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 [[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 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]]), dividing the fifth in two and the fourth in three. The 5th harmonic is found at three perfect fifths up and one generator down, or 17 generators in total, thereby tempering out the [[129140163/128000000|graviton]] ([[ratio]]: 129140163/128000000, {{monzo|legend=1| -13 17 -6 }}); The complement of the acute fourth generator 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 [[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 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]]), dividing the fifth in two and the fourth in three. The 5th harmonic is found at three perfect fifths up and one generator down, or 17 generators in total, thereby tempering out the [[129140163/128000000|graviton]] ([[ratio]]: 129140163/128000000, {{monzo|legend=1| -13 17 -6 }}); The complement of the acute fourth generator 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.