Semaphore and godzilla
Semaphore, of the semaphoresmic clan, is characterized by 49/48 being tempered out, so the generator represents 7/4 and 12/7 (or 8/7 and 7/6) equally. This results in a very low complexity 2.3.7-subgroup 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 the 5th harmonic's intervals are desired, 5/4 can be sensibly mapped to +8 generators by tempering out 81/80, making it a meantone temperament. This temperament is godzilla. Moreover, the generator can be taken to be 26/15, which maps 13/8 to +11 generators by tempering out 91/90 and 105/104. This extends the temperament to the 2.3.5.7.13 subgroup, with an abundance of harmonic resource and little additional damage.
A more accurate but complex mapping of 5 can be found in immunity, or 5/4 itself can be made the period by tempering out 128/125, resulting in triforce.
See Semaphoresmic clan #Semaphore and #Godzilla for technical data.
Interval chains
In the following tables, odd harmonics 1–13 and their inverses are in bold.
Semaphore
| # | Cents* | Approximate ratios |
|---|---|---|
| 0 | 0.0 | 1/1 |
| 1 | 950.7 | 7/4, 12/7 |
| 2 | 701.4 | 3/2 |
| 3 | 452.1 | 9/7, 21/16 |
| 4 | 202.8 | 9/8 |
| 5 | 1153.4 | 27/14, 63/32 |
* In 2.3.7-subgroup CWE tuning, octave reduced
Godzilla
| # | Cents* | Approximate ratios |
|---|---|---|
| 0 | 0.0 | 1/1 |
| 1 | 948.0 | 7/4, 12/7, 26/15 |
| 2 | 696.0 | 3/2 |
| 3 | 444.0 | 9/7, 13/10, 21/16 |
| 4 | 192.0 | 9/8, 10/9 |
| 5 | 1140.0 | 27/14, 39/20, 40/21, 52/27, 63/32 |
| 6 | 888.0 | 5/3 |
| 7 | 636.0 | 10/7, 13/9 |
| 8 | 384.0 | 5/4 |
| 9 | 132.0 | 13/12, 15/14 |
| 10 | 1080.0 | 13/7, 15/8 |
| 11 | 828.0 | 13/8 |
| 12 | 576.0 | 25/18, 39/28, 45/32 |
| 13 | 324.0 | 39/32 |
| 14 | 72.1 | 25/24, 50/49 |
* In 2.3.5.7.13-subgroup CWE tuning, octave reduced
Scales
Scala files:
5-note (proper)
| Small ("minor") interval | 202.8 | 452.1 | 701.4 | 950.7 |
|---|---|---|---|---|
| JI intervals represented | 9/8 | 9/7~13/10 | 3/2 | 7/4~12/7 |
| Large ("major") interval | 249.3 | 498.6 | 747.9 | 997.2 |
| JI intervals represented | 7/6~8/7 | 4/3 | 14/9~20/13 | 16/9 |
9-note (improper)
| Small ("minor") interval | 60.0 | 252.0 | 312.0 | 504.0 | 564.0 | 756.0 | 816.0 | 1008.0 |
|---|---|---|---|---|---|---|---|---|
| JI intervals represented | 7/6~8/7 | 6/5 | 4/3 | 7/5~18/13 | 14/9~20/13 | 8/5~13/8 | 9/5~16/9 | |
| Large ("major") interval | 192.0 | 384.0 | 444.0 | 636.0 | 696.0 | 888.0 | 948.0 | 1140.0 |
| JI intervals represented | 9/8~10/9 | 5/4 | 9/7~13/10 | 10/7~13/9 | 3/2 | 5/3 | 7/4~12/7 |
In 19edo, Godzilla[9] has steps 3 3 1 3 1 3 1 3 1, and contains the following useful scales as subsets:
- Meantone pentic (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 pentic 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).
Tunings
| Euclidean | |||
|---|---|---|---|
| Constrained | Constrained & skewed | Destretched | |
| Tenney | CTE: ~7/4 = 952.2948 ¢ | CWE: ~7/4 = 950.6890 ¢ | POTE: ~7/4 = 949.6154 ¢ |
| Euclidean | |||
|---|---|---|---|
| Constrained | Constrained & skewed | Destretched | |
| Tenney | CTE: ~7/4 = 948.7959 ¢ | CWE: ~7/4 = 947.8216 ¢ | POTE: ~7/4 = 947.3650 ¢ |
Tuning spectrum
| Edo generator |
Unchanged interval (eigenmonzo)* |
Generator (¢) | Comments |
|---|---|---|---|
| 7/6 | 933.129 | ||
| 7\9 | 933.333 | 9cff val | |
| 11\14 | 942.857 | 14cf val, lower bound of 7- and 9-odd-limit diamond monotone | |
| 9/7 | 945.028 | ||
| 7/5 | 945.355 | ||
| 13/7 | 947.170 | ||
| 15\19 | 947.368 | Lower bound of no-11 13-odd-limit diamond monotone No-11 15-odd-limit diamond monotone (singleton) | |
| 5/3 | 947.393 | ||
| 13/9 | 948.088 | ||
| 5/4 | 948.289 | ||
| 13/12 | 948.730 | ||
| 13/8 | 949.139 | ||
| 19\24 | 950.000 | ||
| 3/2 | 950.978 | ||
| 13/10 | 951.405 | ||
| 4\5 | 960.000 | Upper bound of 7-, 9-odd-limit, and no-11 13-odd-limit diamond monotone | |
| 7/4 | 968.826 |
* Besides the octave
Music
- "Change is on the Wind"[dead link] in Godzilla[9]
- Rin's UFO Ride (2020) – in Semaphore[9], 19edo tuning
See also
- Diasem, a max-variety-3 JI detempering of semaphore
- Semaphore–chromatic equivalence continuum