13edo: Difference between revisions

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Seconds and thirds are similar in consonance to 12edo seconds and thirds, and similarly cothirds and coseconds 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. Minor fifths (approximating 11/8) work like tritones and they like to resolve inward to a third. Major fifths (16/11) are the opposite: they like to resolve outward to a cothird. Unlike in 12edo, there is a major difference in quality between fourths and fifths, and their octave inversions. Perfect fourths and minor fifths, despite being dissonant, can both be spread out to make them more consonant. Major fifths and perfect cofourths cannot, hence they should normally not be used directly over the root in a chord (except as passing tones) but over some other note of the chord. For example, analogues to diatonic add7 no5 chords tend to work well.

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 fifths (approximating 11/8) work like tritones and they like to resolve inward to a third. Major fifths (16/11) are the opposite: they like to resolve outward to a cothird. Unlike in 12edo, there is a major difference in quality between fourths and fifths, and their octave inversions. Perfect fourths and minor fifths, despite being dissonant, can both be spread out to make them more consonant. Major fifths and perfect cofourths cannot, hence they should normally not be used directly over the root in a chord (except as passing tones) but over some other note of the chord. For example, analogues to diatonic add7 no5 chords tend to work well.

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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 Seconds and thirds are similar in consonance to 12edo seconds and thirds, and similarly cothirds and coseconds 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. Minor fifths (approximating 11/8) work like tritones and they like to resolve inward to a third. Major fifths (16/11) are the opposite: they like to resolve outward to a cothird. Unlike in 12edo, there is a major difference in quality between fourths and fifths, and their octave inversions. Perfect fourths and minor fifths, despite being dissonant, can both be spread out to make them more consonant. Major fifths and perfect cofourths cannot, hence they should normally not be used directly over the root in a chord (except as passing tones) but over some other note of the chord. For example, analogues to diatonic add7 no5 chords tend to work well.
+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 fifths (approximating 11/8) work like tritones and they like to resolve inward to a third. Major fifths (16/11) are the opposite: they like to resolve outward to a cothird. Unlike in 12edo, there is a major difference in quality between fourths and fifths, and their octave inversions. Perfect fourths and minor fifths, despite being dissonant, can both be spread out to make them more consonant. Major fifths and perfect cofourths cannot, hence they should normally not be used directly over the root in a chord (except as passing tones) but over some other note of the chord. For example, analogues to diatonic add7 no5 chords tend to work well.
 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]]).