.

In addition, [[Joseph Yasser]] talks about the idea of a 12-tone supra-diatonic scale where the 7-tone major scale in 19edo becomes akin to the pentatonic of western music; as it would sound to a future generation, ambiguous and not tonally fortified. As paraphrased "A system in which the undeniable laws of tonal gravity exist, yet in a much more complex tonal universe." Yasser believed that music would eventually move to a 19-tone system with a 12-note supra-diatonic scale would become the standard. While this has yet to happen, Yasser's concept of supra-diatonicity is intriguing and worth exploring for those wanting to extend tonality without sounding too alien.

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=== Adaptive tuning and octave stretch ===

~~Being a zeta integral tuning, the~~ no-11's 13-limit is represented relatively well and consistently. 19edo's negri, sensi and godzilla scales have many 13-limit chords. (You can think of the Sensi[8] [[3L 5s]] mos scale as 19edo's answer to the diminished scale. Both are made of two diminished seventh chords, but Sensi[8] gives you additional ratios of 7 and 13.) Its diminished fifth is also a very accurate approximation of the 23rd harmonic, being only 3.3{{c}} off [[23/16]].

The no-11's 13-limit is represented relatively well and consistently. 19edo's negri, sensi and godzilla scales have many 13-limit chords. (You can think of the Sensi[8] [[3L 5s]] mos scale as 19edo's answer to the diminished scale. Both are made of two diminished seventh chords, but Sensi[8] gives you additional ratios of 7 and 13.) Its diminished fifth is also a very accurate approximation of the 23rd harmonic, being only 3.3{{c}} off [[23/16]].

Practically 19edo can be used ''adaptively'' on instruments which allow you to bend notes up: by different amounts, the 3rd, 5th, 7th, and 13th harmonics are all tuned flat. This is in contrast to 12edo, where this is not possible since the 5th and 7th harmonics are not only much farther from just than they are in 19edo, but fairly sharp already.

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 == Theory ==
 === As an approximation of other temperaments ===
-edo's most salient characteristic is that, having an almost just minor third and perfect fifths and major thirds about seven cents flat, it serves as a good tuning for [[meantone]]. It is also suitable for [[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 19edo is flatter than the usual for meantone, and [[31edo]] is more optimal. Similarly, the generating interval of magic temperament is a major third, and again 19edo's is flatter; [[41edo]] more closely matches it. It does make for a good tuning for muggles, but in 19edo it 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 major sixth, though [[46edo]] is a better sensi tuning.
+edo can be understood as having distinct sharps and flats, rather than sharps and flats being enhamronic, and differs from 17edo in that its minor second is two steps while its chromatic semitone is one, better reflecting melodic intuition. In terms of temperament, its most salient characteristic is that, having an almost just minor third and perfect fifths and major thirds about seven cents flat, it serves as a good tuning for [[meantone]]. In fact, it is nearly identical to the "enharmonic" scale of [[1/3-comma meantone]], and can be considered a closed form thereof.
-However, for all of these 19edo has the practical advantage of requiring fewer pitches, which makes it easier to implement in physical instruments, and many 19edo instruments have been built. 19edo is in fact the second edo, after [[12edo]] which is able to approximate [[5-limit]] intervals and chords with tolerable accuracy (unless you count [[15edo]]), and is the fifth [[zeta integral edo]], after 12edo. It is less successful in the [[7-limit]] (but still better than 12edo), as it conflates the septimal subminor third ([[7/6]]) with the septimal whole tone ([[8/7]]). 19edo 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 scale]]s in 19edo 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.
+However, one drawback is that it does not have a good approximation to the seventh harmonic, being too flat for septimal meantone (like [[31edo]]) and too sharp for flattone (like [[45edo]]). It is also suitable for [[magic]] temperament, because five of its major thirds are equivalent to one of its twelfths. It is also flat of the best tuning range for magic (like [[41edo]]), meaning it supports the alternative extension called "muggles", a kind of "flattone" for magic, which converges with septimal magic at 19edo.
+edo'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 major sixth, though [[46edo]] is a better sensi tuning.
+However, for all of these 19edo has the practical advantage of requiring fewer pitches, which makes it easier to implement in physical instruments, and many 19edo instruments have been built.
+edo is the third edo which is able to accurately approximate the 5-limit after 12edo and 15edo (that is, assuming 15edo's error of 18 cents on 3/2 is acceptable). It is less successful in the [[7-limit]] (but still better than 12edo), as it conflates the septimal subminor third ([[7/6]]) with the septimal whole tone ([[8/7]]), which is called semaphore temperament.
+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 scale]]s in 19edo offering a great abundance of septimal tetrads.
 === As a means of extending harmony ===
-Because 19edo's 5-limit chords are more blended and consonant than those of 12edo, it can be a much better candidate for using alternate forms of harmony such as quartal, secundal, and poly chords. [[William Lynch]] suggests the use of seventh chords of various types to be the fundamental sonorities with a triad deemed as incomplete. Higher extensions involving the 7th harmonic as well as other non-diatonic chord extensions which tend to clash in 12edo blend much better in 19edo.
+Because 19edo's 5-limit chords are more concordant than those of 12edo, it can be a much better candidate for using alternate forms of harmony such as quartal, secundal, and poly chords. [[William Lynch]] suggests the use of seventh chords of various types to be the fundamental sonorities with a triad deemed as incomplete. Higher extensions involving the 7th harmonic as well as other non-diatonic chord extensions which tend to clash in 12edo blend much better in 19edo.
 In addition, [[Joseph Yasser]] talks about the idea of a 12-tone supra-diatonic scale where the 7-tone major scale in 19edo becomes akin to the pentatonic of western music; as it would sound to a future generation, ambiguous and not tonally fortified. As paraphrased "A system in which the undeniable laws of tonal gravity exist, yet in a much more complex tonal universe." Yasser believed that music would eventually move to a 19-tone system with a 12-note supra-diatonic scale would become the standard. While this has yet to happen, Yasser's concept of supra-diatonicity is intriguing and worth exploring for those wanting to extend tonality without sounding too alien.
@@ Line 34: / Line 42: @@
 === Adaptive tuning and octave stretch ===
-Being a zeta integral tuning, the no-11's 13-limit is represented relatively well and consistently. 19edo's negri, sensi and godzilla scales have many 13-limit chords. (You can think of the Sensi[8] [[3L&nbsp;5s]] mos scale as 19edo's answer to the diminished scale. Both are made of two diminished seventh chords, but Sensi[8] gives you additional ratios of 7 and 13.) Its diminished fifth is also a very accurate approximation of the 23rd harmonic, being only 3.3{{c}} off [[23/16]].
+The no-11's 13-limit is represented relatively well and consistently. 19edo's negri, sensi and godzilla scales have many 13-limit chords. (You can think of the Sensi[8] [[3L&nbsp;5s]] mos scale as 19edo's answer to the diminished scale. Both are made of two diminished seventh chords, but Sensi[8] gives you additional ratios of 7 and 13.) Its diminished fifth is also a very accurate approximation of the 23rd harmonic, being only 3.3{{c}} off [[23/16]].
 Practically 19edo can be used ''adaptively'' on instruments which allow you to bend notes up: by different amounts, the 3rd, 5th, 7th, and 13th harmonics are all tuned flat. This is in contrast to 12edo, where this is not possible since the 5th and 7th harmonics are not only much farther from just than they are in 19edo, but fairly sharp already.