Gravity family: Difference between revisions

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The '''gravity family''' tempers out [[graviton]], the 5-limit comma 129140163/128000000 = {{monzo| -13 17 -6 }}. The graviton equals (81/80)<sup>4</sup>/(25/24), so that four 81/80 commas come to a classic chromatic semitone. The generator of gravity temperament is a grave fifth of [[40/27]], and hence the name. It is part of the [[syntonic-chromatic equivalence continuum]], whereby (81/80)<sup>''k''</sup> = 25/24.
The '''gravity family''' tempers out [[graviton]], the 5-limit comma 129140163/128000000 = {{monzo| -13 17 -6 }}. The graviton equals (81/80)<sup>4</sup>/(25/24), so that four 81/80 commas come to a classic chromatic semitone. The generator of gravity temperament is a grave fifth of [[40/27]], and hence the name. It is part of the [[syntonic-chromatic equivalence continuum]], whereby (81/80)<sup>''k''</sup> = 25/24.
Temperaments not discussed here include [[Marvel temperaments #marvo|marvo]].


== Gravity  ==
== Gravity  ==
Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 129140163/128000000
[[Comma list]]: 129140163/128000000


[[Mapping]]: [{{val|1 5 12}}, {{val|0 -6 -17}}]
[[Mapping]]: [{{val| 1 5 12 }}, {{val| 0 -6 -17 }}]


[[POTE generator]]: ~40/27 = 683.156
[[POTE generator]]: ~40/27 = 683.156


{{Val list| 7, 58, 65, 137, 202, 267, 469 }}
{{Val list|legend=1| 7, 37cc, 44c, 51c, 58, 65, 137, 202, 267, 469 }}


[[Badness]]: 0.093184
[[Badness]]: 0.093184


== Harry ==
=== Extensions ===
{{main|Harry}}
Extensions of gravity include harry, gravid and zarvo, considered below, as well as these temperaments discussed elsewhere:
{{see also|Breedsmic temperaments #Harry}}
* ''[[marvo]]'', {225/224, 78125000/78121827} → [[Marvel temperaments #marvo]]
 
== Harry ==
{{main| Harry }}
{{see also| Breedsmic temperaments #Harry }}


Harry temperament can be described as 58&amp;72 temperament, tempering out 7-limit commas 2401/2400 and 19683/19600; 11-limit commas 243/242, 441/440 and 4000/3993, leading to a period of a half octave and a generator of minor semitone tempered between [[21/20]] and [[22/21]]. Harry temperament also equates 14/13 with 27/25 in the 13-limit, 17/16 with 18/17 and 13/11 with 20/17 in the 17-limit.
Harry temperament can be described as 58&amp;72 temperament, tempering out 7-limit commas 2401/2400 and 19683/19600; 11-limit commas 243/242, 441/440 and 4000/3993, leading to a period of a half octave and a generator of minor semitone tempered between [[21/20]] and [[22/21]]. Harry temperament also equates 14/13 with 27/25 in the 13-limit, 17/16 with 18/17 and 13/11 with 20/17 in the 17-limit.
Line 36: Line 38:
[[Badness]]: 0.034077
[[Badness]]: 0.034077


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 49: Line 51:
Badness: 0.015867
Badness: 0.015867


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 62: Line 64:
Badness: 0.013046
Badness: 0.013046


=== 17-limit ===
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Line 75: Line 77:
Badness: 0.012657
Badness: 0.012657


== Gravid ==
== Gravid ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 82: Line 84:
[[Mapping]]: [{{val|1 -1 -5 -14}}, {{val|0 6 17 39}}]
[[Mapping]]: [{{val|1 -1 -5 -14}}, {{val|0 6 17 39}}]


[[Wedgie]]: {{multival|6 17 39 13 45 43}}
{{Multival|legend=1| 6 17 39 13 45 43 }}


[[POTE generator]]: ~27/20 = 517.140
[[POTE generator]]: ~27/20 = 517.140


{{Val list|legend=1| 7d, 58, 65, 123, 181c }}
{{Val list|legend=1| 7d, 44cdd, 51cd, 58, 123, 181c }}


[[Badness]]: 0.131153
[[Badness]]: 0.131153


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 99: Line 101:
POTE generator: ~27/20 = 517.155
POTE generator: ~27/20 = 517.155


Vals: {{Val list| 7d, 58, 65, 123, 181ce }}
Vals: {{Val list| 7d, 44cdde, 51cde, 58, 123, 181ce }}


Badness: 0.047283
Badness: 0.047283


== Zarvo ==
== Zarvo ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 110: Line 112:
[[Mapping]]: [{{val|1 -1 -5 14}}, {{val|0 6 17 -26}}]
[[Mapping]]: [{{val|1 -1 -5 14}}, {{val|0 6 17 -26}}]


[[Wedgie]]: {{multival|6 17 -26 13 -58 -108}}
{{Multival|legend=1| 6 17 -26 13 -58 -108 }}


[[POTE generator]]: ~27/20 = 516.702
[[POTE generator]]: ~27/20 = 516.702


{{Val list|lenegd=1| 7, 65, 72 }}
{{Val list|legend=1| 7, 65, 72, 281d, 353cd, 425bcdd, 497bcdd }}


