User:Overthink/Draft edits: Difference between revisions

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Aside from harmony, it also preserves the melodic resources of 12edo, containing minor and major seconds and thirds. However, it adds several new intervals, including neutral seconds and thirds, so new melodies can be written in 24edo that aren't possible in 12edo. This also means 24edo contains new scales, most notably the neutralized diatonic [[3L 4s]] [[MOS]] with step pattern LssLsLs, where L is a major second and s is a neutral second. These scales also contain chords unfamiliar to 12edo, such as the [[neutral tetrad]].

While the 7th harmonic is poorly tuned, the intervals 24edo has do serve as reasonable substitutes to 7-limit intervals melodically, though it equates [[7/6]] with [[8/7]] due to vanishing of [[49/48]], leading to [[semaphore]]. Nonetheless, scales of semaphore are quite interesting, especially the 9-note [[5L 4s]] MOS. A supermajor chord is available as [0 9 14], and a subminor chord as [0 5 14], though they're better described as ultramajor and inframinor, being interpreted much more accurately as [[10:13:15]] and [[26:30:39|1/(10:13:15)]] respectively. These chords are relatively simple and may serve as alternatives to the regular [[4:5:6]] and [[10:12:15|1/(4:5:6)]] triads as bases for harmony; see [[Extraclassical tonality]].

While the 7th harmonic is poorly tuned, the intervals 24edo has do serve as reasonable substitutes to 7-limit intervals melodically, though it equates [[7/6]] with [[8/7]] due to vanishing of [[49/48]], leading to [[semaphore]]. Nonetheless, scales of semaphore are quite interesting, especially the 9-note [[5L 4s]] MOS. A supermajor chord is available as [0 9 14], and a subminor chord as [0 5 14], though they're better described as ultramajor and inframinor, being interpreted much more accurately as [[10:13:15]] and [[26:30:39|1/(10:13:15)]] respectively, the corresponding temperament being [[barbados]], the 2.3.13/5 temperament tempering out 676/675. These chords are relatively simple and may serve as alternatives to the regular [[4:5:6]] and [[10:12:15|1/(4:5:6)]] triads as bases for harmony; see [[Extraclassical tonality]].

A notable superset of 24edo is [[72edo]], which has good approximations up to the [[19-limit]], and especially the [[11-limit]]. The tunings supplied by [[72edo]] cannot be used for all low-limit just intervals, but they can be used on the 17-limit [[k*N subgroups|3*24 subgroup]] 2.3.125.35.11.325.17.19, making some of the excellent approximations of 72 available in 24edo. Chords based on this subgroup afford considerable scope for harmony, including in particular intervals and chords using only 2, 3, 11, 17, and 19. One will find that 24edo is consistent in the no-7s 19-odd-limit, though the 2.3.11.17.19 [[subgroup]] is where it is the most accurate.

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 Aside from harmony, it also preserves the melodic resources of 12edo, containing minor and major seconds and thirds. However, it adds several new intervals, including neutral seconds and thirds, so new melodies can be written in 24edo that aren't possible in 12edo. This also means 24edo contains new scales, most notably the neutralized diatonic [[3L 4s]] [[MOS]] with step pattern LssLsLs, where L is a major second and s is a neutral second. These scales also contain chords unfamiliar to 12edo, such as the [[neutral tetrad]].
-While the 7th harmonic is poorly tuned, the intervals 24edo has do serve as reasonable substitutes to 7-limit intervals melodically, though it equates [[7/6]] with [[8/7]] due to vanishing of [[49/48]], leading to [[semaphore]]. Nonetheless, scales of semaphore are quite interesting, especially the 9-note [[5L 4s]] MOS. A supermajor chord is available as [0&nbsp;9&nbsp;14], and a subminor chord as [0&nbsp;5&nbsp;14], though they're better described as ultramajor and inframinor, being interpreted much more accurately as [[10:13:15]] and [[26:30:39|1/(10:13:15)]] respectively. These chords are relatively simple and may serve as alternatives to the regular [[4:5:6]] and [[10:12:15|1/(4:5:6)]] triads as bases for harmony; see [[Extraclassical tonality]].
+While the 7th harmonic is poorly tuned, the intervals 24edo has do serve as reasonable substitutes to 7-limit intervals melodically, though it equates [[7/6]] with [[8/7]] due to vanishing of [[49/48]], leading to [[semaphore]]. Nonetheless, scales of semaphore are quite interesting, especially the 9-note [[5L 4s]] MOS. A supermajor chord is available as [0&nbsp;9&nbsp;14], and a subminor chord as [0&nbsp;5&nbsp;14], though they're better described as ultramajor and inframinor, being interpreted much more accurately as [[10:13:15]] and [[26:30:39|1/(10:13:15)]] respectively, the corresponding temperament being [[barbados]], the 2.3.13/5 temperament tempering out 676/675. These chords are relatively simple and may serve as alternatives to the regular [[4:5:6]] and [[10:12:15|1/(4:5:6)]] triads as bases for harmony; see [[Extraclassical tonality]].
 A notable superset of 24edo is [[72edo]], which has good approximations up to the [[19-limit]], and especially the [[11-limit]]. The tunings supplied by [[72edo]] cannot be used for all low-limit just intervals, but they can be used on the 17-limit [[k*N subgroups|3*24&nbsp;subgroup]] 2.3.125.35.11.325.17.19, making some of the excellent approximations of 72 available in 24edo. Chords based on this subgroup afford considerable scope for harmony, including in particular intervals and chords using only 2, 3, 11, 17, and 19. One will find that 24edo is consistent in the no-7s 19-odd-limit, though the 2.3.11.17.19 [[subgroup]] is where it is the most accurate.