Hemfiness temperaments

Hemfiness rank-two temperaments temper out the hemfiness comma, 4096000/4084101 = [15 -5 3 -5⟩ (saquinru-atriyo), the amount by which a stack of three 5/4s and five 32/21s exceed four octaves.

Temperaments dicussed elsewhere include:

• Hemififths
• Nessafof
• Gamera
• Superkleismic
• Quanharuk
• Merman
• Decipentic
• Oquatonic
• Stockhausenic
• Secant
• Thuja
• Jerome
• Progress
• Witcher

Undesemi

Subgroup: 2.3.5.7

Comma list: 4096000/4084101, 95703125/95551488

Mapping: [⟨1 5 5 1], ⟨0 -51 -40 27]]

Optimal tuning (POTE): ~8575/8192 = 80.347

Optimal ET sequence: 15, …, 194, 209, 224, 463, 687, 1150d

Badness: 0.178777

11-limit

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 4000/3993, 180224/180075

Mapping: [⟨1 5 5 1 5], ⟨0 -51 -40 27 -23]]

POTE generator: ~22/21 = 80.347

Optimal ET sequence: 15, …, 194, 209, 224, 463, 1150de

Badness: 0.042318

Piracy

See also: Very high accuracy temperaments § Pirate

Subgroup: 2.3.5.7

Comma list: 4096000/4084101, 48828125/48771072

Mapping: [⟨1 -6 0 9], ⟨0 49 15 -40]]

Optimal tuning (POTE): ~4096/3675 = 185.7609

Optimal ET sequence: 71, 84, 155, 239, 323, 885, 1208d, 1531d

Badness: 0.159305

11-limit

Subgroup: 2.3.5.7.11

Comma list: 6250/6237, 12005/11979, 16384/16335

Mapping: [⟨1 -6 0 9 16], ⟨0 49 15 -40 -81]]

Optimal tuning (POTE): ~49/44 = 185.7671

Optimal ET sequence: 84, 155, 239, 562e, 801e

Badness: 0.092173

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 625/624, 2080/2079, 2205/2197, 12005/11979

Mapping: [⟨1 -6 0 9 16 2], ⟨0 49 15 -40 -81 11]]

Optimal tuning (POTE): ~49/44 = 185.7663

Optimal ET sequence: 84, 155, 239f

Badness: 0.063719

Pirateship

Subgroup: 2.3.5.7.11.13

Comma list: 364/363, 1716/1715, 4096/4095, 6250/6237

Mapping: [⟨1 -6 0 9 16 15], ⟨0 49 15 -40 -81 -73]]

Optimal tuning (POTE): ~39/35 = 185.7621

Optimal ET sequence: 84, 155f, 239, 323e

Badness: 0.073523