Macrodiatonic and microdiatonic scales
Macrodiatonic scales are nonoctave MOS scales that have 5 large and 2 small steps like the diatonic scale, but have a period greater than 2/1 so are stretched. The equivalent term for compressed diatonic scales (period < 2/1) is microdiatonic. Macrodiatonic/microdiatonic scales typically sound completely unrecognizable due to the stretching/squishing, yet are structurally identical to diatonic (with it being possible to translate from diatonic to macrodiatonic/microdiatonic scales "on the fly"). Nonoctave regular temperaments assosciated with macrodiatonic/microdiatonic scales are sometimes termed as macromeantone/micromeantones. However, it is controversial to use the name of the temperament for things that only share a scale pattern rather than harmonic structure.
In broader sense, a scale created by repeating one simple intonation ("fifth" analogue) and it has low otonal limit triad (with "third" analogue which is but not always genspan +4.) But, if 3/2 is used as generator, such as angel and obikhod, another name should be considered.
Examples of macrodiatonic and microdiatonic scales
- 5L 2s<3/2>: Generator is a neogothic major third near 81/64 and 14/11.
- 5L 2s<7/4>: Dark generator is approximately 5/4.
- 5L 2s<9/5>: Generator is approximately 7/5.
- 5L 2s<12/5>: Generator is approximately 5/3, and interestingly, major triads (4:5:6) are stretched to approximately second inversion major triads (3:4:5).
- 5L 2s<3/1>: Generator is approximately 17/9, and 4 generators is vaguely equivalent to 13/9. This relates this scale to the no-twos macromeantone temperament tempering out 85293/83521 in the 3.13.17 subgroup (equating 4 17/9 to 13/9, instead of 4 3/2 to 5/4), as documented on the page for 12edt.
- 5L 2s<4/1>: This is precisely a 200% stretched diatonic scale. Generator is approximately 9/4 (3/22). This can very clearly be interpreted as a temperament tempering out 6561/6400 (81/802) in 4.9.25 for the meantone equivalent or 4096/3969 (64/632) in 4.9.49 for the archy equivalent. This scale is extremely widely spaced, so it may preferable to use the macrochromatic scales 7L 5s<4/1> and 5L 7s<4/1> instead.
In broader sense
Macrodiatonic/microdiatonic
- 9L 2s<3/2>: Generator is approximately 5/4 and 6 generators is 9/8.
- 7L 2s<5/3>: Generator is approximately 4/3 and 4 generators is 8/7.
Longdiatonic/shortdiatonic
- 6L 1s<8/5>: Dark generator is approximately 3/2 and 4 generators is 6/5.
- 3L 4s<7/4>: Dark generator is just 3/2 and 2 generators is just 9/7. Merely this is a lattice by 9/7 and 7/6.
- 3L 4s<9/5>: Dark generator is just 3/2 and 2 generators is just 5/4. Merely this is a lattice by 5/4 and 6/5.
- 7L 2s<5/2>: Dark generator is approximately 3/2 and 5 generators is 6/5.
- 8L 3s<3/1>: Generator is approximately 3/2 and 6 generator is 5/4.