3.5 subgroup: Difference between revisions

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As it is a [[rank-2]] system, stacking 5/3 with tritave-reduction can produce [[MOS scale]]s, just like how Pythagorean tuning famously produces one variation of pentatonic, diatonic and chromatic scales.

The non-trivial MOS scales that are produced are: [[2L 1s (3/1-equivalent)|2L 1s<3/1>]], [[2L 3s (3/1-equivalent)|2L 3s<3/1>]], [[2L 5s (3/1-equivalent))|2L 5s<3/1>]], [[2L 7s (3/1-equivalent)|2L 7s<3/1>]], [[2L 9s (3/1-equivalent)|2L 9s<3/1>]], [[2L 11s (3/1-equivalent)|2L 11s<3/1>]], [[13L 2s (3/1-equivalent)|13L 2s<3/1>]], [[15L 13s (3/1-equivalent)|15L 13s<3/1>]], [[28L 15s (3/1-equivalent)|28L 15s<3/1>]]. Probably the most practical scales are the 11-note (2L 9s), 13-note (2L 11s), and 15-note (13L 2s) scales. The reason for all of the 2L scales is because 5/3 (884 cents) is quite near √3 (951 cents), a fact which is ~~realized by~~ the [[bug]] temperament.

The non-trivial MOS scales that are produced are: [[2L 1s (3/1-equivalent)|2L 1s<3/1>]], [[2L 3s (3/1-equivalent)|2L 3s<3/1>]], [[2L 5s (3/1-equivalent))|2L 5s<3/1>]], [[2L 7s (3/1-equivalent)|2L 7s<3/1>]], [[2L 9s (3/1-equivalent)|2L 9s<3/1>]], [[2L 11s (3/1-equivalent)|2L 11s<3/1>]], [[13L 2s (3/1-equivalent)|13L 2s<3/1>]], [[15L 13s (3/1-equivalent)|15L 13s<3/1>]], [[28L 15s (3/1-equivalent)|28L 15s<3/1>]]. Probably the most practical scales are the 11-note (2L 9s), 13-note (2L 11s), and 15-note (13L 2s) scales. The reason for all of the 2L scales is because 5/3 (884 cents) is quite near √3 (951 cents), a fact which is actually connected to the [[bug]] temperament.

Revision as of 04:49, 19 September 2026 view source CompactStar (talk \| contribs) autopatrolled 5,182 edits No edit summary ← Older edit		Revision as of 04:49, 19 September 2026 view source CompactStar (talk \| contribs) autopatrolled 5,182 edits No edit summary Newer edit →
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	As it is a [[rank-2]] system, stacking 5/3 with tritave-reduction can produce [[MOS scale]]s, just like how Pythagorean tuning famously produces one variation of pentatonic, diatonic and chromatic scales.		As it is a [[rank-2]] system, stacking 5/3 with tritave-reduction can produce [[MOS scale]]s, just like how Pythagorean tuning famously produces one variation of pentatonic, diatonic and chromatic scales.

	The non-trivial MOS scales that are produced are: [[2L 1s (3/1-equivalent)\|2L 1s<3/1>]], [[2L 3s (3/1-equivalent)\|2L 3s<3/1>]], [[2L 5s (3/1-equivalent))\|2L 5s<3/1>]], [[2L 7s (3/1-equivalent)\|2L 7s<3/1>]], [[2L 9s (3/1-equivalent)\|2L 9s<3/1>]], [[2L 11s (3/1-equivalent)\|2L 11s<3/1>]], [[13L 2s (3/1-equivalent)\|13L 2s<3/1>]], [[15L 13s (3/1-equivalent)\|15L 13s<3/1>]], [[28L 15s (3/1-equivalent)\|28L 15s<3/1>]]. Probably the most practical scales are the 11-note (2L 9s), 13-note (2L 11s), and 15-note (13L 2s) scales. The reason for all of the 2L scales is because 5/3 (884 cents) is quite near √3 (951 cents), a fact which is ~~realized by~~ the [[bug]] temperament.		The non-trivial MOS scales that are produced are: [[2L 1s (3/1-equivalent)\|2L 1s<3/1>]], [[2L 3s (3/1-equivalent)\|2L 3s<3/1>]], [[2L 5s (3/1-equivalent))\|2L 5s<3/1>]], [[2L 7s (3/1-equivalent)\|2L 7s<3/1>]], [[2L 9s (3/1-equivalent)\|2L 9s<3/1>]], [[2L 11s (3/1-equivalent)\|2L 11s<3/1>]], [[13L 2s (3/1-equivalent)\|13L 2s<3/1>]], [[15L 13s (3/1-equivalent)\|15L 13s<3/1>]], [[28L 15s (3/1-equivalent)\|28L 15s<3/1>]]. Probably the most practical scales are the 11-note (2L 9s), 13-note (2L 11s), and 15-note (13L 2s) scales. The reason for all of the 2L scales is because 5/3 (884 cents) is quite near √3 (951 cents), a fact which is actually connected to the [[bug]] temperament.