Macrodiatonic and microdiatonic scales: Difference between revisions
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Dummy index (talk | contribs) -obikhod (i intended it as an example of named chain-of-fifth nonoctave scale, now it is clearly wrong) |
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'''Macrodiatonic scales'''{{idiosyncratic}} 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, making them extremely [[stretched tuning|stretched]] versions of the diatonic scale. The equivalent term for compressed diatonic scales (period < 2/1) is '''microdiatonic'''{{idiosyncratic}}. 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. [[User:CompactStar|CompactStar]] suggests that the term macromeantone/micromeantone is only used for temperaments in which the "fifth" analogue is tuned flatter than its untempered interpretation. | '''Macrodiatonic scales'''{{idiosyncratic}} 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, making them extremely [[stretched tuning|stretched]] versions of the diatonic scale. The equivalent term for compressed diatonic scales (period < 2/1) is '''microdiatonic'''{{idiosyncratic}}. 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. [[User:CompactStar|CompactStar]] suggests that the term macromeantone/micromeantone is only used for temperaments in which the "fifth" analogue is tuned flatter than its untempered interpretation. | ||
In a broader sense, a scale created by repeating one simple intonation ("fifth" analogue) and it has a 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 | In a broader sense, a scale created by repeating one simple intonation ("fifth" analogue) and it has a 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 {{mos scalesig|8L 3s<3/1>|link=1}}, another name should be considered. The terms longdiatonic and shortdiatonic have been proposed to refer to the latter, most likely by [[User:Dummy index|Dummy index]]. | ||
== Notation == | == Notation == | ||
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* [[Ed5/3|7L 2s<5/3>]]: Generator is approximately 4/3 and 4 generators is 8/7. 6:7:8 triad is homologous to minor triad on the known circle of fifths. | * [[Ed5/3|7L 2s<5/3>]]: Generator is approximately 4/3 and 4 generators is 8/7. 6:7:8 triad is homologous to minor triad on the known circle of fifths. | ||
=== Longdiatonic/shortdiatonic === | === Longdiatonic/shortdiatonic === | ||
* | * 2L 1s<4/3> | ||
* [[3L 1s (3/2-equivalent)|3L 1s<3/2>]] | * [[3L 1s (3/2-equivalent)|3L 1s<3/2>]] | ||
* [[6L 1s (8/5-equivalent)|6L 1s<8/5>]]: Dark generator is approximately 3/2 and 4 generators is 6/5. | * [[6L 1s (8/5-equivalent)|6L 1s<8/5>]]: Dark generator is approximately 3/2 and 4 generators is 6/5. | ||