6656/6655: Difference between revisions
Cmloegcmluin (talk | contribs) "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence |
m Link and formatting |
||
| Line 4: | Line 4: | ||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
'''6656/6655''', the '''jacobin comma''', [https://en.xen.wiki/index.php?title=List_of_superparticular_intervals&diff=next&oldid=18864 apparently named] by [[Gene Ward Smith]] in 2014, is a [[13-limit]] (also 2.5.11.13 [[subgroup]]) [[superparticular]] interval of about 0.26{{cent}}. 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 × [[sparkisma|14400/14399]]. | '''6656/6655''', the '''jacobin comma''', [https://en.xen.wiki/index.php?title=List_of_superparticular_intervals&diff=next&oldid=18864 apparently named] by [[Gene Ward Smith]] in 2014, is a [[13-limit]] (also 2.5.11.13 [[subgroup]]) [[superparticular]] interval of about 0.26{{cent}}. 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]] × [[sparkisma|14400/14399]]. | ||
== Temperaments == | == Temperaments == | ||
By tempering it out, the '''jacobin temperament''' is defined. Perhaps most remarkably, '''[[1789edo]]''' is an edo that [[support]]s 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. | By tempering it out, the '''jacobin temperament''' is defined. Perhaps most remarkably, '''[[1789edo]]''' is an edo that [[support]]s 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 | [[Subgroup]]: 2.3.5.7.11.13 | ||
[[Mapping]]: <br> | [[Mapping]]: <br> | ||
| Line 18: | Line 18: | ||
{{val| 0 0 0 0 1 3 }}] | {{val| 0 0 0 0 1 3 }}] | ||
: mapping generators: ~2, ~3, ~5, ~7, ~11 | |||
{{Optimal ET sequence|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 }} | {{Optimal ET sequence|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 == | ||
* [[Unnoticeable comma]] | * [[Unnoticeable comma]] | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
[[Category:Jacobin]] | [[Category:Jacobin]] | ||