Keegic temperaments: Difference between revisions

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Keegic rank-two temperaments temper out the keega, {{monzo|-3 1 -3 3}} = 1029/1000, the difference three [[7/5]]s and perfect eleventh [[8/3]].
{{Technical data page}}
'''Keegic''' [[rank two temperament]]s temper out the keega, {{monzo|-3 1 -3 3}} = 1029/1000, the difference three [[7/5]]s and perfect eleventh [[8/3]].


Temperaments discussed elsewhere include [[Very low accuracy temperaments|antitonic]], [[Trienstonic clan|kangaroo]], [[Kleismic family|keemun]], [[Meantone family|liese]], [[Archytas clan|progress]], [[Mint temperaments|subklei]], and [[Marvel temperaments|triton]].
Temperaments discussed elsewhere include [[Very low accuracy temperaments|antitonic]], [[Trienstonic clan|kangaroo]], [[Kleismic family|keemun]], [[Meantone family|liese]], [[Archytas clan|progress]], [[Mint temperaments|subklei]], and [[Marvel temperaments|triton]].


== Aurora ==
== Aurora ==
The ''aurora'' temperament (13&amp;21) is very strongly related to the '''[[Logarithmic phi|golden father tuning]]''' (generator: <math>\frac{3-\sqrt{5}}{2}</math> octave = 458.3592135001 cents). It has a temperament structure superficially similar to [[Father family|father]], with extremely flat fourths (sub-fourths/ultra-major third) or sharp fifths (super-fifths/ultra-minor sixths). However, unlike father, 12 of these bad fourths reach a more in tune fifth, which is useful for creating resolutions when using a large enough gamut, such as the [[13L 8s]] MOS which has two good major &amp; minor chords.
: ''For the 5-limit version, see [[Diaschismic–gothmic equivalence continuum #Goldis]].''
 
The ''aurora'' temperament ({{nowrap| 13 & 21 }}) is very strongly related to the [[Logarithmic phi|golden oneirotonic tuning]] (generator: {{nowrap| (3 - sqrt(5))/2 }} octave = 458.3592135001 cents). It has a temperament structure superficially similar to [[father]], with extremely flat fourths (sub-fourths/ultra-major third) or sharp fifths (super-fifths/ultra-minor sixths). However, unlike father, 12 of these bad fourths reach a more in tune fifth, which is useful for creating resolutions when using a large enough gamut, such as the [[13L 8s]] mos which has two good major & minor chords.


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
Line 11: Line 14:


[[Mapping]]: [{{val|1 -3 5 7}}, {{val|0 12 -7 -11}}]
[[Mapping]]: [{{val|1 -3 5 7}}, {{val|0 12 -7 -11}}]
{{Multival|legend=1|12 -7 -11 -39 -51 -6}}


[[POTE generator]]: ~21/16 = 458.348
[[POTE generator]]: ~21/16 = 458.348


{{Val list|legend=1| 8bd, 13, 21, 34, 55, 89d, 144cdd }}
{{Optimal ET sequence|legend=1| 8bd, 13, 21, 34, 55, 89d, 144cdd }}


[[Badness]]: 0.242134
[[Badness]]: 0.242134
Line 29: Line 30:
POTE generator: ~21/16 = 458.413
POTE generator: ~21/16 = 458.413


Optimal GPV sequence: {{Val list| 8bd, 13, 21, 34, 55e, 89dee }}
{{Optimal ET sequence|legend=1| 8bd, 13, 21, 34, 55e, 89dee }}


Badness: 0.116654
Badness: 0.116654
Line 42: Line 43:
POTE generator: ~13/10 = 458.444
POTE generator: ~13/10 = 458.444


Optimal GPV sequence: {{Val list| 8bd, 13, 21, 34, 55e, 89deef }}
{{Optimal ET sequence|legend=1| 8bd, 13, 21, 34, 55e, 89deef }}


Badness: 0.066541
Badness: 0.066541
Line 55: Line 56:
POTE generator: ~13/10 = 458.444
POTE generator: ~13/10 = 458.444


Optimal GPV sequence: {{Val list| 8bd, 13, 21, 34, 55e, 89deef }}
{{Optimal ET sequence|legend=1| 8bd, 13, 21, 34, 55e, 89deef }}


Badness: 0.044148
Badness: 0.044148
Line 68: Line 69:
POTE generator: ~13/10 = 458.444
POTE generator: ~13/10 = 458.444


Optimal GPV sequence: {{Val list| 8bd, 13, 21, 34, 55eh, 89deefhh }}
{{Optimal ET sequence|legend=1| 8bd, 13, 21, 34, 55eh, 89deefhh }}