[[Badness]]: 0.096840
[[Badness]]: 0.096840


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 127: Line 129:
POTE generator: ~27/20 = 516.691
POTE generator: ~27/20 = 516.691


Vals: {{Val list| 7, 65, 72 }}
Vals: {{Val list| 7, 65, 72, 353cd }}


Badness: 0.034773
Badness: 0.034773


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 140: Line 142:
POTE generator: ~27/20 = 516.667
POTE generator: ~27/20 = 516.667


Vals: {{Val list| 7, 65f, 72, 79 }}
Vals: {{Val list| 7, 65f, 72 }}


Badness: 0.027584
Badness: 0.027584


[[Category:Theory]]
[[Category:Regular temperament theory]]
[[Category:Temperament family]]
[[Category:Temperament family]]
[[Category:Gravity]]
[[Category:Gravity]]
[[Category:Gravity family| ]] <!-- main article -->
[[Category:Gravity family| ]] <!-- main article -->
[[Category:Rank 2]]

Revision as of 10:36, 11 June 2021

The gravity family tempers out graviton, the 5-limit comma 129140163/128000000 = [-13 17 -6⟩. The graviton equals (81/80)4/(25/24), so that four 81/80 commas come to a classic chromatic semitone. The generator of gravity temperament is a grave fifth of 40/27, and hence the name. It is part of the syntonic-chromatic equivalence continuum, whereby (81/80)k = 25/24.

Gravity

Subgroup: 2.3.5

Comma list: 129140163/128000000

Mapping: [⟨1 5 12], ⟨0 -6 -17]]

POTE generator: ~40/27 = 683.156

Template:Val list

Badness: 0.093184

Extensions

Extensions of gravity include harry, gravid and zarvo, considered below, as well as these temperaments discussed elsewhere:

Harry

Main article: Harry
See also: Breedsmic temperaments § Harry

Harry temperament can be described as 58&72 temperament, tempering out 7-limit commas 2401/2400 and 19683/19600; 11-limit commas 243/242, 441/440 and 4000/3993, leading to a period of a half octave and a generator of minor semitone tempered between 21/20 and 22/21. Harry temperament also equates 14/13 with 27/25 in the 13-limit, 17/16 with 18/17 and 13/11 with 20/17 in the 17-limit.

Subgroup: 2.3.5.7

Comma list: 2401/2400, 19683/19600

Mapping: [⟨2 4 7 7], ⟨0 -6 -17 -10]]

Wedgie: ⟨⟨ 12 34 20 26 -2 -49 ]]

POTE generator: ~21/20 = 83.156

Template:Val list

Badness: 0.034077

11-limit

Subgroup: 2.3.5.7.11

Comma list: 243/242, 441/440, 4000/3993

Mapping: [⟨2 4 7 7 9], ⟨0 -6 -17 -10 -15]]

POTE generator: ~21/20 = 83.167

Vals: Template:Val list

Badness: 0.015867

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 243/242, 351/350, 441/440, 676/675

Mapping: [⟨2 4 7 7 9 11], ⟨0 -6 -17 -10 -15 -26]]

POTE generator: ~21/20 = 83.116

Vals: Template:Val list

Badness: 0.013046

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 221/220, 243/242, 289/288, 351/350, 441/440

Mapping: [⟨2 4 7 7 9 11 9], ⟨0 -6 -17 -10 -15 -26 -6]]

POTE generator: ~21/20 = 83.168

Vals: Template:Val list

Badness: 0.012657

Gravid

Subgroup: 2.3.5.7

Comma list: 126/125, 1605632/1594323

Mapping: [⟨1 -1 -5 -14], ⟨0 6 17 39]]

Wedgie: ⟨⟨ 6 17 39 13 45 43 ]]

POTE generator: ~27/20 = 517.140

Template:Val list

Badness: 0.131153

11-limit

Subgroup: 2.3.5.7.11

Comma list: 126/125, 243/242, 896/891

Mapping: [⟨1 -1 -5 -14 -3], ⟨0 6 17 39 15]]

POTE generator: ~27/20 = 517.155

Vals: Template:Val list

Badness: 0.047283

Zarvo

Subgroup: 2.3.5.7

Comma list: 4375/4374, 33075/32768

Mapping: [⟨1 -1 -5 14], ⟨0 6 17 -26]]

Wedgie: ⟨⟨ 6 17 -26 13 -58 -108 ]]

POTE generator: ~27/20 = 516.702

Template:Val list

Badness: 0.096840

11-limit

Subgroup: 2.3.5.7.11

Comma list: 243/242, 385/384, 4000/3993

Mapping: [⟨1 -1 -5 14 -3], ⟨0 6 17 -26 15]]

POTE generator: ~27/20 = 516.691

Vals: Template:Val list

Badness: 0.034773

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 169/168, 243/242, 325/324, 385/384

Mapping: [⟨1 -1 -5 14 -3 8], ⟨0 6 17 -26 15 -10]]

POTE generator: ~27/20 = 516.667

Vals: Template:Val list

Badness: 0.027584

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