24edo: Difference between revisions
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| rowspan="2" |minor | | rowspan="2" |minor | ||
| fourthward wa | | fourthward wa | ||
| style="white-space: nowrap;" | (a, b), b < | | style="white-space: nowrap;" | (a, b), b < −1 | ||
| 32/27, 16/9 | | 32/27, 16/9 | ||
|- | |- | ||
| gu | | gu | ||
| style="white-space: nowrap;" | (a, b, | | style="white-space: nowrap;" | (a, b, −1) | ||
| 6/5, 9/5 | | 6/5, 9/5 | ||
|- | |- | ||
| Line 350: | Line 350: | ||
|- | |- | ||
| lu | | lu | ||
| style="white-space: nowrap;" | (a, b, 0, 0, | | style="white-space: nowrap;" | (a, b, 0, 0, −1) | ||
| 12/11, 18/11 | | 12/11, 18/11 | ||
|- | |- | ||
| Line 364: | Line 364: | ||
| upmajor | | upmajor | ||
| ru | | ru | ||
| style="white-space: nowrap;" | (a, b, 0, | | style="white-space: nowrap;" | (a, b, 0, −1) | ||
| 9/7, 12/7 | | 9/7, 12/7 | ||
|} | |} | ||
| Line 370: | Line 370: | ||
Ups and downs notation can be used to name chords. See [[24edo Chord Names]] and [[Ups and Downs Notation #Chords and Chord Progressions]]. | Ups and downs notation can be used to name chords. See [[24edo Chord Names]] and [[Ups and Downs Notation #Chords and Chord Progressions]]. | ||
===William Lynch's notation=== | === William Lynch's notation === | ||
24edo breaks intervals into two sets of five categories. {{dash|Infra, Minor, Neutral, Major, Ultra| | 24edo breaks intervals into two sets of five categories. {{dash|Infra, Minor, Neutral, Major, Ultra|space|med}} for seconds, thirds, sixths, and sevenths; and {{dash|diminished, narrow, perfect, wide, augmented|space|med}} for fourths, fifths, unison, and octave. | ||
For other strange enharmonics, wide and narrow can be used in conjunction with augmented and diminished intervals such as 550 cents being called a narrow diminished fifth and 850 cents being called a wide augmented fifth. | For other strange enharmonics, wide and narrow can be used in conjunction with augmented and diminished intervals such as 550 cents being called a narrow diminished fifth and 850 cents being called a wide augmented fifth. | ||
| Line 446: | Line 446: | ||
* Arto Sub Seventh Tendo Thirteenth or artsub7^13 = Arto tetrad with an arto seventh and a tendo thirteenth on top Minor Seventh Flat Five Arto Ninth Super Eleventh or m7b5^9^11 | * Arto Sub Seventh Tendo Thirteenth or artsub7^13 = Arto tetrad with an arto seventh and a tendo thirteenth on top Minor Seventh Flat Five Arto Ninth Super Eleventh or m7b5^9^11 | ||
===Quartertone accidentals=== | === Quartertone accidentals === | ||
Besides ups and downs, there are various systems for notating quarter tones. Here are some of them, along with their pros and cons. | Besides ups and downs, there are various systems for notating quarter tones. Here are some of them, along with their pros and cons. | ||
====Mainstream quartertone notation==== | ==== Mainstream quartertone notation ==== | ||
[[Category:IMPORTDEBUG - Change External Images]] | [[Category:IMPORTDEBUG - Change External Images]] | ||
{{Sharpness-sharp2|24}} | {{Sharpness-sharp2|24}} | ||
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! rowspan="2" | [[Comma list]] | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal<br>8ve stretch (¢) | ! rowspan="2" | Optimal<br />8ve stretch (¢) | ||
! colspan="2" | Tuning error | ! colspan="2" | Tuning error | ||
|- | |- | ||
| Line 529: | Line 529: | ||
| 2.3.5.11 | | 2.3.5.11 | ||
| 81/80, 121/120, 128/125 | | 81/80, 121/120, 128/125 | ||
|{{mapping| 24 38 56 83 }} | | {{mapping| 24 38 56 83 }} | ||
| | | −1.08 | ||
| 2.82 | | 2.82 | ||
| 5.63 | | 5.63 | ||
| Line 536: | Line 536: | ||
| 2.3.5.11.13 | | 2.3.5.11.13 | ||
| 66/65, 81/80, 128/125, 144/143 | | 66/65, 81/80, 128/125, 144/143 | ||
|{{mapping| 24 38 56 83 89 }} | | {{mapping| 24 38 56 83 89 }} | ||
| | | −1.37 | ||
| 2.59 | | 2.59 | ||
| 5.19 | | 5.19 | ||
| Line 543: | Line 543: | ||
| 2.3.5.11.13.17 | | 2.3.5.11.13.17 | ||
| 51/50, 66/65, 81/80, 128/125, 144/143 | | 51/50, 66/65, 81/80, 128/125, 144/143 | ||
|{{mapping| 24 38 56 83 89 98 }} | | {{mapping| 24 38 56 83 89 98 }} | ||
| | | −0.94 | ||
| 2.55 | | 2.55 | ||
| 5.11 | | 5.11 | ||
| Line 550: | Line 550: | ||
| 2.3.5.11.13.17.19 | | 2.3.5.11.13.17.19 | ||
| 51/50, 66/65, 76/75, 81/80, 128/125, 144/143 | | 51/50, 66/65, 76/75, 81/80, 128/125, 144/143 | ||
|{{mapping| 24 38 56 83 89 98 102 }} | | {{mapping| 24 38 56 83 89 98 102 }} | ||
| | | −0.89 | ||
| 2.37 | | 2.37 | ||
| 4.74 | | 4.74 | ||
| Line 564: | Line 564: | ||
{| class="commatable wikitable center-1 center-2 right-4 center-5" | {| class="commatable wikitable center-1 center-2 right-4 center-5" | ||
|- | |- | ||
! [[Harmonic limit|Prime<br>limit]] | ! [[Harmonic limit|Prime<br />limit]] | ||
! [[Ratio]]<ref group="note">{{rd}}</ref> | ! [[Ratio]]<ref group="note">{{rd}}</ref> | ||
! [[Monzo]] | ! [[Monzo]] | ||
| Line 914: | Line 914: | ||
{| class="wikitable center-1 center-2" | {| class="wikitable center-1 center-2" | ||
|- | |- | ||
! Periods<br>per 8ve | ! Periods<br />per 8ve | ||
! Generator | ! Generator | ||
! Name | ! Name | ||
| Line 924: | Line 924: | ||
| 1 | | 1 | ||
| 5\24 | | 5\24 | ||
| [[Godzilla]] (24)<br>[[Bridgetown]] | | [[Godzilla]] (24)<br />[[Bridgetown]] | ||
|- | |- | ||
| 1 | | 1 | ||