Badness: 0.037621
Badness: 0.037621
Line 81: Line 82:
POTE generator: ~13/10 = 458.430
POTE generator: ~13/10 = 458.430


Optimal GPV sequence: {{Val list| 8bd, 13, 21, 34, 55eh, 89deefhh }}
{{Optimal ET sequence|legend=1| 8bd, 13, 21, 34, 55eh, 89deefhh }}


Badness: 0.030236
Badness: 0.030236


[[Category:Temperament collection]]
=== 29-limit ===
[[Category:Mirwomo]]
Subgroup: 2.3.5.7.11.13.17.19.23.29
 
Comma list: 56/55, 76/75, 105/104, 116/115, 145/143, 161/160, 170/169, 221/220
 
Mapping: [{{val|1 -3 5 7 5 6 6 5 3 6}}, {{val|0 12 -7 -11 -4 -6 -5 -2 4 -3}}]
 
POTE generator: ~13/10 = 458.426
 
{{Optimal ET sequence|legend=1| 8bd, 13, 21, 34, 55eh, 89deefhh }}
 
Badness: 0.025201
 
[[Category:Temperament collections]]
[[Category:Pages with mostly numerical content]]
[[Category:Keegic]]
[[Category:Rank 2]]
[[Category:Rank 2]]

Latest revision as of 00:37, 24 June 2025

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

Keegic rank two temperaments temper out the keega, [-3 1 -3 3 = 1029/1000, the difference three 7/5s and perfect eleventh 8/3.

Temperaments discussed elsewhere include antitonic, kangaroo, keemun, liese, progress, subklei, and triton.

Aurora

For the 5-limit version, see Diaschismic–gothmic equivalence continuum #Goldis.

The aurora temperament (13 & 21) is very strongly related to the golden oneirotonic tuning (generator: (3 - sqrt(5))/2 octave = 458.3592135001 cents). It has a temperament structure superficially similar to father, with extremely flat fourths (sub-fourths/ultra-major third) or sharp fifths (super-fifths/ultra-minor sixths). However, unlike father, 12 of these bad fourths reach a more in tune fifth, which is useful for creating resolutions when using a large enough gamut, such as the 13L 8s mos which has two good major & minor chords.

Subgroup: 2.3.5.7

Comma list: 1029/1000, 28672/28125

Mapping: [1 -3 5 7], 0 12 -7 -11]]

POTE generator: ~21/16 = 458.348

Optimal ET sequence8bd, 13, 21, 34, 55, 89d, 144cdd

Badness: 0.242134

11-limit

Subgroup: 2.3.5.7.11

Comma list: 56/55, 1029/1000, 5632/5625

Mapping: [1 -3 5 7 5], 0 12 -7 -11 -4]]

POTE generator: ~21/16 = 458.413

Optimal ET sequence8bd, 13, 21, 34, 55e, 89dee

Badness: 0.116654

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 56/55, 105/104, 512/507, 637/625

Mapping: [1 -3 5 7 5 6], 0 12 -7 -11 -4 -6]]

POTE generator: ~13/10 = 458.444

Optimal ET sequence8bd, 13, 21, 34, 55e, 89deef

Badness: 0.066541

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 56/55, 105/104, 170/169, 221/220, 375/374

Mapping: [1 -3 5 7 5 6 6], 0 12 -7 -11 -4 -6 -5]]

POTE generator: ~13/10 = 458.444

Optimal ET sequence8bd, 13, 21, 34, 55e, 89deef

Badness: 0.044148

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 56/55, 76/75, 105/104, 170/169, 190/187, 221/220

Mapping: [1 -3 5 7 5 6 6 5], 0 12 -7 -11 -4 -6 -5 -2]]

POTE generator: ~13/10 = 458.444

Optimal ET sequence8bd, 13, 21, 34, 55eh, 89deefhh

Badness: 0.037621

23-limit

Subgroup: 2.3.5.7.11.13.17.19.23

Comma list: 56/55, 76/75, 105/104, 161/160, 170/169, 190/187, 221/220

Mapping: [1 -3 5 7 5 6 6 5 3], 0 12 -7 -11 -4 -6 -5 -2 4]]

POTE generator: ~13/10 = 458.430

Optimal ET sequence8bd, 13, 21, 34, 55eh, 89deefhh

Badness: 0.030236

29-limit

Subgroup: 2.3.5.7.11.13.17.19.23.29

Comma list: 56/55, 76/75, 105/104, 116/115, 145/143, 161/160, 170/169, 221/220

Mapping: [1 -3 5 7 5 6 6 5 3 6], 0 12 -7 -11 -4 -6 -5 -2 4 -3]]

POTE generator: ~13/10 = 458.426

Optimal ET sequence8bd, 13, 21, 34, 55eh, 89deefhh

Badness: 0.025201