1156/1155: Difference between revisions

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== 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 [[quadrantonismic chords]] are enabled.

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. This tempers the [[harmonic series segment]] of quartertones, 32::36, to reduce it to three equidistant elements: 33/32, 34/33~35/34, 36/35.

Alternatively, 1089/1088 ({{S|33}}) can be added to the comma list, which reduces the segment to two distinct elements: 33/32~34/33~35/34, 36/35; 1225/1224 ({{S|35}}) works similarly, resulting in 33/32, 34/33~35/34~36/35. Tempering out both 1089/1088 and 1225/1224 while observing 1156/1155 is another major option, resulting in 33/32~34/33, 35/34~36/35, and merging all these temperaments will lead to [[uniwiz]], a rank-3 temperament with a single quartertone representing all the differently sized quartertones in the 2.3.5.7.11.17-subgroup.

=== Quadrantonic ===

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 == 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 [[quadrantonismic chords]] are enabled.
+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. This tempers the [[harmonic series segment]] of quartertones, 32::36, to reduce it to three equidistant elements: 33/32, 34/33~35/34, 36/35.
+Alternatively, 1089/1088 ({{S|33}}) can be added to the comma list, which reduces the segment to two distinct elements: 33/32~34/33~35/34, 36/35; 1225/1224 ({{S|35}}) works similarly, resulting in 33/32, 34/33~35/34~36/35. Tempering out both 1089/1088 and 1225/1224 while observing 1156/1155 is another major option, resulting in 33/32~34/33, 35/34~36/35, and merging all these temperaments will lead to [[uniwiz]], a rank-3 temperament with a single quartertone representing all the differently sized quartertones in the 2.3.5.7.11.17-subgroup.
 === Quadrantonic ===