Macrodiatonic and microdiatonic scales: Difference between revisions
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'''Macrodiatonic scales''' are [[nonoctave]] [[MOS scale]]s 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 temperament]]s assosciated with macrodiatonic/microdiatonic scales are sometimes termed as macro[[meantone]]/micromeantones. However, it is controversial to use the | '''Macrodiatonic scales''' are [[nonoctave]] [[MOS scale]]s 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 temperament]]s assosciated with macrodiatonic/microdiatonic scales are sometimes termed as macro[[meantone]]/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 | 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 == | == Examples of macrodiatonic and microdiatonic scales == | ||
* [[5L 2s (3/2-equivalent)|5L 2s<3/2>]]: | * [[5L 2s (3/2-equivalent)|5L 2s<3/2>]]: Generator is a neogothic major third near [[81/64]] and [[14/11]]. | ||
* [[Ed7/4|5L 2s<7/4>]]: | * [[Ed7/4|5L 2s<7/4>]]: Dark generator is approximately 5/4. | ||
* [[Ed9/5|5L 2s<9/5>]]: | * [[Ed9/5|5L 2s<9/5>]]: Generator is approximately 7/5. | ||
* [[5L 2s (12/5-equivalent)|5L 2s<12/5>]]: | * [[5L 2s (12/5-equivalent)|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-equivalent)|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 (3/1-equivalent)|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]]. | ||
== In | == In broader sense == | ||
* [[EDF|9L 2s<3/2>]]: | === Macrodiatonic/microdiatonic === | ||
* [[ | * [[EDF|9L 2s<3/2>]]: Generator is approximately 5/4 and 6 generators is 9/8. | ||
* [[ | * [[Ed5/3|7L 2s<5/3>]]: Generator is approximately 4/3 and 4 generators is 8/7. | ||
* [[3L 4s (9/5-equivalent)|3L 4s<9/5>]]: | === Longdiatonic/shortdiatonic === | ||
* [[Ed8/5|6L 1s<8/5>]]: Dark generator is approximately 3/2 and 4 generators is 6/5. | |||
* [[3L 4s (9/5-equivalent)|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. | |||
[[Category:7-tone scales]] | [[Category:7-tone scales]] | ||
Revision as of 05:09, 1 July 2023
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.
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<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.