Lockerbie

Lockerbie is a rank two temperament, initially defined as the 103 & 270 temperament.

It is defined upwards to the 17-limit.

Its generator is 120/77 or 77/60.

The temperament derives its name from the Scottish town, where a flight numbered 103 crashed with 270 casualties, and the temperament is defined as 103 & 270, hence the name. The name is proposed by Eliora, who favours it due to simplicity, ease of pronunciation and relation to numbers 103 and 270.

Other vals which support it are 373, 167, 643, 206be, 437p, 476e, 64be.

Lockerbie

5-limit

Subgroup: 2.3.5

Comma list: [91 51 -74⟩

Mapping: ⟨1 49 35], ⟨0 -74 -51]

Optimal tuning (POTE): ~[-35 -20 29⟩ = 768.893

7-limit

Subgroup: 2.3.5.7

Comma list: 2401/2400, 26748301344768/26702880859375

Mapping: ⟨1 49 35 31], ⟨0 -74 -51 -44]

Optimal tuning (POTE): ~5971968/3828125 = 768.893

11-limit

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 2401/2400, 766656/765625

Mapping: ⟨1 49 35 31 56], ⟨0 -74 -51 -44 -82]

Optimal tuning (POTE): ~120/77 = 768.892

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 1001/1000, 1716/1715, 3025/3024, 4225/4224

Mapping: ⟨1 49 35 31 56 21], ⟨0 -74 -51 -44 -82 -27]

Optimal tuning (POTE): ~120/77 = 768.891

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 715/714, 936/935, 1001/1000, 1225/1224, 4225/4224

Mapping: ⟨1 49 35 31 56 21 31], ⟨0 -74 -51 -44 -82 -27 -42]

Optimal tuning (POTE): ~120/77 = 768.893

41-limit extension

Lockerbie temperament also has a unique 41st harmonic-themed extension (more precisely, 2.3.5.7.11.13.17.41 subgroup), where the generator below 600 cents is also on the same step in 103 or 270 as 41/32, which means that 616/615 is tempered out.

2.3.5.7.11.13.17.41 subgroup

Subgroup: 2.3.5.7.11.13.17.41

Comma list: 616/615, 715/714, 936/935, 1001/1000, 1225/1224, 4225/4224

Mapping: ⟨1 49 35 31 56 21 31 6], ⟨0 -74 -51 -44 -82 -27 -42 -1]

Optimal tuning (POTE): ~41/32 = 768.893