13edo scales: Difference between revisions
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Being a 7-note scale, the unison to octave interval categories remain the same as in the diatonic scale, except that we now have major fourths (6\13, approx. 11/8) and minor fourths (5\13, approx. 21/16), and their inversions minor and major fifths. An interesting feature is that you can switch whether you perceive an interval as minor or major by approaching it from opposite directions: for example, a minor sixth can be made to sound like a diatonic major sixth by walking up whole-whole-half-whole-whole steps from the tonic or like a diatonic minor sixth by walking down two whole steps. | Being a 7-note scale, the unison to octave interval categories remain the same as in the diatonic scale, except that we now have major fourths (6\13, approx. 11/8) and minor fourths (5\13, approx. 21/16), and their inversions minor and major fifths. An interesting feature is that you can switch whether you perceive an interval as minor or major by approaching it from opposite directions: for example, a minor sixth can be made to sound like a diatonic major sixth by walking up whole-whole-half-whole-whole steps from the tonic or like a diatonic minor sixth by walking down two whole steps. | ||
===Scale=== | ===Scale=== | ||
Sortable table of intervals in the Ryonian mode ( | Sortable table of intervals in the Ryonian mode. (Harmonics are in bold; this is useful for seeing a chord's complexity when you sort the intervals according to the generator chain.) | ||
{| class="wikitable sortable sorted" | {| class="wikitable sortable sorted" | ||
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| Line 110: | Line 110: | ||
|- | |- | ||
| | 1, 8 | | | 1, 8 | ||
| style="text-align:right;" | 0 | | style="text-align:right;" | 0, 1200 | ||
| | J | | | J | ||
| | '''1/1''' | | | '''1/1''', '''2/1''' | ||
| | 0 | | | 0 | ||
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The names I use for the oneirotonic interval classes are borrowed from diatonic interval categories: "second", "third", "fourth", "tritone" (4-step intervals), "fifth" (5-step intervals), "sixth" (6-step intervals), "seventh" (7-step intervals) and octave. You just have to remember that there's an extra category between fourths and fifths and that fourths and fifths are dissonant. Like in archeotonic you can change the perception of an interval by approaching it from different directions, but in oneirotonic it will change what diatonic interval class you hear it as: say, as both a third and a fourth, rather than both a major and a minor third. | The names I use for the oneirotonic interval classes are borrowed from diatonic interval categories: "second", "third", "fourth", "tritone" (4-step intervals), "fifth" (5-step intervals), "sixth" (6-step intervals), "seventh" (7-step intervals) and octave. You just have to remember that there's an extra category between fourths and fifths and that fourths and fifths are dissonant. Like in archeotonic you can change the perception of an interval by approaching it from different directions, but in oneirotonic it will change what diatonic interval class you hear it as: say, as both a third and a fourth, rather than both a major and a minor third. | ||
===Scale=== | ===Scale=== | ||
The Dylathian mode is the most otonal mode, and is the basis for Kentaku note names JKLMNOPQJ (J is approx. 180 Hz, or an 11/8 above middle C). Sortable table of Dylathian | The Dylathian mode is the most otonal mode, and is the basis for Kentaku note names JKLMNOPQJ (J is approx. 180 Hz, or an 11/8 above middle C). Sortable table of Dylathian (Harmonics are in bold; this is useful for seeing a chord's complexity when you sort the intervals according to the generator chain): | ||
{| class="wikitable sortable sorted" | {| class="wikitable sortable sorted" | ||
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| style="text-align:right;" | 0, 1200 | | style="text-align:right;" | 0, 1200 | ||
| | J | | | J | ||
| | '''1/1''' | | | '''1/1''', '''2/1''' | ||
| | 0 | | | 0 | ||
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The brightest mode is LsLsLsLss or 0-2-3-5-6-8-9-11-12-13. The triad 4:11:13 occurs on degrees 1, 2, 3, 5, 7 and 9; these can be extended to either 4:10:11:13:17, 4:9:11:13:21, or 4:5:9:11:13 depending on what degree you're on. Since you get 21/16 as the minor version of 11/8, you also get two 8:13:17:21's with the same interval classes, on degrees 6 and 8. Degree 4 has a 4:5:11. | The brightest mode is LsLsLsLss or 0-2-3-5-6-8-9-11-12-13. The triad 4:11:13 occurs on degrees 1, 2, 3, 5, 7 and 9; these can be extended to either 4:10:11:13:17, 4:9:11:13:21, or 4:5:9:11:13 depending on what degree you're on. Since you get 21/16 as the minor version of 11/8, you also get two 8:13:17:21's with the same interval classes, on degrees 6 and 8. Degree 4 has a 4:5:11. | ||
Sortable table | Sortable table of LsLsLsLss (Harmonics are in bold; this is useful for seeing a chord's complexity when you sort the intervals according to the generator chain.): | ||
{| class="wikitable sortable sorted" | {| class="wikitable sortable sorted" | ||
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! | # generators up | ! | # generators up | ||
|- | |- | ||
| | 1 | | | 1, 10 | ||
| style="text-align:right;" | 0 | | style="text-align:right;" | 0, 1200 | ||
| | J | | | J | ||
| | '''1/1''' | | | '''1/1''', '''2/1''' | ||
| | 0 | | | 0 | ||
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The decatonic scale is excellent for 4:5:13 triads. It's generated by a major third, and two of them span a 4:5:13 triad, spanning degrees 1-4-8, and three of them span a 4:5:13:21 tetrad. This means that 8 of the 10 degrees have a 4:5:13 triad, and 7 of them in turn have a 4:5:13:21. | The decatonic scale is excellent for 4:5:13 triads. It's generated by a major third, and two of them span a 4:5:13 triad, spanning degrees 1-4-8, and three of them span a 4:5:13:21 tetrad. This means that 8 of the 10 degrees have a 4:5:13 triad, and 7 of them in turn have a 4:5:13:21. | ||
The LsssLssLss mode is the only mode that has a 4:5:9:13:21 on the tonic. If you want an 11/8 instead of a 21/16 you can sharpen the 5th degree to get LssLsssLsss which is the only mode to have a 4:5:9:11:13 on the tonic. Sortable table of LsssLssLss | The LsssLssLss mode is the only mode that has a 4:5:9:13:21 on the tonic. If you want an 11/8 instead of a 21/16 you can sharpen the 5th degree to get LssLsssLsss which is the only mode to have a 4:5:9:11:13 on the tonic. Sortable table of LsssLssLss (Harmonics are in bold; this is useful for seeing a chord's complexity when you sort the intervals according to the generator chain.): | ||
{| class="wikitable sortable sorted" | {| class="wikitable sortable sorted" | ||
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! | # generators up | ! | # generators up | ||
|- | |- | ||
| | 1 | | | 1, 11 | ||
| style="text-align:right;" | 0 | | style="text-align:right;" | 0, 1200 | ||
| | J | | | J | ||
| | '''1/1''' | | | '''1/1''', '''2/1''' | ||
| | 0 | | | 0 | ||
|- | |- | ||