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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 = ? | Complexity 1 = 37
| Odd limit 1 = 5 | Mistuning 1 = 0.90 | Complexity 1 = 37
| Odd limit 2 = (2.3.5.11) 15 | Mistuning 2 = ? | Complexity 2 = 51
| 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 [[40/27|classical grave fifth (40/27)]], six of which stacked reach the interval class of [[4/3]], 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 [[square superparticular#Sk/S(k + 1) (ultraparticulars)|S9/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 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]].  
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]].


For technical data, see [[Gravity family #Gravity]].  
{{tdlink|Gravity family #Gravity}}
 
 
[[File:Gravity_construction.png|alt=Gravity construction.png|960x320px]]
 
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]].


== Intervals ==
== Intervals ==
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== Tunings ==
== Tunings ==
{{todo|add tuning spectrum|inline=1}}
[[File:Gravity tuning spectrum.png|thumb|alt=Gravity.png|600x560px|A chart of the tuning spectrum of gravity, showing the offsets of prime harmonics 3, 5, and 11, and odds 9 and 15, as a function of the generator; all edo tunings are shown with vertical lines whose length indicates the edo's tolerance, i.e. half of its step size in either direction of just, and some small edos supporting the temperament are labeled.]]
 
=== Tuning spectrum ===
{| class="wikitable center-all left-4"
! EDO<br>generator
! [[Eigenmonzo|Eigenmonzo<br>(unchanged interval)]]*
! Generator (¢)
! Comments
|-
| '''[[7edo|3\7]]'''
|
| '''514.2857'''
| '''Lower bound of 5- to 15-odd-limit diamond monotone'''
|-
|
| [[11/9]]
| 515.8026
|
|-
| [[79edo|34\79]]
|
| 516.4557
|
|-
|
| [[10/9]]
| 516.4807
| 1/5-comma
|-
|
| [[11/6]]
| 516.5959
|
|-
| [[72edo|31\72]]
|
| 516.6667
|
|-
| [[209edo|90\209]]
|
| 516.7464
|
|-
|
| [[11/8]]
| 516.7545
| (2.3.5.11) 11-odd-limit minimax tuning
|-
|
| [[5/3]]
| 516.7599
| 2/11-comma, (2.3.5.11) 15-odd-limit minimax tuning
|-
| [[137edo|59\137]]
|
| 516.7883
|
|-
|
| [[25/24]]
| 516.8097
| 5/28-comma
|-
| [[202edo|87\202]]
|
| 516.8317
|
|-
|
| [[5/4]]
| 516.8420
| 3/17-comma, 5- and 9-odd-limit minimax tuning
|-
| [[267edo|115\267]]
|
| 516.8539
|
|-
|
| [[15/8]]
| 516.8812
| 4/23-comma
|-
| [[65edo|28\65]]
|
| 516.9231
|
|-
|
| [[3/2]]
| 516.9925
| 1/6-comma
|-
| [[123edo|53\123]]
|
| 517.0732
|
|-
|
| [[15/11]]
| 517.1188
|
|-
| [[58edo|25\58]]
|
| 517.2414
|
|-
|
| [[20/11]]
| 517.4979
|
|-
| [[51edo|22\51]]
|
| 517.6471
| 51ce val
|-
|
| [[27/20]]
| 519.5513
| Untempered tuning
|-
| '''[[30edo|13\30]]'''
|
| '''520.0000'''
| 30bccee val, '''upper bound of (2.3.5.11) 11- and 15-odd-limit diamond monotone'''
|-
| '''[[23edo|10\23]]'''
|
| '''521.7391'''
| 23bcccee val, '''upper bound of (2.3.5) 5- and 9-odd-limit diamond monotone'''
|}
<nowiki/>* Besides the octave


[[Category:Temperaments]]
[[Category:Gravity| ]] <!-- Main article -->
[[Category:Gravity| ]] <!-- Main article -->
[[Category:Rank-2 temperaments]]
[[Category:Gravity family]]
[[Category:Gravity family]]
Retrieved from "https://en.xen.wiki/w/Gravity"