10-form
The 10-form describes the structure based around a set of 10 pitch classes or high-level interval regions per octave, as opposed to the conventional 7. It is the simplest form that makes the fundamental distinctions necessary to represent the full 7-limit, expanding on the 7-form by adding three new interval classes: the chthonic, the tritone, and the ouranic. Important chthonics in this system are 7/6 and 8/7; their complements are 12/7 and 7/4 respectively, which are ouranics; 10/7 and 7/5 fall into the tritone category.
Chords
10-form harmony can be constructed out of:
- Fundamental triad: 0-3-6\10
- Fundamental tetrad: 0-3-6-8\10
Notes about distinctions
9/7, while conventionally a third, is generally a kind of imperfect fourth here. Same goes for 7/6 and being a chthonic, rather than a third.
Important scales
Blackdye
Blackdye is constructed as an "indecisive zarlino" of sorts, adding small steps called aberrismas in order to allow for finer control over the intervals used. Alternatively, it may be conceptualized as two Pythagorean pentic scales offset by 10/9.
Pentawood
Blackwood[10], or pentawood, has the notable feature of every note of the scale having either a major or a minor chord built on it, which not even mosdiatonic has (as mosdiatonic has a diminished chord). However, this is at the cost of the fifth necessarily being tuned rather sharply. The scale has only two modes, which may be considered major and minor, and as a 1\5-octave scale lacks a single chain of identical intervals capable of describing it. It can be compared to diaschismic[10]; instead of linking the third and ouranic, it makes the ouranic a perfect interval, with no distinctions available within the MOS form of the scale. Pentawood includes the structure of archy temperament.
Additionally, pentawood is a tempering of the aforementioned blackdye.
Diaschismic[10]
Called jaric temperament-agnostically, this scale (with the pattern ssssLssssL) is represented by pajara temperament. Diaschismic[10], along with taric, lemon, and lime, gives the 3\10 (representing the simplest 5-limit intervals 5/4 and 6/5) the same distinction as the 8\10 (representing the intervals 12/7 and 7/4), always separating them by a tritone in any given MOS mode. Therefore, the qualities of the two can be linked to form a major/minor dichotomy based upon the harmonic tetrad.
