Gravity: Difference between revisions
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| Pergen = (P8, P19/6) | | Pergen = (P8, P19/6) | ||
| Color name = Lala-tribiguti | | Color name = Lala-tribiguti | ||
| Odd limit 1 = 5 | Mistuning 1 = | | Odd limit 1 = 5 | Mistuning 1 = 0.90 | Complexity 1 = 37 | ||
| Odd limit 2 = (2.3.5.11) 15 | Mistuning 2 = | | Odd limit 2 = (2.3.5.11) 15 | Mistuning 2 = 1.48 | Complexity 2 = 51 | ||
}} | }} | ||
'''Gravity''' is a [[rank-2 temperament|rank-2]] [[regular temperament|temperament]] and parent of the [[gravity family]], [[generator|generated]] by a [[ | '''Gravity''' is a [[rank-2 temperament|rank-2]] [[regular temperament|temperament]] and parent of the [[gravity family]], [[generator|generated]] by a [[27/20|classical acute fourth (27/20)]], six of which stacked reach the interval [[6/1]] (which octave reduces to the perfect fifth, [[3/2]]), and thereby characterized by the vanishing of the [[129140163/128000000|graviton]] ([[ratio]]: 129140163/128000000, {{monzo|legend=1| -13 17 -6 }}); the 5th harmonic is found at three perfect fifths up and one generator down, or 17 generators in total. The complement of the acute fourth is the grave fifth, [[40/27]], whence the temperament's name. | ||
Gravity is most naturally seen as a [[2.3.5.11 subgroup]] temperament, sometimes known as '''larry'''. Here | Gravity is most naturally seen as a [[2.3.5.11 subgroup]] temperament, sometimes known as '''larry'''. Here {{S|9/S10}} = [[8019/8000]] is tempered out, so that two intervals of 40/27 reach [[11/10]], and S10/S11 = [[4000/3993]] is tempered out, so that three intervals of 11/10 reach 4/3. These equivalences also imply that [[243/242]] is tempered out; three 27/20 fourths reach [[11/9]], which is thus equated to [[27/22]] and acts as an exact neutral third. Gravity's generator lies close to the fifth of [[7edo]], implying that the [[MOS scale]]s of gravity [[cluster temperament|cluster]] heavily around 7edo, and in this interpretation the comma reached after 7 generators simultaneously represents S9 = [[81/80]], S10 = [[100/99]], and S11 = [[121/120]]. In fact, gravity can be completely defined by making this equivalence between three adjacent square superparticulars, being the most accurate of the 5 temperaments definable in such a way. | ||
Strong extensions with prime 7 include [[gravid]] (58 & 65), 58 & 65d, [[marvo]] (65d & 72), and [[zarvo]] (65 & 72). However, the most notable extension of gravity is [[harry]] (58 & 72), which splits the octave in two and extends well to the 13- and [[17-limit]]. | Strong extensions with prime 7 include [[gravid]] (58 & 65), 58 & 65d, [[marvo]] (65d & 72), and [[zarvo]] (65 & 72). However, the most notable extension of gravity is [[harry]] (58 & 72), which splits the octave in two and extends well to the 13- and [[17-limit]]. | ||
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| [[11/8]] | | [[11/8]] | ||
| 516.7545 | | 516.7545 | ||
| | | (2.3.5.11) 11-odd-limit minimax tuning | ||
|- | |- | ||
| | | | ||
| [[5/3]] | | [[5/3]] | ||
| 516.7599 | | 516.7599 | ||
| 2/11-comma | | 2/11-comma, (2.3.5.11) 15-odd-limit minimax tuning | ||
|- | |- | ||
| [[137edo|59\137]] | | [[137edo|59\137]] | ||
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| 516.8097 | | 516.8097 | ||
| 5/28-comma | | 5/28-comma | ||
|- | |- | ||
| [[202edo|87\202]] | | [[202edo|87\202]] | ||
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| [[5/4]] | | [[5/4]] | ||
| 516.8420 | | 516.8420 | ||
| 3/17-comma | | 3/17-comma, 5- and 9-odd-limit minimax tuning | ||
|- | |- | ||
| [[267edo|115\267]] | | [[267edo|115\267]] | ||
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<nowiki/>* Besides the octave | <nowiki/>* Besides the octave | ||
[[Category:Gravity| ]] <!-- Main article --> | [[Category:Gravity| ]] <!-- Main article --> | ||
[[Category:Rank-2 temperaments]] | [[Category:Rank-2 temperaments]] | ||
[[Category:Gravity family]] | [[Category:Gravity family]] | ||