Pentadacus: Difference between revisions

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In terms of strong extensions to the 5.7.11.13 subgroup, there are the c57 & c71 extension which maps [[13/5]] to -20 generators (but this requires the usage of the 14L 15s MOS to access 13/5), and the c15 & c29 extension which maps [[13/5]] to -6 generators (but it has high [[error]]). These are roughly equal in Dirichlet [[badness]].

The best extension to the 5.7.11.13 subgroup is actually the weak extension [[User:2^67-1]] has named ''Pentapassion'', that tempers out the Cuthbert comma [[847/845]]. This halves the generator into a semitone of roughly 97 cents, and 17 of these new generators reach 13/5 (so essentially 8.5 of the original generator). It is so named because the generator is close to the generator of [[Passion]] temperament. Interestingly, the first few steps of Pentapassion can sound like [[12edo]] (like how Pentadacus can sound like 6edo), although it quickly becomes out-of-tune after stacking a few generators.

The best extension to the 5.7.11.13 subgroup is actually the weak extension [[User:2^67-1]] has named ''Pentapassion'', that tempers out the Cuthbert comma [[847/845]]. This halves the generator into a semitone of roughly 97 cents, and 17 of these new generators reach 13/5 (so essentially 8.5 of the original generator). It is so named because the generator is close to the generator of [[Passion]] temperament. Interestingly, the first few steps of Pentapassion can sound like [[12edo]] (like how Pentadacus can sound like 6edo), although it quickly becomes out-of-tune after stacking a few generators. Pentapassion can be used with a 28L 1s<5/1> MOS.

== Interval chain ==

{| class="wikitable center-1 right-2"

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 In terms of strong extensions to the 5.7.11.13 subgroup, there are the c57 & c71 extension which maps [[13/5]] to -20 generators (but this requires the usage of the 14L 15s MOS to access 13/5), and the c15 & c29 extension which maps [[13/5]] to -6 generators (but it has high [[error]]). These are roughly equal in Dirichlet [[badness]].
-The best extension to the 5.7.11.13 subgroup is actually the weak extension [[User:2^67-1]] has named ''Pentapassion'', that tempers out the Cuthbert comma [[847/845]]. This halves the generator into a semitone of roughly 97 cents, and 17 of these new generators reach 13/5 (so essentially 8.5 of the original generator). It is so named because the generator is close to the generator of [[Passion]] temperament. Interestingly, the first few steps of Pentapassion can sound like [[12edo]] (like how Pentadacus can sound like 6edo), although it quickly becomes out-of-tune after stacking a few generators.
+The best extension to the 5.7.11.13 subgroup is actually the weak extension [[User:2^67-1]] has named ''Pentapassion'', that tempers out the Cuthbert comma [[847/845]]. This halves the generator into a semitone of roughly 97 cents, and 17 of these new generators reach 13/5 (so essentially 8.5 of the original generator). It is so named because the generator is close to the generator of [[Passion]] temperament. Interestingly, the first few steps of Pentapassion can sound like [[12edo]] (like how Pentadacus can sound like 6edo), although it quickly becomes out-of-tune after stacking a few generators. Pentapassion can be used with a 28L 1s<5/1> MOS.
 == Interval chain ==
 {| class="wikitable center-1 right-2"