Gunn: Difference between revisions

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fix technical error (all temperaments in the same family have the same rank; compton family refers to rank-2)
Paly: Moving temperament data
 
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'''Gunn''' is a [[rank-3 temperament]] that tempers out the [[Pythagorean comma]], as well as [[729/728]], [[273/272]], [[153/152]], [[364/363]], and [[1729/1728]]. This temperament is notable for acting as a high-limit map for [[24edo]] or [[72edo]] that tempers out many 19-limit commas such as the [[semitonisma]] and [[sylvisma]]. Furthermore, this temperament tempers out the [[rastma]], so it can be thought of as a very high-limit intersection of compton and rastmic.
'''Gunn''' is a [[fractional-octave temperaments|24th-octave]] [[rank-3 temperament]] that tempers out [[729/728]], [[273/272]], [[153/152]], [[364/363]], and [[1729/1728]]. This temperament is notable for acting as a high-limit map for [[24edo]] or [[72edo]] that tempers out many 19-limit commas such as the [[semitonisma]] and [[sylvisma]]. Furthermore, this temperament tempers out the [[rastma]], so it can be thought of as a very high-limit intersection of compton and rastmic. In addition, it tempers out the [[pythagorean comma]].  


== Technical temperament data ==
''For technical temperament data, go to [[Rastmic rank-3 clan#Gunn]].''
[[Subgroup]]: 2.3.5.7.11.13.17.19
 
[[Comma list]]: 729/728, 273/272, 153/152, 364/363, 1729/1728
 
{{Mapping|legend=1|24 38 48 48 83 108 98 102 | 0 0 1 0 0 0 0 0 | 0 0 0 1 0 -1 0 0 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~33/32 = 50.030{{c}}, ~5/4 = 384.859{{c}}, ~7/4 = 965.679{{c}}
: [[error map]]: {{val| +0.724 -0.809 -0.007 -1.700 +1.185 -2.949 -2.000 +5.563 }}
* [[CWE]]: ~33/32 = 50.000{{c}}, ~5/4 = 384.837{{c}}, ~7/4 = 965.136{{c}}
: error map: {{val| -0.000 -1.955 -1.476 -3.690 -1.318 -5.663 -4.955 2.487 }}
 
Supporting ETs: {{Edos| 24p, 72, 48f, 24c, 24df, 48cf, 48d, 96d, 48cd, 24cdf }}
 
[[Badness]] (Sintel): 3.285


== Paly ==
== Paly ==
Adding the [[syntonic comma]] or the [[schisma]] to the list of commas tempered out results in Paly, a meantone/compton temperament. Notably, this temperament performs much worse with prime 5 than Gunn, likely due to prime 5 being mapped onto the 24edo-ish structure.
Adding the [[syntonic comma]] or the [[schisma]] to the list of commas tempered out results in Paly, a meantone/compton temperament. Notably, this temperament performs much worse with prime 5 than Gunn, likely due to prime 5 being mapped onto the 24edo-ish structure.


=== Technical temperament data ===
''For technical temperament data, go to [[Compton family#Catler]].''
[[Subgroup]]: 2.3.5.7.11.13.17.19
 
[[Comma list]]: 81/80, 91/90, 51/50, 128/125, 76/75, 121/120
 
{{Mapping|legend=1|24 38 56 48 83 108 98 102|0 0 0 1 0 -1 0 0}}
 
[[Optimal tuning]]s:
* [[WE]]: ~33/32 = 49.994{{c}}, ~7/4 = 965.340{{c}}
: [[error map]]: {{val| -0.144 -2.183 +13.350 -3.774 -1.816 -6.516 -5.543 +1.875 }}
* [[CWE]]: ~33/32 = 50.000{{c}}, ~7/4 = 965.449{{c}}
: error map: {{val| -0.000 -1.955 +13.686 -3.377 -1.318 -5.977 -4.955 +2.487 }}
 
Edo join: 24 & 48cf
 
[[Badness]] (Sintel): 2.383


== Etymology ==
== Etymology ==

Latest revision as of 16:44, 10 August 2026

Gunn
Subgroups 2.3.5.7.11.13.17.19
Comma basis 729/728, 273/272, 153/152, 364/363, 1729/1728
Reduced mapping ⟨24; 0 1 0 0 0 0 0; 0 0 1 0 -1 0 0]
ET join 24c & 24 & 72
Generators (CWE) ~33/32 = 50.00 ¢, ~5/4 = 384.84 ¢, ~7/4 = 965.14 ¢
MOS scales n/a
Ploidacot n/a
Minimax error -odd-limit:  ¢
Target scale size -odd-limit: notes

Gunn is a 24th-octave rank-3 temperament that tempers out 729/728, 273/272, 153/152, 364/363, and 1729/1728. This temperament is notable for acting as a high-limit map for 24edo or 72edo that tempers out many 19-limit commas such as the semitonisma and sylvisma. Furthermore, this temperament tempers out the rastma, so it can be thought of as a very high-limit intersection of compton and rastmic. In addition, it tempers out the pythagorean comma.

For technical temperament data, go to Rastmic rank-3 clan#Gunn.

Paly

Adding the syntonic comma or the schisma to the list of commas tempered out results in Paly, a meantone/compton temperament. Notably, this temperament performs much worse with prime 5 than Gunn, likely due to prime 5 being mapped onto the 24edo-ish structure.

For technical temperament data, go to Compton family#Catler.

Etymology

The name is coined after the name of User:Zeta Function's former high school. In addition, its high complexity also accurately reflects the nerdy nature of Gunn HS and stands in contrast to the simplicity of Compton. The name of Paly is derived from Palo Alto High School, the other high school in Palo Alto.