Undecimal primodality: Difference between revisions

11:22 (1p:2p)

  11:          2/1            1200.000000 octave

Secondly, it's "fifth region" is, of course, split in the first octave. No first octave prime families ever contain a 2:3 except /2 itself. As such, Undecimal gives us 753.6 and 648.6 cent "prime fifth" options. These can be challenging to yield as "believable" fifths but by embracing them, one can gain access to new harmonic spaces not typically considered. If a perfect fifth is desired, reaching into the second octave of Undecimal fulfills this while preserving all the previously discussed intervals.  

Undecimal has quality super and neutral intervals. The 11:15 at 536.9c is a remarkable superfourth. It's a highly active, interval which has a tendency to bridge almost all the intervals in the family together. The 11:15 superfourth is very tunable by ear and has it's own distinct identity rather than sounding like a flatter version of 8:11. Additionally, it forms a parallel relationship with the 11:20 superminor seventh at 1034.9c. Between the two, a 3:4 relationship exists similar to the familiar perfect fourth relationship between 4 and b7 in 12edo. However, in this family the relationship is shifted much higher to super fourth and superminor seventh. Between this brighter super 4-b7 relationship and the sharper 3-7 relationship, tertian or 12edo-esque structures rendered in Undecimal tend to sound brighter than /13, /17, and /19 color variants. Neutral intervals appear in the first octave as 11:12 and 11:18, 150.6c neutral second and an 852c neutral sixth from 11:18. The 11:19 at 948 cents contributes a unique middle-augmented sixth which tends to sound more like a hypermajor sixth when surrounded by the sharper Undecimal intervals.  

22:44 (2p:4p)

all previous intervals omitted to reduce clutter

  22:          2/1            1200.000000 octave

First, let's examine the second octave's relationship to 12edo major and minor since most ears reading this have their senses rooted in that system. The 37/22 acts identically to 12edos major sixth as it's less than .02 cents away at 900 cents. 35/22 also sits within 4 cents of the 12edo minor sixth. These intervals often come into play when rendering tertian harmony in /11. These can be used to evoke fresh but familiar sensations in average listeners such as demonstrated in [https://youtu.be/3iWRlf3wrPs Spiritualistica] and [https://youtu.be/PIhFupdwv3M Timelessness]. 31/22 as 593.7 cents offers a lush tritone with it's own attractive quality which can operate as a tritone parallel for Maj#11 or 7#11 sounds.

The second octave grants us an acute major second, 25/22 at 221.3 cents and a lower minor second with 23/22 at 76.9 cents. The 25/22 major second runs sharp along with the 417, 537, and 1119 "diatonic" major intervals. As a result when joined by those intervals, the system begins to sound uniformly sharp but regular (if all are sharp, none are sharp). By contrast, the first octave only gives the neutral second from 12/11 which tends to act more xen relative to the "diatonic" intervals. These colors can be interplayed to form a wide variety of possibilities across an axis of familiarity or novelty relative to your ear.  

Undecimal also grants "opposite" color intervals in the form of second octave intervals that go flat relative to key interval areas rather than uniformly sharp like the majority of Undecimal. These "relatively flatter" intervals can be seen in 41/22 at 1077.7 cents as a relatively darker maj7, 29/22 at 478 cents as a subfourth relative to the 417 cent 14/11. These can be combined with the "prime fifths" from the first octave to generate startling combinations which push, pull, and subvert expectation like 22:28:34:41:52:58.