13edo: Difference between revisions

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[[Kentaku's_Approach_to_13EDO|More on William Lynch's 13 EDO octaton approach]]

==Inthar's thoughts on 13edo==

~~Note on terminology~~: I often use "cofourth", "cothird", and "cosecond" for octave complements of a fourth, third or second in place of sixth, seventh and eighth. The terms describe their melodic behavior being similar to octave complements of fourths, thirds, and seconds, and work in both archaeotonic and oneirotonic contexts.

:[[13edo/Inthar]]

~~Both archaeotonic and oneirotonic modes are partly analogous to diatonic modes, though some of them sound more like combinations of different modes.~~

~~===Archaeotonic===~~

The archaeotonic scale is overall brighter, more "majory" and more concordant than the oneirotonic scale: there are more 4:5:9 chords and chords involving the 11th and 13th harmonics, and extremely dissonant intervals such as 16/11 and 32/21 are less common.

~~===Oneirotonic===~~

The darker, damper, more "minory" cousin of archaeotonic. Only 2 out of 8 oneirotonic modes (Dylathian and Ilarnekian) are "major" in the sense of having a major third, and both sound pretty bittersweet.

~~Like in archaeotonic, 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, 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 are more consonant than their inversions major fifths and perfect cofourths; 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]]).

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

~~===Chords===~~

~~Oneirotonic provides unique tetrads taking every second degree of the scale, JLNP or KMOQ. They're quite spicy, might want to try different voicings?~~

~~J-L-K (4:5:9) and its minor counterpart J-Lb-K work well with an added cothird or cosecond, even when the resulting chord does not approximate an obvious JI chord.~~

~~todo: try added cofourths or fifths, describe chords with two additions or more~~

=Mapping to Standard Keyboards=

@@ Line 424: / Line 424: @@
 [[Kentaku's_Approach_to_13EDO|More on William Lynch's 13 EDO octaton approach]]
 ==Inthar's thoughts on 13edo==
-Note on terminology: I often use "cofourth", "cothird", and "cosecond" for octave complements of a fourth, third or second in place of sixth, seventh and eighth. The terms describe their melodic behavior being similar to octave complements of fourths, thirds, and seconds, and work in both archaeotonic and oneirotonic contexts.
+:[[13edo/Inthar]]
-Both archaeotonic and oneirotonic modes are partly analogous to diatonic modes, though some of them sound more like combinations of different modes.
-===Archaeotonic===
-The archaeotonic scale is overall brighter, more "majory" and more concordant than the oneirotonic scale: there are more 4:5:9 chords and chords involving the 11th and 13th harmonics, and extremely dissonant intervals such as 16/11 and 32/21 are less common.
-===Oneirotonic===
-The darker, damper, more "minory" cousin of archaeotonic. Only 2 out of 8 oneirotonic modes (Dylathian and Ilarnekian) are "major" in the sense of having a major third, and both sound pretty bittersweet.
-Like in archaeotonic, 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, 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 are more consonant than their inversions major fifths and perfect cofourths; 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]]).
-Basic chord progressions can move by perfect fourths or major seconds: J major-M minor-P minor-Ob major-J major (in Ilarnekian) or J major-K major-O major-M major-J major (in Dylathian)
-===Chords===
-Oneirotonic provides unique tetrads taking every second degree of the scale, JLNP or KMOQ. They're quite spicy, might want to try different voicings?
-J-L-K (4:5:9) and its minor counterpart J-Lb-K work well with an added cothird or cosecond, even when the resulting chord does not approximate an obvious JI chord.
-todo: try added cofourths or fifths, describe chords with two additions or more
 =Mapping to Standard Keyboards=