13edo scales: Difference between revisions

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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.

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 ~~cothird~~. 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. 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.

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

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