Garischismic clan

The garischismic clan of temperaments tempers out the garischisma, [25 -14 0 -1⟩ = 33554432/33480783. The head of this clan is gary, which is generated by a perfect fifth. Two apotomes i.e. 14 fifths octave reduced make a septimal major second (8/7). Equivalently stated, the harmonic seventh (7/4) is found at the double diminished octave (C-Cbb).

The second comma of the comma list determines which full 7-limit family member we are looking at. Garibaldi adds the schisma, or equivalently 225/224 and finds 5/4 at the diminished fourth. Cotoneum adds 10976/10935 and finds 5/4 at the septuple diminished octave. These are generated by the fifth as is gary.

Newt adds 2401/2400, slicing the fifth in two. Sextile adds 250047/250000 with a 1/3-octave period. Trident adds 6144/6125, slicing the twelfth in three. Satin adds 2100875/2097152, slicing the fourth in three. Vulture adds 4375/4374, slicing the twelfth in four. World calendar adds 390625/388962 with a 1/4-octave period as well as a bisect generator. Quintagar adds 3136/3125, slicing the fourth in five. Paramity adds 65625/65536, slicing the eleventh in five.

Garibaldi → Schismatic family (+225/224)
Cotoneum → Hemimage temperaments (+10976/10935)
Newt → Breedsmic temperaments (+2401/2400)
Sextile → Landscape microtemperaments (+250047/250000)
Satin → Canousmic temperaments (+2100875/2097152)
Trident → Tricot family (+6144/6125)
Vulture → Vulture family (+4375/4374)
Quintagar → Quindromeda family (+3136/3125)
Paramity → Amity family (+65625/65536)
Garistearn → Stearnsmic clan (+118098/117649)

Gary

Subgroup: 2.3.7

Comma list: 33554432/33480783

Sval mapping: [⟨1 2 -3], ⟨0 -1 14]]

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.2079

Optimal ET sequence: 12, 29, 41, 94, 135, 364, 499, 634, 3035bd, 3669bd, 4303bd, 4937bbdd, 5571bbdd

Badness: 0.0135

2.3.7.11 subgroup

Subgroup: 2.3.7.11

Comma list: 19712/19683, 41503/41472

Sval mapping: [⟨1 2 -3 13], ⟨0 -1 14 -23]]

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.2292

Optimal ET sequence: 12e, 41, 94, 135, 716, 851, 986, 1121, 1256

Badness: 0.00731

World calendar

World calendar tempers out the dimcomp comma and the garischisma, and can be described as the 12 & 364 temperament. The name derives from a certain calendar layout by the same name.

Subgroup: 2.3.5.7

Comma list: 390625/388962, 33554432/33480783

Mapping: [⟨4 1 -44 86], ⟨0 2 -13 -28]]

mapping generators: ~25/21, ~91125/57344

Optimal tuning (POTE): ~25/21 = 1\4, ~91125/57344 = 801.0947

Optimal ET sequence: 12, …, 352, 364

Badness: 0.292