13edo scales: Difference between revisions

Cheat sheet of important [[MOS]] scale types with L = major second, s = minor second:

| archeotonic (LLLLLLs)

| major second

| oneirotonic (LLsLsLLs)

| minor fourth

| nonatonic (LsLsLsLss)

| minor third

| decatonic (LssLsssLss)

| major third

| '''1/1''', '''2/1'''

| '''9/8''', 10/9, 11/10, 19/17, 21/19  

| '''5/4''', 11/9, 16/13, 26/21

| '''11/8''', 18/13, 26/19   

| 8/5, '''13/8''', 18/11, 21/13

 

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.

 

=== Scale ===

 

The Dylathian mode is the most otonal mode, and is the basis for Kentaku note names JKLMNOPQJ (J is approx. 180 Hz, or an 11/8 above middle C). Sortable table of Dylathian (Harmonics are in bold; this is useful for seeing a chord's complexity when you sort the intervals according to the generator chain):

 

| L

| 923.08

 

Despite being melodically familiar, oneirotonic may be the most harmonically complex of the 13edo scales; the most common consonant triad is a fairly complex 4:9:21. Hence oneirotonic especially benefits from either using inharmonic timbres in addition to harmonic ones, or using a well-tempered or [[primodal]] JI version of 13edo. The availability of primes also varies greatly by mode: for example, only Dylathian, Ilarnekian and Sarnathian have a 5/4 on the tonic, and only Mnarian, Kadathian, Hlanithian and Sarnathian have an 11/8 on the tonic.

 

 

How I think about the 8 oneirotonic modes:

 

#Celephaïsian: 2 1 2 2 1 2 2 1 (the oneirotonic melodic minor. Very classical-sounding; Easley Blackwood's 13-note etude uses this as its home mode.)

 

 

The brighter modes can be viewed as providing a distorted version of diatonic functional harmony. For example, in the Dylathian mode, the 4:5:9 triad on the sixth degree can sound like both "V" and "III of iv" depending on context. Basic chord progressions can move by minor fourths, thirds, or major seconds: for example, 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).

 

 

 

 

*[1 3 1] [2 1] [1 2 2] is a kind of Phrygian dominant scale (which also contains 1 3 1 2 2 2 2, a chromatic modification of the Zo-Kalarian mode of the archeotonic scale).

 

 

 

| Ilarnekian 2 2 1 2 1 2 2 1 || ↔ || Ryonian    2 2 2 2 2 2 1

Generated by 3\13, the 276.9-cent minor third approximating [[13/11]], this scale sounds a little like the octatonic scale in 12edo with an extra small step inserted. Two of these make an 11/8 and three make a 13/8, making this scale very good for 4:11:13 triads. (In terms of regular temperament theory, this makes 13edo a tuning for the [[Color notation|bithotrilu]] temperament that tempers out the bithotrilu comma 1352/1331 = {{monzo|3 0 0 0 -3 2}}, aka "lovecraft temperament".) [[17edo]] also supports bithotrilu temperament and thus has a similar 4L 5s scale, generated by the 4\17 minor third. Similar scales also exist in 22edo and 31edo with flatter generators, but they use a [[Orwell|different temperament]] and won't approximate the 13th harmonic.

| '''1/1''', '''2/1'''

| '''9/8''', 10/9, 11/10, 19/17, 21/19

| 7/6, 13/11, 20/17, '''19/16''', 22/19  

| 13/10, 17/13, '''21/16''', 22/17  

| '''11/8''', 18/13, 26/19  

| 8/5, '''13/8''', 18/11, 21/13  

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