Gravity: Difference between revisions
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| Title = Gravity; Larry | | Title = Gravity; Larry | ||
| Subgroups = 2.3.5, 2.3.5.11 | | Subgroups = 2.3.5, 2.3.5.11 | ||
| Comma basis = [[129140163/128000000]] (2.3.5); <br> [[243/242]], [[4000/3993]] (2.3.5.11) | | Comma basis = [[129140163/128000000]] (2.3.5); <br>[[243/242]], [[4000/3993]] (2.3.5.11) | ||
| Edo join 1 = 7 | Edo join 2 = 58 | | Edo join 1 = 7 | Edo join 2 = 58 | ||
| Mapping = 1; 6 17 15 | | Mapping = 1; 6 17 15 | ||
| Generators = 27/20 | Generators tuning = 516.8 | Optimization method = CWE | |||
| MOS scales = [[2L 5s]], [[7L 2s]], [[7L 9s]], …, [[7L 51s]] | |||
| Pergen = (P8, P19/6) | | Pergen = (P8, P19/6) | ||
| Color name = Lala-tribiguti | | Color name = Lala-tribiguti | ||
| Odd limit 1 = 5 | Mistuning 1 = 0.90 | Complexity 1 = 23 | | Odd limit 1 = 5 | Mistuning 1 = 0.90 | Complexity 1 = 23 | ||
| Odd limit 2 = | | Odd limit 2 = 2.3.5.11 15 | Mistuning 2 = 1.48 | Complexity 2 = 30 | ||
}} | }} | ||
'''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 [[6/1|6th harmonic]] (which octave reduces to the perfect fifth, [[3/2]]), dividing the fifth in two and the fourth in three. The [[5/1|5th harmonic]] is found at three perfect fifths up and one generator down, or 17 generators in total, thereby tempering out the [[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 follows. | |||
Gravity is most naturally seen as a [[2.3.5.11 subgroup|2.3.5.11-subgroup]] temperament, sometimes known as '''larry'''. Here [[8019/8000]] ([[S-expression|S9/S10]]) is tempered out, so that two intervals of 40/27 reach [[11/10]], and [[4000/3993]] ([[S-expression|S10/S11]]) 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 [[81/80]] ({{S|9}}), [[100/99]] ({{S|10}}), and [[121/120]] ({{S|11}}). 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]]. | ||
For technical data, see [[Gravity family #Gravity]]. | |||
== Intervals == | == Intervals == | ||
[[File:Gravity construction.png|thumb|right|alt=Gravity construction.png|A pictorial representation of the process of constructing the heptatonic mos of 2.3.5.11 gravity. Splitting 3/2 in two and splitting 4/3 in three are equivalent to splitting 6/1 in six, and Gravity[7] is equivalent to the scale obtained by octave-reducing [[6ed6]].|960x320px]] | |||
=== Interval chain === | === Interval chain === | ||
In the following table, odd | In the following table, [[odd harmonic]]s 1–15 are labeled in '''bold'''. | ||
{| class="wikitable sortable center-1 right-2" | {| class="wikitable sortable center-1 right-2" | ||
! | ! # | ||
! Cents* | ! Cents* | ||
! class="unsortable" | Approximate ratios | ! class="unsortable" | Approximate ratios | ||
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| '''15/8''' | | '''15/8''' | ||
|} | |} | ||
<nowiki />* In 2.3.5.11-subgroup [[CTE tuning]] | <nowiki/>* In 2.3.5.11-subgroup [[CTE tuning]] | ||
=== As a detempering of 7et === | === As a detempering of 7et === | ||
{{ | {{Todo|inline=1|complete section|comment = Add detempering info.}} | ||
== Tunings == | == Tunings == | ||
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=== Tuning spectrum === | === Tuning spectrum === | ||
{| class="wikitable center-all left-4" | {| class="wikitable center-all left-4" | ||
! | ! Edo<br>generator | ||
! [[Eigenmonzo|Eigenmonzo<br>(unchanged interval)]]* | ! [[Eigenmonzo|Eigenmonzo<br>(unchanged interval)]]* | ||
! Generator (¢) | ! Generator (¢) | ||
| Line 185: | Line 180: | ||
| [[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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| | | | ||
| '''520.0000''' | | '''520.0000''' | ||
| 30bccee val, '''upper bound of | | 30bccee val, '''upper bound of 2.3.5.11 11- and 15-odd-limit diamond monotone''' | ||
|- | |- | ||
| '''[[23edo|10\23]]''' | | '''[[23edo|10\23]]''' | ||
| | | | ||
| '''521.7391''' | | '''521.7391''' | ||
| 23bcccee val, '''upper bound of | | 23bcccee val, '''upper bound of 2.3.5 5- and 9-odd-limit diamond monotone''' | ||
|} | |} | ||
<nowiki/>* Besides the octave | <nowiki/>* Besides the octave | ||