13edo scales: Difference between revisions

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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.

Oneirotonic provides 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. One could use it to 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.

Oneirotonic provides two kinds of 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. One could use it to 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 copies of 8:11:13 in oneirotonic, O-K-M or L-P-J in J Ilarnekian, are contained in the two Orwell tetrads.

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.

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 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.
-Oneirotonic provides 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. One could use it to 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.
+Oneirotonic provides two kinds of 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. One could use it to 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 copies of 8:11:13 in oneirotonic, O-K-M or L-P-J in J Ilarnekian, are contained in the two Orwell tetrads.
 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.