Semaphore and Godzilla
Semaphore, of the Slendro clan, is characterized by the vanishing of 49/48, so the generator represents 8/7 and 7/6 equally. This results in a very low complexity 2.3.7 temperament, with the drawback that most intervals of 7 must be out of tune by at least half of the comma 49/48, or about 18 cents. Semaphore is a play on the words "semi-" and "fourth."
If 5 is mapped at all, it can be sensibly mapped to -8 generators by tempering out 81/80, making it a meantone temperament. This temperament is called godzilla.
Temperament data
- Main article: Meantone family #Godzilla
Godzilla (19&24, 2.3.5.7)
Period: 1\1
Optimal (POTE) generator: ~8/7 = 252.635
EDO generators: 3\14, 4\19, 5\24, 7\33, 9\43
Scales (Scala files):
Interval chains
Semaphore
| 198.46 | 448.85 | 699.23 | 949.62 | 0 | 250.38 | 500.77 | 751.15 | 1001.54 |
| 9/8 | 9/7 | 3/2 | 12/7~7/4 | 1/1 | 8/7~7/6 | 4/3 | 14/9 | 16/9 |
Godzilla
| 378.92 | 631.56 | 884.19 | 1136.83 | 189.46 | 442.10 | 694.73 | 947.37 | 0 | 252.63 | 505.27 | 757.90 | 1010.54 | 63.17 | 315.81 | 568.44 | 821.08 |
| 5/4~16/13 | 10/7~13/9 | 5/3 | 27/14 | 10/9~9/8 | 9/7~13/10 | 3/2 | 12/7~7/4~26/15 | 1/1 | 8/7~7/6~15/13 | 4/3 | 14/9~20/13 | 16/9~9/5 | 28/27~21/20 | 6/5 | 7/5~18/13 | 8/5~13/8 |
MOS scales
5-note (proper)
| Small ("minor") interval | 198.46 | 448.85 | 699.23 | 949.62 |
| JI intervals represented | 9/8 | 9/7~13/10 | 3/2 | 12/7~7/4~26/15 |
| Large ("major") interval | 250.38 | 500.77 | 751.15 | 1001.54 |
| JI intervals represented | 8/7~7/6~15/13 | 4/3 | 14/9~20/13 | 16/9 |
9-note (improper)
see 5L 4s
| Small ("minor") interval | 63.17 | 252.63 | 315.81 | 505.27 | 568.44 | 757.90 | 821.08 | 1010.54 |
| JI intervals represented | 8/7~7/6~15/13 | 6/5 | 4/3 | 7/5~18/13 | 14/9~20/13 | 8/5~13/8 | 16/9~9/5 | |
| Large ("major") interval | 189.46 | 378.92 | 442.10 | 631.56 | 694.73 | 884.19 | 947.37 | 1136.83 |
| JI intervals represented | 10/9~9/8 | 5/4 | 9/7~13/10 | 10/7~13/9 | 3/2 | 5/3 | 12/7~7/4~26/15 |
In 19edo, godzilla[9] has steps 3 3 1 3 1 3 1 3 1, and contains the following useful scales as subsets:
- Meantone pentatonic (5 3 5 3 3)
- Altered diatonic I (3 4 3 1 3 4 1)
- Altered diatonic II (3 4 3 1 4 3 1)
- Altered diatonic III (4 3 3 1 4 3 1)
- Altered diatonic IV (3 3 4 1 3 4 1)
It does not, however, contain the ordinary diatonic scale. Godzilla[9] thus expands on the pentatonic scale, but in a different way than diatonic scales do.
The four heptatonic subsets can be regarded as chromatic alterations of the diatonic scale, or alternatively as variants of Archytas' septimal diatonic scale, but with a greatly exaggerated difference between the two different whole tone sizes. All five of these subsets are very expressive melodically. Godzilla[9] combines all of these and is expressive in its own right; it could even be thought of as 19edo's answer to the well-loved supra[7] diatonic scale of 17edo, as both are improper and made up of whole-tones and third-tones.
Like supra[7], godzilla[9] is well stocked with subminor and supermajor triads; in this case they can be viewed as 6:7:9 and 10:13:15 since 19edo is a biome temperament. Godzilla[9] has only one each of the more stable 5-limit major and minor triads, which might be considered a drawback, but could also be considered a strength for helping to establish a clearer tonal center (since all triads other than the tonic have tension in them).
See also
- Diasem, a max-variety-3 JI detempering of semaphore