Diatonic
Diatonic is a kind of scale characterized by the division of the octave into 5 large steps (L) and 2 small steps (s) in an LLsLLLs pattern, or any rotation thereof. The most widespread diatonic is the MOS form, 5L 2s, where the large steps are equally sized and the small steps are also equally sized. When diatonic is used as an adjective on the wiki to describe something other than a scale, the MOS is what it usually refers to (for example, the diatonic major third is the major third in the MOS diatonic scale). However, other similar scales may be called diatonic as well.
MOS diatonic
The MOS diatonic scale is 5L 2s, tuned most simply in 12edo. It is the basic scale for a number of rank-2 temperaments, such as meantone, archy, and schismic. It can be formed by stacking seven perfect fifths and octave-reducing. MOS diatonic has seven modes, from classical music theory:
| Mode name | Pattern | 2nd | 3rd | 4th | 5th | 6th | 7th |
|---|---|---|---|---|---|---|---|
| Locrian | sLLsLLL | m | m | P | d | m | m |
| Phrygian | sLLLsLL | m | m | P | P | m | m |
| Aeolian (Minor) | LsLLsLL | M | m | P | P | m | m |
| Dorian | LsLLLsL | M | m | P | P | M | m |
| Mixolydian | LLsLLsL | M | M | P | P | M | m |
| Ionian (Major) | LLsLLLs | M | M | P | P | M | M |
| Lydian | LLLsLLs | M | M | A | P | M | M |
Greek diatonic scales
Diatonic may be defined more broadly according to the Greek diatonic genus. In Greek music, a diatonic scale is constructed from identical tetrachords spanning a perfect fourth each, and separated by a Pythagorean major second, such that
a) the largest interval in the tetrachord is at most half of its total span
b) the middle interval in the tetrachord is not the smallest.
As such, the scale pattern for a generalized diatonic (in its Phrygian mode) may be sABCsAB, where C is an approximation of 9/8 and A and B are both intervals that are larger than s but no larger than half the tetrachord's span.
An example of a Greek diatonic is Ptolemy's intense diatonic, where C and A are equated to 9/8, B is 10/9, and s is 16/15. This results in the scale pattern sLMLsLM, which may more abstractly be called 'zarlino' or 'nicetone', and has fourteen modes rather than seven due to its chirality (for example, mosdiatonic Ionian LLsLLLs becomes two modes: LH-Ionian (MLsLMLs) and RH-Ionian (LMsLMLs).)
Another example of a Greek diatonic is the equable diatonic, which is a tuning where C is 9/8, B is 10/9, A is 11/10, and s is 12/11. This has the property of being easily expressible as a utonal sequence 1/(18:20:22:24:27:30:33:36).
The simplest rank-3 diatonic tunings are those found in 14edo (3-2-1-2-3-2-1) and 15edo (3-2-1-3-2-3-1). Note that in both cases, the largest interval in the tetrachord is exactly half of its width. This is similar to the edge-case found with the tuning of MOS diatonic in 5edo or 7edo.
Straddle-fifth diatonic scales
A straddle-fifth system has a sharp and a flat fifth, which combine to create a 9/8 wholetone. So, in those systems, a diatonic scale analogous to the MOS diatonic may be generated by alternating the two fifths. This creates an LLmLLLs pattern, notably meaning there are multiple varieties of small step, rather than multiple varieties of large step. Again, there are fourteen modes, because, for example, there are again two Ionian modes: LLsLLLm and LLmLLLs. Note that the perfect fourth is always based on one variety of fifth, and the perfect fifth is always the other.
