Bug family

The 5-limit parent of the bug family is bug, a temperament of sorts which tempers out 27/25, the large limma, or approximately one step of 9edo. The monzo for 27/25 is |0 3 -2>, the dual of which is <<2 3 0||. The generator for bug is 5/3, two of which give the 3, and three of which give the 5. Bug may be described as the 4&5 temperament, and 14edo is a good bug tuning, though wide latitude in these matters is possible. 4, 5, or 9 note MOS are a place to start with it.

Bug has a 7-limit extension, beep, via the normal comma list [27/25, 36/35] which can also be obtained by adding 21/20. Beep has the curious property that if we know what the beep tempering is, and we know what the ennealimmal tempering is, we can reconstruct 7-limit JI.

Bug

Comma: 27/25

POTE temperament: 260.388

Map: [<1 0 0|, <0 2 3|]

EDOs: 4, 5, 9, 14, 23, 106

Badness: 0.0328

Beep

Commas: 21/20, 27/25

POTE temperament: ~6/5 = 263.395

Map: [<1 0 0 2|, <0 2 3 1|]

Wedgie: <<2 3 1 0 -4 -6||

EDOs: 4, 5, 9, 32, 41

Badness: 0.0186

Pentoid

Commas: 21/20, 27/25, 99/98

POTE temperament: ~6/5 = 264.312

Map: [<1 0 0 2 5|, <0 2 3 1 -2|]

EDOs: 4, 5, 9, 50, 59

Badness: 0.0226

13-limit

Commas: 21/20, 26/25, 27/25, 33/32

POTE generator: ~6/5 = 263.935

Map: [<1 0 0 2 5 -1|, <0 2 3 1 -2 6|]

EDOs: 5,9, 32bcde, 41bcdef, 50bcdef

Badness: 0.0212

Pento

Commas: 21/20, 27/25, 45/44

POTE generator: ~6/5 = 265.847

Map: [<1 0 0 2 -2|, <0 2 3 1 7|]

EDOs: 9

Badness: 0.0228

Mite

Commas: 27/25, 28/25

POTE generator: ~6/5 = 240.712

Map: [<1 0 0 -2|, <0 2 3 6|]

Wedgie: <<2 3 6 0 4 6||

EDOs: 1cdd, 5

Badness: 0.0548