6656/6655: Difference between revisions
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+some basic temperament data |
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== Temperaments == | == Temperaments == | ||
By tempering it out, the '''jacobin temperament''' is defined. Perhaps most remarkably, '''[[1789edo]]''' is an edo that supports the jacobin temperament. | By tempering it out, the '''jacobin temperament''' is defined. Perhaps most remarkably, '''[[1789edo]]''' is an edo that supports the jacobin temperament. You may find a list of good JI-approximating edos that support this temperament below. Although it is more rational to use such edos for this temperament, 1789edo has a unique position due to its number of steps being a hallmark year of the French Revolution. | ||
Subgroup: 2.3.5.7.11.13 | |||
[[Comma list]]: 6656/6655 | |||
[[Mapping]]: <br> | |||
[{{val| 1 0 0 0 0 -9 }}, <br> | |||
{{val| 0 1 0 0 0 0 }}, <br> | |||
{{val| 0 0 1 0 0 1 }}, <br> | |||
{{val| 0 0 0 1 0 0 }}, <br> | |||
{{val| 0 0 0 0 1 3 }}] | |||
Mapping generators: ~2, ~3, ~5, ~7, ~11 | |||
{{Val list|legend=1| 9, 15, 22, 26, 31f, 37, 39df, 41, 46, 63, 72, 87, 111, 152f, 183, 198, 224, 270, 494, 764, 1012, 1084, 1236, 1506, 2814, 2901, 3125, 3395, 8026e, 8296e, 11421e, 11691e, 12927e, 13421e, 16322ee, 16816ee }} | |||
== See also == | == See also == | ||
Revision as of 10:43, 6 October 2021
| Interval information |
reduced
6656/6655, the jacobin comma, is a 13-limit (also 2.5.11.13 subgroup) superparticular interval of about 0.26012 cents. It is the difference between a stack of three 11/8 superfourths and one 13/10 naiadic plus an octave. In terms of commas, it is the difference between 364/363 and 385/384, between 2080/2079 and 3025/3024 as well as between 4096/4095 and 10648/10647.
Temperaments
By tempering it out, the jacobin temperament is defined. Perhaps most remarkably, 1789edo is an edo that supports the jacobin temperament. You may find a list of good JI-approximating edos that support this temperament below. Although it is more rational to use such edos for this temperament, 1789edo has a unique position due to its number of steps being a hallmark year of the French Revolution.
Subgroup: 2.3.5.7.11.13
Comma list: 6656/6655
Mapping:
[⟨1 0 0 0 0 -9],
⟨0 1 0 0 0 0],
⟨0 0 1 0 0 1],
⟨0 0 0 1 0 0],
⟨0 0 0 0 1 3]]
Mapping generators: ~2, ~3, ~5, ~7, ~11