13edo scales: Difference between revisions

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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.

===Chords===

Like in archaeotonic, seconds and thirds are similar in consonance to 12edo seconds and thirds, and similarly sixths and sevenths are similar to diatonic sixths and sevenths. ~~Perfect~~ fourths (21/16) are dissonant, but they work a lot like diatonic perfect fourths do e.g. in "sus24" chords that resolve down to thirds, and can also be spread out to make convincing 4:9:21 chords which are common in oneirotonic.

Like in archaeotonic, seconds and thirds are similar in consonance to 12edo seconds and thirds, and similarly sixths and sevenths are similar to diatonic sixths and sevenths. Minor fourths (21/16) are dissonant, but they work a lot like diatonic perfect fourths do e.g. in "sus24" chords that resolve down to thirds, and can also be spread out to make convincing 4:9:21 chords which are common in oneirotonic.

As in archeotonic harmony, root-third-ninth chords may be considered basic harmonic triads; oneirotonic scales have 5 such triads, 2 "major" and 3 "minor". J-L-K (4:5:9) and its minor counterpart J-Lb-K work well with an added sixth or seventh, even when the resulting chord does not approximate an obvious JI chord.

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Oneirotonic provides two Orwell tetrads, made of three stacked minor thirds making one minor sixth; we get them by taking every second degree of the scale, JLNP or KMOQ. They sound like squashed diminished chords, but not quite. One could play an earbending trick where a movement up a major third and up 3 minor thirds will get you back to where you started unlike in 12edo. The two Orwell tetrads contain the two copies of 8:11:13 in oneirotonic, Q-M-O or L-P-J in J Ilarnekian.

Minor tritones (approximating 11/8) work like tritones and they like to resolve inward to a third. Major tritones (16/11) are the opposite: they like to resolve outward to a sixth. Unlike in 12edo, fourths and tritones, and their octave inversions are very different in quality. ~~Perfect~~ fourths and minor tritones are more consonant than their inversions major tritones and ~~perfect~~ fifths; they can also both be spread out to make them more consonant, whereas their inversions cannot.

Minor tritones (approximating 11/8) work like tritones and they like to resolve inward to a third. Major tritones (16/11) are the opposite: they like to resolve outward to a sixth. Unlike in 12edo, fourths and tritones, and their octave inversions are very different in quality. Minor fourths and minor tritones are more consonant than their inversions major tritones and major fifths; they can also both be spread out to make them more consonant, whereas their inversions cannot.

The diminished fourth can work either like the diatonic diminished fourth, or (uniquely in 13edo among all oneirotonic tunings) serve as an extra 5/4 in the scale and can be part of extra consonant chords (such as the aforementioned Beloved Extra Special Chord representing both 8:10:11:13 and 13:16:18:21, which occurs as O-J-K-M in J Ilarnekian, but it only represents 13:16:18:21 in other oneirotonic-supporting tunings such as [[31edo]]).

Basic chord progressions can move by ~~perfect~~ fourths or major seconds: J major-M minor-P minor-O major-J major (in Ilarnekian) or J major-K major-O# major-M major-J major (in Dylathian)

Basic chord progressions can move by minor fourths or major seconds: J major-M minor-P minor-O major-J major (in Ilarnekian) or J major-K major-O# major-M major-J major (in Dylathian)

===Modal harmony===

@@ Line 89: / Line 89: @@
 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.
 ===Chords===
-Like in archaeotonic, seconds and thirds are similar in consonance to 12edo seconds and thirds, and similarly sixths and sevenths are similar to diatonic sixths and sevenths. Perfect fourths (21/16) are dissonant, but they work a lot like diatonic perfect fourths do e.g. in "sus24" chords that resolve down to thirds, and can also be spread out to make convincing 4:9:21 chords which are common in oneirotonic.
+Like in archaeotonic, seconds and thirds are similar in consonance to 12edo seconds and thirds, and similarly sixths and sevenths are similar to diatonic sixths and sevenths. Minor fourths (21/16) are dissonant, but they work a lot like diatonic perfect fourths do e.g. in "sus24" chords that resolve down to thirds, and can also be spread out to make convincing 4:9:21 chords which are common in oneirotonic.
 As in archeotonic harmony, root-third-ninth chords may be considered basic harmonic triads; oneirotonic scales have 5 such triads, 2 "major" and 3 "minor". J-L-K (4:5:9) and its minor counterpart J-Lb-K work well with an added sixth or seventh, even when the resulting chord does not approximate an obvious JI chord.
@@ Line 95: / Line 95: @@
 Oneirotonic provides two Orwell tetrads, made of three stacked minor thirds making one minor sixth; we get them by taking every second degree of the scale, JLNP or KMOQ. They sound like squashed diminished chords, but not quite. One could play an earbending trick where a movement up a major third and up 3 minor thirds will get you back to where you started unlike in 12edo. The two Orwell tetrads contain the two copies of 8:11:13 in oneirotonic, Q-M-O or L-P-J in J Ilarnekian.
-Minor tritones (approximating 11/8) work like tritones and they like to resolve inward to a third. Major tritones (16/11) are the opposite: they like to resolve outward to a sixth. Unlike in 12edo, fourths and tritones, and their octave inversions are very different in quality. Perfect fourths and minor tritones are more consonant than their inversions major tritones and perfect fifths; they can also both be spread out to make them more consonant, whereas their inversions cannot.
+Minor tritones (approximating 11/8) work like tritones and they like to resolve inward to a third. Major tritones (16/11) are the opposite: they like to resolve outward to a sixth. Unlike in 12edo, fourths and tritones, and their octave inversions are very different in quality. Minor fourths and minor tritones are more consonant than their inversions major tritones and major fifths; they can also both be spread out to make them more consonant, whereas their inversions cannot.
 The diminished fourth can work either like the diatonic diminished fourth, or (uniquely in 13edo among all oneirotonic tunings) serve as an extra 5/4 in the scale and can be part of extra consonant chords (such as the aforementioned Beloved Extra Special Chord representing both 8:10:11:13 and 13:16:18:21, which occurs as O-J-K-M in J Ilarnekian, but it only represents 13:16:18:21 in other oneirotonic-supporting tunings such as [[31edo]]).
-Basic chord progressions can move by perfect fourths or major seconds: J major-M minor-P minor-O major-J major (in Ilarnekian) or J major-K major-O# major-M major-J major (in Dylathian)
+Basic chord progressions can move by minor fourths or major seconds: J major-M minor-P minor-O major-J major (in Ilarnekian) or J major-K major-O# major-M major-J major (in Dylathian)
 ===Modal harmony===