19edo: Difference between revisions
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== Theory == | == Theory == | ||
19edo can be understood as having distinct sharps and flats, rather than sharps and flats being enharmonic, and differs from 17edo in that its minor second is two steps while its chromatic semitone is one, better reflecting melodic intuition. | |||
=== As an approximation of other temperaments === | === As an approximation of other temperaments === | ||
Having an almost just minor third and perfect fifths and major thirds about 7 cents flat, 19edo serves as a good tuning for [[meantone]]. Unlike 12edo, where [[enharmonic]] notes are conflated, 19edo distinguishes them, and differs from [[17edo]] in that its [[diatonic semitone]] is wider than the [[chromatic semitone]], rather than narrower. In fact, it is nearly identical to the enharmonic scale of [[1/3-comma meantone]], and can be considered a closed form thereof. | Having an almost just minor third and perfect fifths and major thirds about 7 cents flat, 19edo serves as a good tuning for [[meantone]]. Unlike 12edo, where [[enharmonic]] notes are conflated, 19edo distinguishes them, and differs from [[17edo]] in that its [[diatonic semitone]] is wider than the [[chromatic semitone]], rather than narrower. In fact, it is nearly identical to the enharmonic scale of [[1/3-comma meantone]], and can be considered a closed form thereof. | ||
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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. Finally, [[46edo]] shows us a better sensi tuning. | 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. Finally, [[46edo]] shows us 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 in fact the second edo, after [[12edo]] which is able to approximate [[5-limit]] intervals and chords with tolerable accuracy (unless you count [[15edo]] | 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]], which has a 18c sharp fifth). 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]], and [[triton]]/[[liese]]. 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. | ||
=== As a means of extending harmony === | === As a means of extending harmony === | ||