No-twos subgroup temperaments: Difference between revisions

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Discovered and named by {{u|CompactStar}} in 2026, Pentadacus is an efficient 5.7.11 subgroup temperament generated by a [[meantone]]-esque small whole tone interval that represents [[55/49]]. Stacking 3 of these tones gives [[7/5]] and 7 of them give [[11/5]]. It is a no-twos version of [[~~undecimal didacus|~~didacus]], and is named as a play on "didacus", with the "di-" part being rebracketed as the Greek prefix for 2 and changed to "penta-" (5).

Discovered and named by {{u|CompactStar}} in 2026, Pentadacus is an efficient 5.7.11 subgroup temperament generated by a [[meantone]]-esque small whole tone interval that represents [[55/49]]. Stacking 3 of these tones gives [[7/5]] and 7 of them give [[11/5]], basically making it a compressed [[14ed5]] generator chain. It is a no-twos version of 2.5.7.11 [[didacus]], and is named as a play on "didacus", with the "di-" part being rebracketed as the Greek prefix for 2 and changed to "penta-" (5).

[[Subgroup]]: 5.7.11

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[[Badness]] (Sintel): 0.216

=== Pentapassion ===

Named by [[User:2^67-1|Cole]] in 2026, Pentapassion is a [[weak extension]] of Pentadacus to the 5.7.11.13 subgroup that splits the generator in half, making the new generator a semitone. [[13/5]] (the pentave-reduced 13th harmonic) is found at 17 of these new generators up. It is named in reference to the octave-equivalent [[Passion]] temperament, which has a similar generator, and in both temperaments [[7/5]] is mapped to 6 generators up.

[[Subgroup]]: 5.7.11.13

[[Comma list]]: [[847/845]], 831875/823543

: mapping generators: ~5, ~343/325

[[Optimal tuning]]s:

* [[WE]]: ~5 = 2785.855{{c}}, ~343/325 = 97.393{{c}}

: [[error map]]: {{val| -0.459 +1.384 -1.968 +1.000 }}

* [[CWE]]: ~5 = 2786.314{{c}}, ~343/325 = 97.386{{c}}

: error map: {{val| 0.000 +1.803 -1.601 +1.347 }}

[[Optimal ET sequence]]: TBA

[[Badness]] (Sintel): 0.277

== Antipyth ==

@@ Line 973: / Line 973: @@
 {{Main| Pentadacus }}
-Discovered and named by {{u|CompactStar}} in 2026, Pentadacus is an efficient 5.7.11 subgroup temperament generated by a [[meantone]]-esque small whole tone interval that represents [[55/49]]. Stacking 3 of these tones gives [[7/5]] and 7 of them give [[11/5]]. It is a no-twos version of [[undecimal didacus|didacus]], and is named as a play on "didacus", with the "di-" part being rebracketed as the Greek prefix for 2 and changed to "penta-" (5).
+Discovered and named by {{u|CompactStar}} in 2026, Pentadacus is an efficient 5.7.11 subgroup temperament generated by a [[meantone]]-esque small whole tone interval that represents [[55/49]]. Stacking 3 of these tones gives [[7/5]] and 7 of them give [[11/5]], basically making it a compressed [[14ed5]] generator chain. It is a no-twos version of 2.5.7.11 [[didacus]], and is named as a play on "didacus", with the "di-" part being rebracketed as the Greek prefix for 2 and changed to "penta-" (5).
 [[Subgroup]]: 5.7.11
@@ Line 991: / Line 991: @@
 [[Badness]] (Sintel): 0.216
+=== Pentapassion ===
+Named by [[User:2^67-1|Cole]] in 2026, Pentapassion is a [[weak extension]] of Pentadacus to the 5.7.11.13 subgroup that splits the generator in half, making the new generator a semitone. [[13/5]] (the pentave-reduced 13th harmonic) is found at 17 of these new generators up. It is named in reference to the octave-equivalent [[Passion]] temperament, which has a similar generator, and in both temperaments [[7/5]] is mapped to 6 generators up.
+[[Subgroup]]: 5.7.11.13
+[[Comma list]]: [[847/845]], 831875/823543
+{{Mapping|legend=3| 1 1 1 1 | 0 6 14 17 }}
+: mapping generators: ~5, ~343/325
+[[Optimal tuning]]s:
+* [[WE]]: ~5 = 2785.855{{c}}, ~343/325 = 97.393{{c}}
+: [[error map]]: {{val| -0.459 +1.384 -1.968 +1.000 }}
+* [[CWE]]: ~5 = 2786.314{{c}}, ~343/325 = 97.386{{c}}
+: error map: {{val| 0.000 +1.803 -1.601 +1.347 }}
+[[Optimal ET sequence]]: TBA
+[[Badness]] (Sintel): 0.277
 == Antipyth ==