1156/1155: Difference between revisions
m Cleanup |
m Misc. cleanup |
||
| Line 4: | Line 4: | ||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
'''1156/1155''', the '''quadrantonisma''', is | '''1156/1155''', the '''quadrantonisma''', is an [[unnoticeable comma|unnoticeable]] [[17-limit]] no-13 [[superparticular]] [[comma]] measuring about 1.41 [[cent]]s. It may be properly described as the ''septendecimal quartertones comma'', since it is the difference between [[34/33]] and [[35/34]], the two 17-limit quartertones. | ||
== Commatic relations == | == Commatic relations == | ||
| Line 19: | Line 19: | ||
== Temperaments == | == Temperaments == | ||
[[Tempering out]] this comma in the 17-limit results in the rank-6 '''quadrantonismic | [[Tempering out]] this comma in the 17-limit results in the rank-6 '''quadrantonismic''' temperament, or in the 2.3.5.7.11.17 subgroup, the rank-5 '''quadrantonic''' temperament. In either case [[35/33]] is split into two equal parts, each representing 34/33~35/34, and enables [[quadrantonismic chords]]. If [[9801/9800]] is also added to the comma list, the quartertone above becomes literally a quarter of [[9/8]] and is tuned exactly middle of [[33/32]], the undecimal quartertone, and [[36/35]], the septimal quartertone. | ||
=== Quadrantonic === | === Quadrantonic === | ||
| Line 37: | Line 37: | ||
| ⟨ || 0 || 0 || 0 || 0 || -2 || -1 || ]] | | ⟨ || 0 || 0 || 0 || 0 || -2 || -1 || ]] | ||
|} | |} | ||
: mapping generators: ~2, ~3, ~5, ~7, ~34/11 | : mapping generators: ~2, ~3, ~5, ~7, ~34/11 | ||
| Line 62: | Line 61: | ||
| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ]] | | ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ]] | ||
|} | |} | ||
: mapping generators: ~2, ~3, ~5, ~7, ~34/11, ~13 | : mapping generators: ~2, ~3, ~5, ~7, ~34/11, ~13 | ||
| Line 73: | Line 71: | ||
== See also == | == See also == | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
[[Category:Quadrantonismic]] | [[Category:Quadrantonismic]] | ||
[[Category:Commas named for the intervals they stack]] | [[Category:Commas named for the intervals they stack]] | ||