Gunn

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 0 1 0 0 0 0 0; 0 0 0 1 0 -1 0 0]
ET join	24c & 24 & 72
Generators (CWE)	~33/32 = 50.000 ¢, ~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 temperament is a rank-3 temperament in the Compton family 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.

Technical temperament data

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 729/728, 273/272, 153/152, 364/363, 1729/1728

Mapping: [⟨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 tunings:

• WE: ~33/32 = 50.030 ¢, ~5/4 = 384.859 ¢, ~7/4 = 965.679 ¢

error map: ⟨+0.724 -0.809 -0.007 -1.700 +1.185 -2.949 -2.000 +5.563]

• CWE: ~33/32 = 50.000 ¢, ~5/4 = 384.837 ¢, ~7/4 = 965.136 ¢

error map: ⟨-0.000 -1.955 -1.476 -3.690 -1.318 -5.663 -4.955 2.487]

Optimal ET sequence: 24p, 72, 48f, 24c, 24df, 48cf, 48d, 96d, 48cd, 24cdf

Badness (Sintel): 3.285

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.

Technical temperament data

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 81/80, 91/90, 51/50, 128/125, 76/75, 121/120

Mapping: [⟨24 38 56 48 83 108 98 102], ⟨0 0 0 1 0 -1 0 0]]

Optimal tunings:

• WE: ~33/32 = 49.994 ¢, ~7/4 = 965.340 ¢

error map: ⟨-0.144 -2.183 +13.350 -3.774 -1.816 -6.516 -5.543 +1.875]

• CWE: ~33/32 = 50.000 ¢, ~7/4 = 965.449 ¢

error map: ⟨-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

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.