19edo: Difference between revisions
→Theory: link cent; better language |
m →Theory: grammar |
||
| (2 intermediate revisions by 2 users not shown) | |||
| Line 17: | Line 17: | ||
== Theory == | == 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. | 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 56: | Line 56: | ||
== Intervals == | == Intervals == | ||
{| class="wikitable right-1 right-2 | {| class="wikitable right-1 right-2" | ||
|- | |- | ||
! [[Degree|#]] | ! [[Degree|#]] | ||
! [[Cent]]s | ! [[Cent]]s | ||
! | ! [[Interval category|Interval categories]] | ||
! Approximated ratios<ref group="note">As a [[2.3.5.7.13 subgroup|2.3.5.7.13-subgroup]] temperament.</ref> | ! Approximated ratios<ref group="note">As a [[2.3.5.7.13 subgroup|2.3.5.7.13-subgroup]] temperament.</ref> | ||
|- | |- | ||
| Line 85: | Line 85: | ||
| 4 | | 4 | ||
| 252.6 | | 252.6 | ||
| Augmented second<br | | Augmented second<br>Diminished third | ||
| [[7/6]], [[8/7]], [[15/13]] | | [[7/6]], [[8/7]], [[15/13]] | ||
|- | |- | ||
| Line 956: | Line 956: | ||
| 23 | | 23 | ||
| [[70/69]] | | [[70/69]] | ||
| {{monzo| 1 -1 1 1 0 0 0 0 -}} | | {{monzo| 1 -1 1 1 0 0 0 0 -1 }} | ||
| 24.91 | | 24.91 | ||
| Twethuzoyo | | Twethuzoyo | ||
| Line 1,037: | Line 1,037: | ||
| M2 | | M2 | ||
| [[1L 5s]], [[6L 1s]], [[6L 7s]] | | [[1L 5s]], [[6L 1s]], [[6L 7s]] | ||
| [[Deutone]]<br>[[Spell]] | | [[Deutone]] <br>[[Xenial]] / [[Sensamagic clan #Xenia|Xenia]] <br>[[Spell]] | ||
|- | |- | ||
| 4 | | 4 | ||
| Line 1,043: | Line 1,043: | ||
| A2, d3 | | A2, d3 | ||
| [[1L 3s]], [[4L 1s]], <br>[[5L 4s]], [[5L 9s]] | | [[1L 3s]], [[4L 1s]], <br>[[5L 4s]], [[5L 9s]] | ||
| [[Godzilla]] | | [[Godzilla]] / [[Helayo]] | ||
|- | |- | ||
| 5 | | 5 | ||
| Line 1,073: | Line 1,073: | ||
| A4 | | A4 | ||
| [[2L 3s]], [[2L 5s]], [[2L 7s]], <br>[[2L 9s]], [[2L 11s]], [[2L 13s]], <br>[[2L 15s]] | | [[2L 3s]], [[2L 5s]], [[2L 7s]], <br>[[2L 9s]], [[2L 11s]], [[2L 13s]], <br>[[2L 15s]] | ||
| [[Liese]] | | [[Liese]] <br>[[Triton]] / [[pycnic]] | ||
|} | |} | ||