Vishdelismic clan

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

The vishdelismic clan of rank-3 temperaments tempers out the vishdelisma (monzo: [14 -3 -1 0 -2⟩, ratio: 5632/5625).

For the rank-4 temperament, see Catalog of rank-4 temperaments #Vishdelismic (5632/5625).

Vishdelic

The head of this clan is vishdelic, which finds 11/9 as a stack of four 5/4 major thirds minus an octave.

Subgroup: 2.3.5.11

Comma list: 5632/5625

Mapping: [⟨1 0 0 -9], ⟨0 1 0 2], ⟨0 0 1 4]]

mapping generators: ~2, ~3, ~5

Optimal tunings:

• WE: ~2 = 1199.8976 ¢, ~3/2 = 702.1145 ¢, ~5/4 = 386.7638 ¢

error map: ⟨-0.102 +0.057 +0.245 -0.136]

• CWE: ~2 = 1200.0000 ¢, ~3/2 = 702.1309 ¢, ~5/4 = 386.7770 ¢

error map: ⟨0.000 +0.176 +0.463 +0.052]

Optimal ET sequence: 31, 34, 53, 65, 87, 118, 152, 270, 335, 605, 940, 1092, 1362c, 1697c, 2302c

Badness (Sintel): 0.183

Overview to extensions

Temperaments discussed elsewhere are:

• Minerva (+176/175) → Marvel family
• Zelda (+385/384) → Horwell family
• Belobog (+441/440) → Hemimean family
• Jupiter (+540/539) → Porwell family
• Mendel (+1375/1372) → Moctdelismic clan
• Zisa (+2401/2400) → Breed family

The rest are considered below.

Ganesha

For the 7-limit version, see Miscellaneous 7-limit temperaments #Quasiorwellismic.

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 5632/5625

Mapping: [⟨1 0 0 -22 -9], ⟨0 1 0 1 2], ⟨0 0 1 10 4]]

Optimal tunings:

• WE: ~2 = 1199.9176 ¢, ~3/2 = 702.1769 ¢, ~5/4 = 386.6642 ¢

error map: ⟨-0.082 +0.139 +0.186 +0.075 -0.390]

• CWE: ~2 = 1200.0000 ¢, ~3/2 = 702.1836 ¢, ~5/4 = 386.6860 ¢

error map: ⟨0.000 +0.229 +0.372 +0.218 -0.207]

Optimal ET sequence: 31, 65d, 87, 118, 152, 239, 270, 962, 1232, 1502

Badness (Sintel): 0.469

Loki

Subgroup: 2.3.5.7.11

Comma list: 5632/5625, 9801/9800

Mapping: [⟨2 0 0 -21 -18], ⟨0 1 0 4 2], ⟨0 0 1 3 4]]

mapping generators: ~99/70, ~3, ~5

Optimal tunings:

• WE: ~99/70 = 599.9481 ¢, ~3/2 = 702.1195 ¢, ~5/4 = 386.7636 ¢

error map: ⟨-0.104 +0.061 +0.242 -0.005 -0.128]

• CWE: ~99/70 = 600.0000 ¢, ~3/2 = 702.1647 ¢, ~5/4 = 386.7768 ¢

error map: ⟨0.000 +0.210 +0.463 +0.163 +0.119]

Optimal ET sequence: 12, 22, 34d, 56d, 74d, 84de, 96d, 118, 130, 152, 248, 270, 670, 822, 940, 1092, 1362c, 2032c, 2302c

Badness (Sintel): 0.592

Baffin

For the 7-limit version, see Miscellaneous 7-limit temperaments #Decovulture.

Baffin tempers out the olympia and the seascape comma in addition to the vishdelisma, so that the 3rd harmonic is split in halves. This leads naturally to a 13-limit temperament where 676/675, 1001/1000, 2080/2079 and 4096/4095 are all tempered out.

It was named by Gene Ward Smith some time before 2011 for Baffin Island, as part of a series of island-themed names.

Subgroup: 2.3.5.7.11

Comma list: 5632/5625, 131072/130977

Mapping: [⟨1 0 0 13 -9], ⟨0 2 0 -7 4], ⟨0 0 1 -2 4]]

mapping generators: ~2, ~400/231, ~5

Optimal tunings:

• WE: ~2 = 1199.9208 ¢, ~400/231 = 950.9957 ¢, ~5/4 = 386.7656 ¢

error map: ⟨-0.079 +0.036 +0.293 -0.040 -0.193]

• CWE: ~2 = 1200.0000 ¢, ~400/231 = 951.0635 ¢, ~5/4 = 386.7769 ¢

error map: ⟨0.000 +0.172 +0.463 +0.176 +0.044]

Optimal ET sequence: 34, 43, 53, 87, 130, 183, 270, 670, 940, 1210, 2063c

Badness (Sintel): 1.17

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 676/675, 1001/1000, 4096/4095

Mapping: [⟨1 0 0 13 -9 1], ⟨0 2 0 -7 4 3], ⟨0 0 1 -2 4 1]]

Optimal tunings:

• WE: ~2 = 1199.9633 ¢, ~400/231 = 951.0591 ¢, ~5/4 = 386.7388 ¢
• CWE: ~2 = 1200.0000 ¢, ~400/231 = 951.0896 ¢, ~5/4 = 386.7451 ¢

Optimal ET sequence: 34, 43, 53, 87, 130, 183, 217, 270, 940, 1210f

Badness (Sintel): 0.565

Complexity spectrum: 15/13, 16/15, 13/12, 4/3, 16/13, 5/4, 18/13, 13/10, 6/5, 9/8, 11/10, 8/7, 7/5, 15/11, 10/9, 13/11, 15/14, 11/8, 7/6, 14/13, 12/11, 9/7, 11/9, 14/11