Generators for rank two 7-limit temperaments

Here is an old list of 45 temperaments, with generators for two
canonical generator pairs. The first is period-generator, where the
"generator" is minimal under the condition it is greater than 1. The
second is the Hermite genrerator pair.

Decimal [4, 2, 2, -6, -8, -1]
[7/5, 7/6] [7/5, 7/4]

Dominant seventh [1, 4, -2, 4, -6, -16]
[2, 4/3] [2, 3]

Diminished [4, 4, 4, -3, -5, -2]
[6/5, 15/14] [6/5, 3]

Blackwood [0, 5, 0, 8, 0, -14]
[7/6, 21/20] [7/6, 5]

Augie [3, 0, 6, -7, 1, 14]
[5/4, 15/14] [5/4, 3]

Pajara [2, -4, -4, -11, -12, 2]
[7/5, 15/14] [7/5, 3]

Hexadecimal [1, -3, 5, -7, 5, 20]
[2, 4/3] [2, 3]

Negri [4, -3, 2, -14, -8, 13]
[2, 15/14] [2, 15/14]

Kemun [6, 5, 3, -6, -12, -7]
[2, 6/5] [2, 6/5]

Augmented [3, 0, -6, -7, -18, -14]
[5/4, 16/15] [5/4, 3]

Godzilla [2, 8, 1, 8, -4, -20]
[2, 7/6] [2, 7/4]

Meantone [1, 4, 10, 4, 13, 12]
[2, 4/3] [2, 3]

Injera [2, 8, 8, 8, 7, -4]
[7/5, 15/14] [7/5, 3]

Doublewide [8, 6, 6, -9, -13, -3]
[7/5, 7/6] [7/5, 6/5]

Porcupine [3, 5, -6, 1, -18, -28]
[2, 10/9] [2, 10/9]

Superpyth [1, 9, -2, 12, -6, -30]
[2, 4/3] [2, 3]

Muggles [5, 1, -7, -10, -25, -19]
[2, 5/4] [2, 5/4]

Beatles [2, -9, -4, -19, -12, 16]
[2, 49/40] [2, 49/40]

Flattone [1, 4, -9, 4, -17, -32]
[2, 4/3] [2, 3]

Magic [5, 1, 12, -10, 5, 25]
[2, 5/4] [2, 5/4]

Myna [10, 9, 7, -9, -17, -9]
[2, 6/5] [2, 5/3]

Sensi [7, 9, 13, -2, 1, 5]
[2, 9/7] [2, 14/9]

Orwell [7, -3, 8, -21, -7, 27]
[2, 7/6] [2, 7/6]

Miracle [6, -7, -2, -25, -20, 15]
[2, 15/14] [2, 15/14]

Valentine [9, 5, -3, -13, -30, -21]
[2, 21/20] [2, 21/20]

Mothra [3, 12, -1, 12, -10, -36]
[2, 8/7] [2, 8/7]

Garibaldi [1, -8, -14, -15, -25, -10]
[2, 4/3] [2, 3]

Superkleismic [9, 10, -3, -5, -30, -35]
[2, 6/5] [2, 6/5]

Squares [4, 16, 9, 16, 3, -24]
[2, 9/7] [2, 9/7]

Semififths [2, 8, -11, 8, -23, -48]
[2, 128/105] [2, 128/105]

Diaschismic [2, -4, -16, -11, -31, -26]
[45/32, 16/15] [45/32, 3]

Octacot [8, 18, 11, 10, -5, -25]
[2, 21/20] [2, 21/20]

Augene [5, -11, -12, -29, -33, 3]
[2, 7/5] [2, 7/5]

Rodan [3, 17, -1, 20, -10, -50]
[2, 8/7] [2, 8/7]

Shrutar [4, -8, 14, -22, 11, 55]
[45/32, 28/27] [45/32, 35/24]

Catakleismic [6, 5, 22, -6, 18, 37]
[2, 6/5] [2, 6/5]

Hemiwuerschmidt [16, 2, 5, -34, -37, 6]
[2, 28/25] [2, 25/14]

Hemikleismic [12, 10, -9, -12, -48, -49]
[2, 35/32] [2, 35/32]

Hemithirds [15, -2, -5, -38, -50, -6]
[2, 28/25] [2, 28/25]

Wizard [12, -2, 20, -31, -2, 52]
[343/243, 245/216] [343/243, 245/216]

Waage [0, 12, 24, 19, 38, 22]
[200/189, 81/80] [200/189, 5]

Slender [13, -10, 6, -46, -27, 42]
[2, 49/48] [2, 49/48]

Amity [5, 13, -17, 9, -41, -76]
[2, 128/105] [2, 128/105]

Hemififths [2, 25, 13, 35, 15, -40]
[2, 49/40] [2, 49/40]

Ennealimmal [18, 27, 18, 1, -22, -34]
[27/25, 36/35] [27/25, 5/3]

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:

> Augene [5, -11, -12, -29, -33, 3]
> [2, 7/5] [2, 7/5]

Should be "Tritonic".