6656/6655: Difference between revisions
+some basic temperament data |
17-limit factorization |
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| Color name = thotrilu-agu comma | | Color name = thotrilu-agu comma | ||
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'''6656/6655''', the '''jacobin comma''', is a [[13-limit]] (also 2.5.11.13 [[subgroup]]) [[superparticular]] interval of about 0.26012 [[cent]]s. 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]]. | '''6656/6655''', the '''jacobin comma''', is a [[13-limit]] (also 2.5.11.13 [[subgroup]]) [[superparticular]] interval of about 0.26012 [[cent]]s. 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]]. In the 17-limit, it factors neatly into 12376/12375 × 14400/14399. | ||
== Temperaments == | == Temperaments == | ||
Revision as of 13:22, 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. In the 17-limit, it factors neatly into 12376/12375 × 14400/14399.
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