847/845: Difference between revisions

(One intermediate revision by the same user not shown)

Line 4:

| Comma = yes

}}

'''847/845''', the '''cuthbert comma''', is a [[small comma|small]] [[13-limit]] (also [[5.7.11.13 subgroup|5.7.11.13-subgroup]]) [[comma]] measuring about 4.09{{cent}}. It is the difference between [[7/5]] and a stack of two [[13/11]]'s~~. It is also the difference between [[125/121]] and [[175/169]]~~.

'''847/845''', the '''cuthbert comma''', is a [[small comma|small]] [[13-limit]] (also [[5.7.11.13 subgroup|5.7.11.13-subgroup]]) [[comma]] measuring about 4.09{{cent}}. It is the difference between [[7/5]] and a stack of two [[13/11]]'s.

In terms of full 13-limit commas, it is the difference between the following superparticular pairs:

Line 19:

[[Tempering out]] this comma in the 13-limit results in the rank-5 '''cuthbert''' temperament and enables the [[cuthbert chords]].

Tempering it out in the 5.7.11.13 subgroup leads to an extremely efficient rank-3 temperament, and tempering it out in the 7/5.11/5.13/5 subgroup leads to a rank-2 temperament containing the 5:7:11:13 chord~~. Both have a natural weak extension to prime 3 by tempering out 1575/1573, enabling 5:7:11:13:15~~.

Tempering it out in the 5.7.11.13 subgroup leads to an extremely efficient rank-3 temperament, and tempering it out in the 7/5.11/5.13/5 subgroup leads to a restriction of the rank-2 temperament [[edson]] containing the 5:7:11:13 chord.

[[Category:Cuthbert]]

[[Category:Commas with unknown etymology]]

@@ Line 4: / Line 4: @@
 | Comma = yes
 }}
-'''847/845''', the '''cuthbert comma''', is a [[small comma|small]] [[13-limit]] (also [[5.7.11.13 subgroup|5.7.11.13-subgroup]]) [[comma]] measuring about 4.09{{cent}}. It is the difference between [[7/5]] and a stack of two [[13/11]]'s. It is also the difference between [[125/121]] and [[175/169]].
+'''847/845''', the '''cuthbert comma''', is a [[small comma|small]] [[13-limit]] (also [[5.7.11.13 subgroup|5.7.11.13-subgroup]]) [[comma]] measuring about 4.09{{cent}}. It is the difference between [[7/5]] and a stack of two [[13/11]]'s.
 In terms of full 13-limit commas, it is the difference between the following superparticular pairs:
@@ Line 19: / Line 19: @@
 [[Tempering out]] this comma in the 13-limit results in the rank-5 '''cuthbert''' temperament and enables the [[cuthbert chords]].
-Tempering it out in the 5.7.11.13 subgroup leads to an extremely efficient rank-3 temperament, and tempering it out in the 7/5.11/5.13/5 subgroup leads to a rank-2 temperament containing the 5:7:11:13 chord. Both have a natural weak extension to prime 3 by tempering out 1575/1573, enabling 5:7:11:13:15.
+Tempering it out in the 5.7.11.13 subgroup leads to an extremely efficient rank-3 temperament, and tempering it out in the 7/5.11/5.13/5 subgroup leads to a restriction of the rank-2 temperament [[edson]] containing the 5:7:11:13 chord.
 [[Category:Cuthbert]]
 [[Category:Commas with unknown etymology]]