Semaphore and godzilla

Semaphore; Godzilla

Subgroups	2.3.7, 2.3.5.7, 2.3.5.7.13
Comma basis	49/48 (2.3.7); 49/48, 81/80 (2.3.5.7); 49/48, 81/80, 91/90 (L7.13)
Reduced mapping	⟨1; 2 8 1 11]
ET join	5 & 19
Generators (CWE)	~7/4 = 947.8 ¢
MOS scales	4L 1s, 5L 4s, 5L 9s, 5L 14s
Ploidacot	alpha-dicot
Pergen	(P8, P4/2)
Color name	Zozoti
Minimax error	9-odd-limit: 20.5 ¢; 2.3.5.7.13 15-odd-limit: 20.5 ¢
Target scale size	9-odd-limit: 9 notes; 2.3.5.7.13 15-odd-limit: 14 notes

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.

For technical information, see Semaphoresmic clan #Semaphore and #Godzilla. For a discussion on 11- and 13-limit extensions, see Godzilla extensions.

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:

• Semaphore5
• Semaphore9
• Semaphore14

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)

Main article: 5L 4s

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

2.3.7-subgroup norm-based tunings

	Euclidean
	Constrained	Constrained & skewed	Destretched
Tenney	CTE: ~7/4 = 952.2948 ¢	CWE: ~7/4 = 950.6890 ¢	POTE: ~7/4 = 949.6154 ¢

7-limit norm-based tunings

	Euclidean
	Constrained	Constrained & skewed	Destretched
Tenney	CTE: ~7/4 = 948.7959 ¢	CWE: ~7/4 = 947.8216 ¢	POTE: ~7/4 = 947.3650 ¢

2.3.5.7.13-subgroup norm-based tunings

	Euclidean
	Constrained	Constrained & skewed	Destretched
Tenney	CTE: ~7/4 = 948.9311 ¢	CWE: ~7/4 = 948.0037 ¢	POTE: ~7/4 = 947.5708 ¢

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	7-, 9-odd-limit, no-11 13- and 15-odd-limit minimax
	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

Cameron Bobro

• Godzilla Example

Igliashon Jones

• "Change is on the Wind"^{[dead link]} in Godzilla[9]

Roncevaux

• Só no Contratempo
• O que a gente quer

Starshine

• 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