Semaphore and godzilla
Semaphore, of the Semiphore family, 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.
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 |
MOSes
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)
| 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).
Modal harmony of Godzilla[9]
- 221212121 Megalon
- 212212121 Biollante
- 212122121 Gigan
- 212121221 Hedorah
- 212121212 Ebirah
- 122121212 Dagahra
- 121221212 Shockirus
- 121212212 Gabara
- 121212122 Minilla
One can think of godzilla[9] modes as being built from two pentachords (division of the perfect fourth into four intervals) plus a whole tone. The possible pentachords are 2121, 1221, and 1212.