19edo: Difference between revisions

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== Theory ==

19edo is 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 18-[[cent]]-sharp fifth). Having an almost just minor third and perfect fifths and major thirds about 7 cents flat, it 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.

19edo is 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 18-[[cent]]-sharp fifth). Having an almost just minor third and perfect fifths and major thirds about 7 cents flat, it 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.

It is less successful in the [[7-limit]] as it conflates the septimal subminor third ([[7/6]]) with the septimal whole tone ([[8/7]]), but it is still better than 12edo overall.

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| 23

| [[70/69]]

| {{monzo| 1 -1 1 1 0 0 0 0 -}}

| {{monzo| 1 -1 1 1 0 0 0 0 -1 }}

| 24.91

| Twethuzoyo

Line 1,037:

| M2

| [[1L 5s]], [[6L 1s]], [[6L 7s]]

| [[Deutone]] [[Spell]]

| [[Deutone]] [[Xenial]] / [[Sensamagic clan #Xenia|Xenia]] [[Spell]]

|-

| 4

Line 1,043:

| A2, d3

| [[1L 3s]], [[4L 1s]], [[5L 4s]], [[5L 9s]]

| [[Godzilla]]

| [[Godzilla]] / [[Helayo]]

|-

| 5

Line 1,073:

| A4

| [[2L 3s]], [[2L 5s]], [[2L 7s]], [[2L 9s]], [[2L 11s]], [[2L 13s]], [[2L 15s]]

| [[Liese]] / [[~~pycnic~~]]~~ ~~[[~~Triton~~]]

| [[Liese]] [[Triton]] / [[pycnic]]

|}

@@ Line 17: / Line 17: @@
 == Theory ==
-edo is 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 18-[[cent]]-sharp fifth). Having an almost just minor third and perfect fifths and major thirds about 7 cents flat, it 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.
+edo is 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 18-[[cent]]-sharp fifth). Having an almost just minor third and perfect fifths and major thirds about 7 cents flat, it 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.
 It is less successful in the [[7-limit]] as it conflates the septimal subminor third ([[7/6]]) with the septimal whole tone ([[8/7]]), but it is still better than 12edo overall.
@@ Line 956: / Line 956: @@
 | 23
 | [[70/69]]
-| {{monzo| 1 -1 1 1 0 0 0 0 -}}
+| {{monzo| 1 -1 1 1 0 0 0 0 -1 }}
 | 24.91
 | Twethuzoyo
@@ Line 1,037: / Line 1,037: @@
 | M2
 | [[1L&nbsp;5s]], [[6L&nbsp;1s]], [[6L&nbsp;7s]]
-| [[Deutone]]<br>[[Spell]]
+| [[Deutone]] <br>[[Xenial]] / [[Sensamagic clan #Xenia|Xenia]] <br>[[Spell]]
 |-
 | 4
@@ Line 1,043: / Line 1,043: @@
 | A2, d3
 | [[1L&nbsp;3s]], [[4L&nbsp;1s]], <br>[[5L&nbsp;4s]], [[5L&nbsp;9s]]
-| [[Godzilla]]
+| [[Godzilla]] / [[Helayo]]
 |-
 | 5
@@ Line 1,073: / Line 1,073: @@
 | A4
 | [[2L&nbsp;3s]], [[2L&nbsp;5s]], [[2L&nbsp;7s]], <br>[[2L&nbsp;9s]], [[2L&nbsp;11s]], [[2L&nbsp;13s]], <br>[[2L&nbsp;15s]]
-| [[Liese]] / [[pycnic]]<br>[[Triton]]
+| [[Liese]] <br>[[Triton]] / [[pycnic]]
 |}