User:Aura/Aura's introduction to 159edo: Difference between revisions

159edo contains all the intervals of 53edo, however, as some of the interpretations differ due 159edo having different mappings for certain primes, those differences show up in how harmonies are constructed.  Furthermore, just as with 24edo can be thought of as essentially having two fields of 12edo separated by a quartertone, 159edo can be thought of as having three fields of 53edo, each separated from the others by a third of a 53edo step on either side.  This even lends to 159edo having its own variation on the [[Dinner Party Rules]]—represented here by the Harmonic Compatibility Rating and Melodic Compatibility Rating columns where 10 is a full-blown friend relative to the root and −10 if a full-blown enemy relative to the root.  Note that the Harmonic Compatibility and Melodic Compatibility ratings are based on octave-equivalence, and that some of the ratings are still speculative.

! rowspan="2" colspan="3" | Interval names

| G↓

| G#↓↓, Ab↓

| Ab↑↑, G#↑

| Ad<\, G#↑, Ab↑↑

| A↑

| B↑, Cd<\, Cb↑↑, A##

| Cb<, Bt<↓, B↑/

Although 159edo inherits [[53edo]]'s close approximations of both the [[5-limit]] Zarlino scale and the [[3-limit]] [[diatonic]] MOS, these are not the only scales that one can use for fixed-pitch diatonic music.  In fact, both of them are less than optimal for many facets of traditional Western classical music in this system, seeing as for the most part, each of the traditional diatonic modes has its own optimized scale in the 5-limit.  The reason for this is that in non-meantone 5-limit systems such as 159edo, one inevitably has to deal with the ~[[40/27]] wolf fifth and the ~[[27/20]] wolf fourth, and there's only two ideal positions in the scale for those intervals to be situated in fixed-pitch diatonic music. For major modes, the ~27/20 wolf fourth is ideally situated between the ~[[5/4]] major third and the ~[[27/16]] major sixth, while for the minor modes and the diatonic blighted mode Locrian, the ~40/27 wolf fifth is ideally situated between the ~[[6/5]] minor third and the ~[[16/9]] minor seventh.  Not only that, but it also pays to distinguish the Pythagorean major and minor thirds from their Ptolemaic counterparts as both types of major and minor third have distinct roles to play in the 5-limit diatonic music of the multiples of 53edo- and that includes 159edo itself.

As a consequence of this particular scale structure, you have the following basic chords- note that this list is not exhaustive...

| III

| VII

| This tetrad is a typical dominant seventh for 5-limit music

| Greater Ptolemaic Half-Diminished

| This dissonant tetrad is an unexpected option for imperfect half cadences in the 5-limit

With the above scale steps and chords, this variation of Ionian in 159edo is considerably more tonally stable than its more familiar counterpart from 12edo and 24edo.