The Flashmob

The Flashmob is a collection of temperaments of different ranks that all temper out 12376/12375, the flashma, a 17-limit comma associated with precise systems that model high-limit JI.

Temperaments discussed elsewhere include:

• Minutes → 60th-octave temperaments#Minutes
• Mercury → 80th-octave temperaments#Mercury

Hafnium

Hafnium is a period-72 temperament created by temperament-merging 4320edo and 5544edo, equal temperaments notable for their high divisibility. Named after the 72nd element.

Subgroup: 2.3.5.7.11.13

Comma list: 9801/9800, 250047/250000, 184549376/184528125, 463373664/463203125

Mapping: [⟨72 72 462 876 1302 1193], ⟨0 1 -7 -16 -25 -22]]

Mapping generators: ~105/104 = 1\72, ~3/2 = 701.948

Optimal tuning (CTE): ~3/2 = 701.948

Vals: Template:Val list

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 9801/9800, 12376/12375, 21879/21875, 194481/194480, 1713660/1713481, 97144749/97140736

Mapping: [⟨72 72 462 876 1302 1193 547], ⟨0 1 -7 -16 -25 -22 -6]]

Mapping generators: ~105/104 = 1\72, ~3/2 = 701.948

Optimal tuning (CTE): ~3/2 = 701.948

Vals: Template:Val list

2.3.5.7.11.13.17.31 subgroup

Since 4320edo and 5544edo have good 31st and 37th harmonics, addition of these subgroups is prescribed.

Subgroup: 2.3.5.7.11.13.17.31

Comma list: 9801/9800, 10881/10880, 12376/12375, 57629/57624, 179712/179707, 61456384/61448625

Sval mapping: [⟨72 72 462 876 1302 1193 547 356], ⟨0 1 -7 -16 -25 -22 -6 6]]

Mapping generators: ~105/104 = 1\72, ~3/2 = 701.948

Optimal tuning (CTE): ~3/2 = 701.948

2.3.5.7.11.13.17.31.37 subgroup

37/22 is mapped to exact three-quarters of the octave.

Subgroup: 2.3.5.7.11.13.17.31

Comma list: 10881/10880, 12376/12375, 16576/16575, 93093/93092, 954304/954261, 2737889/2737800, 126607131/126605120

Sval mapping: [⟨72 72 462 876 1302 1193 547 356 378], ⟨0 1 -7 -16 -25 -22 -6 6 -25]]

Mapping generators: ~105/104 = 1\72, ~3/2 = 701.948

Optimal tuning (CTE): ~3/2 = 701.948