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]].

'''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]].

== 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

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[[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

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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]], [[Marvel temperaments|triton]], [[Augmented family|trisected]], and [[Sensamagic clan|xenia]].
 == 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
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 [[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