Godzilla extensions: Difference between revisions
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All these extensions have the same mapping for 13 |
Complete interval table |
||
| Line 26: | Line 26: | ||
| 0 | | 0 | ||
| 0.0 | | 0.0 | ||
| 1/1 | | '''1/1''' | ||
| | | | ||
| | | | ||
| Line 34: | Line 34: | ||
| 1 | | 1 | ||
| 948.0 | | 948.0 | ||
| 7/4, 12/7, 26/15 | | '''7/4''', 12/7, 26/15 | ||
| 22/13 | | 22/13 | ||
| | | | ||
| Line 42: | Line 42: | ||
| 2 | | 2 | ||
| 696.0 | | 696.0 | ||
| 3/2 | | '''3/2''' | ||
| 22/15 | | 22/15 | ||
| 16/11 | | '''16/11''' | ||
| | | | ||
| | | | ||
| Line 58: | Line 58: | ||
| 4 | | 4 | ||
| 192.0 | | 192.0 | ||
| 9/8, 10/9 | | '''9/8''', 10/9 | ||
| 11/10 | | 11/10 | ||
| 12/11 | | 12/11 | ||
| Line 86: | Line 86: | ||
| | | | ||
| 22/15 | | 22/15 | ||
| 16/11 | | '''16/11''' | ||
|- | |- | ||
| 8 | | 8 | ||
| Line 114: | Line 114: | ||
| 11 | | 11 | ||
| 828.0 | | 828.0 | ||
| 13/8 | | '''13/8''' | ||
| 11/7 | | 11/7 | ||
| | | | ||
| Line 123: | Line 123: | ||
| 576.0 | | 576.0 | ||
| 25/18 | | 25/18 | ||
| 11/8 | | '''11/8''' | ||
| 15/11 | | 15/11 | ||
| | | | ||
| Line 130: | Line 130: | ||
| 13 | | 13 | ||
| 324.0 | | 324.0 | ||
| | | 39/32 | ||
| | | | ||
| 13/11 | | 13/11 | ||
| Line 138: | Line 138: | ||
| 14 | | 14 | ||
| 72.1 | | 72.1 | ||
| 25/24 | | 25/24, 50/49 | ||
| | | | ||
| | | | ||
| Line 162: | Line 162: | ||
| 17 | | 17 | ||
| 516.1 | | 516.1 | ||
| 65/49, 75/56 | |||
| | | | ||
| | | | ||
| | | '''11/8''' | ||
| 15/11 | | 15/11 | ||
|- | |- | ||
| 18 | | 18 | ||
| 264.1 | | 264.1 | ||
| 65/56, 75/64 | |||
| | |||
| | |||
| | |||
| 13/11 | |||
|- | |||
| 19 | |||
| 12.1 | |||
| 169/168, 225/224, 195/196 | |||
| | | | ||
| | | | ||
| | | | ||
| | | | ||
|} | |} | ||
<nowiki/>* In 2.3.5.7.13-subgroup [[CWE tuning]] | <nowiki/>* In 2.3.5.7.13-subgroup [[CWE tuning]], octave reduced | ||
[[Category:Godzilla]] | [[Category:Godzilla]] | ||
[[Category:Temperament extensions]] | [[Category:Temperament extensions]] | ||
Latest revision as of 07:50, 23 May 2026
Godzilla has various competing extensions for prime 11. The following temperaments are discussed in this article:
- Tridecimal godzilla (14cf & 19) – tempering out 45/44, 49/48, 78/77, and 81/80;
- Semafour (14cf & 19e) – tempering out 33/32, 49/48, 55/54, and 91/90;
- Varan (19e & 24) – tempering out 49/48, 66/65, 77/75, and 81/80;
- Baragon (19 & 24) – tempering out 49/48, 56/55, 81/80, and 91/90.
Tridecimal godzilla maps prime 11 such that 10/9 and 11/10 are tempered together and that 13/11 is tempered together with 7/6~15/13~8/7 semifourth cluster. Semafour swaps in a less complex and less accurate mapping for 11, so that 4/3 and 11/8 are tempered together. Similarly, varan tempers together 6/5 and 13/11. Finally, baragon swaps in a less complex mapping for prime 11, so that 7/5 and 11/8 are tempered together.
Interval chain
| # | Cents* | Approximate ratios | ||||
|---|---|---|---|---|---|---|
| 2.3.5.7.13 subgroup | Full 13-limit extensions | |||||
| Godzilla | Semafour | Varan | Baragon | |||
| 0 | 0.0 | 1/1 | ||||
| 1 | 948.0 | 7/4, 12/7, 26/15 | 22/13 | |||
| 2 | 696.0 | 3/2 | 22/15 | 16/11 | ||
| 3 | 444.0 | 9/7, 13/10, 21/16 | 14/11 | |||
| 4 | 192.0 | 9/8, 10/9 | 11/10 | 12/11 | ||
| 5 | 1140.0 | 25/13, 27/14, 39/20, 40/21 | ||||
| 6 | 888.0 | 5/3 | 18/11 | 22/13 | ||
| 7 | 636.0 | 10/7, 13/9 | 22/15 | 16/11 | ||
| 8 | 384.0 | 5/4 | 11/9 | 14/11 | ||
| 9 | 132.0 | 13/12, 15/14 | 11/10 | 12/11 | ||
| 10 | 1080.0 | 13/7, 15/8 | 11/6 | 20/11 | ||
| 11 | 828.0 | 13/8 | 11/7 | 18/11 | ||
| 12 | 576.0 | 25/18 | 11/8 | 15/11 | ||
| 13 | 324.0 | 39/32 | 13/11 | 11/9 | ||
| 14 | 72.1 | 25/24, 50/49 | ||||
| 15 | 1020.1 | 25/14 | 11/6 | 20/11 | ||
| 16 | 768.1 | 25/16 | 11/7 | |||
| 17 | 516.1 | 65/49, 75/56 | 11/8 | 15/11 | ||
| 18 | 264.1 | 65/56, 75/64 | 13/11 | |||
| 19 | 12.1 | 169/168, 225/224, 195/196 | ||||
* In 2.3.5.7.13-subgroup CWE tuning, octave reduced