Gravity: Difference between revisions

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'''Gravity''' is a [[rank-2 temperament|rank-2]] [[regular temperament|temperament]] and parent of the [[gravity family]], [[generator|generated]] by a [[40/27|classical ~~grave fifth~~ (40/27)]], six of which stacked reach the interval ~~class of~~ [[4/3]] ~~(three octaves up~~), and thereby characterized by the vanishing of the [[129140163/128000000|graviton]] ([[ratio]]: 129140163/128000000, {{monzo|legend=1| -13 17 -6 }}).

'''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 {{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.

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-'''Gravity''' is a [[rank-2 temperament|rank-2]] [[regular temperament|temperament]] and parent of the [[gravity family]], [[generator|generated]] by a [[40/27|classical grave fifth (40/27)]], six of which stacked reach the interval class of [[4/3]] (three octaves up), and thereby characterized by the vanishing of the [[129140163/128000000|graviton]] ([[ratio]]: 129140163/128000000, {{monzo|legend=1| -13 17 -6 }}).
+'''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 {{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.