Macrodiatonic and microdiatonic scales

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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.

Notation

Macrodiatonic and microdiatonic scales can be notated using the standard diatonic notation, if intervals are reinterpreted to be understood as their stretched or compressed counterparts.

Examples of macrodiatonic and microdiatonic scales

  • 5L 2s<4/3>: Generator is a neogothic minor third.
  • 5L 2s<3/2>: Generator is a neogothic major third near 81/64 and 14/11. In the half-prime subgroup paradigm it may be interpreted as 63/50 (relating to the 3/2.5/2.7/2 subgroup version of sirius temperament).
  • 5L 2s<7/4>: Generator is approximately 7/5 (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 (or rather more like macroarchy, with the 17/9 being stretched) 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.
  • 5L 2s<5/1>: Generator is approximately 13/5 or 18/7. Relates to Hyperpyth temperament.

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. The minor triad are more affinity for equave (10:12:15:18) than the major triad (20:25:30:36).
  • 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 generators is 5/4.