1156/1155: Difference between revisions

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'''1156/1155''', the '''quadrantonisma''', is a [[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.  
'''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 ==
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== Temperaments ==
== Temperaments ==
[[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.
[[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 ===
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| ⟨ || 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


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| ⟨ || 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  


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== See also ==
== See also ==
* [[Unnoticeable comma]]
* [[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]]