Xenharmonic Wiki

6656/6655: Difference between revisions

← Older edit

Eliora (talk | contribs)

2 user groups
3,645 edits
VisualWikitext
Cleanup
Eliora (talk | contribs)
autopatrolled, emailconfirmed
3,645 edits
 
(6 intermediate revisions by 3 users not shown)
Line 9: Line 9:


== Temperaments ==
== Temperaments ==
By tempering it out, the '''jacobin temperament''' is defined. Interestingly, [[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 1789edo has a unique position due to its number of steps being a hallmark year of the French Revolution, it is more rational to use the other edos for this temperament. Miscellaneous temperaments tempering out this comma are collected in [[The Jacobins]].
By tempering it out, the '''jacobin temperament''' is defined. Interestingly, [[1789edo]] is an edo that [[support]]s the jacobin temperament - and is consistent to distance 2 on the subgroup 2.5.11.13, the subgroup of the comma. Although 1789edo has a unique position due to its number of steps being a hallmark year of the {{W|French Revolution}}, it is more rational to use the other edos for this temperament. Miscellaneous temperaments tempering out this comma are collected in [[The Jacobins]].


The 17-limit factorization shows us a natural path of extension, also given below.  
The 17-limit factorization shows us a natural path of extension by adding 12376/12375. Equally, it can be conceptualized as a rank-2 temperament in 2.13/10.11 subgroup, in which case it is called ''jacobin-naiadic'', after [[13/10]] being called a naiadic by interval class.


=== Jacobin ===
See [[The Jacobins#Jacobin]] for technical data.
[[Subgroup]]: 2.3.5.7.11.13
 
[[Comma list]]: 6656/6655
 
[[Mapping]]: <br>
{| class="right-all"
|-
| [⟨ || 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
 
{{Optimal ET sequence|legend=1| 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 }}
 
==== Septendecimal jacobin ====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 6656/6655, 12376/12375
 
Mapping: <br>
{| class="right-all"
|-
| [⟨ || 1 || 0 || 0 || 0 || 0 || -9 || 6 || ],
|-
| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || 2 || ],
|-
| ⟨ || 0 || 0 || 1 || 0 || 0 || 1 || 2 || ],
|-
| ⟨ || 0 || 0 || 0 || 1 || 0 || 0 || -1 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 1 || 3 || -2 || ]]
|}
 
Optimal ET sequence: {{Optimal ET sequence| 15g, 22, 37g, 39dfg, 41g, 50, 63g, 72, 111, 152f, 159, 183, 239f, 248, 270, 311, 422, 494, 581, 742, 764, 814, 1075, 1236, 1395, 1506, 2000, 2581, 2814, 2901, 3323, 3395, 8296e, 11691e, 16322ee, 17086cdeeg, 21223cdeefg }}


== Etymology ==
== Etymology ==
This comma was apparently named by [[Gene Ward Smith]] in 2014 for reasons unknown<ref>[https://en.xen.wiki/index.php?title=List_of_superparticular_intervals&diff=next&oldid=18864 Xenharmonic Wiki | ''List of superparticular intervals (Revision as of 23:46, 13 June 2014 by Wikispaces>genewardsmith)'']</ref>.  
This comma was apparently named by [[Gene Ward Smith]] in 2014 for reasons unknown<ref>[https://en.xen.wiki/index.php?title=List_of_superparticular_intervals&diff=next&oldid=18864 Xenharmonic Wiki | ''List of superparticular intervals (Revision as of 23:46, 13 June 2014 by Wikispaces>genewardsmith)'']</ref>. An hypothesis is that "jacobin" refers to the {{w|Jacobins}}, a political group founded in 1789 during the French Revolution, since this comma is tempered out by [[1789edo]], a tuning which, furthermore, is [[consistent]] to distance 2 in the 2.5.11.13-subgroup-limited [[13-odd-limit]], reinforcing the importance of this comma in this tuning.


== See also ==
== See also ==
Line 67: Line 25:
[[Category:Jacobin]]
[[Category:Jacobin]]
[[Category:Commas with unknown etymology]]
[[Category:Commas with unknown etymology]]
{{Todo|add etymology|comment=I know it's something to do with the French Revolution, but what, exactly? Spell it all out please, why exactly does the name "jacobin" uniquely fit this particular comma?}}
Retrieved from "https://en.xen.wiki/w/6656/6655"