Very low accuracy temperaments: Difference between revisions

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== Quint ==

Quint preserves the 5-limit mapping of 5edo, and harmonic 7 is mapped to an independent generator. As harmonic 7 is ~~way more~~ accurately approximated ~~than 5~~ by 5edo, this temperament provides little improvement ~~to 5edo's 7-limit tuning~~, so ~~in what way this temperament~~ is ~~useful remains unexplained~~. It would make much more sense to, for example, preserve the 2.3.7-subgroup structure of 5edo and give prime 5 an independent generator instead, which is exactly what [[blackwood]] does.

Quint preserves the 5-limit mapping of 5edo, and harmonic 7 is mapped to an independent generator. As harmonic 7 is already quite accurately approximated by 5edo for its size, this temperament provides little improvement, so it is only provided below for bookkeeping purposes. It would make much more sense to, for example, preserve the 2.3.7-subgroup structure of 5edo and give prime 5 an independent generator instead, which is exactly what [[blackwood]] does.

[[Subgroup]]: 2.3.5.7

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: Mapping generators: ~6/5, ~7

[[Optimal tuning]]s:

* [[WE]]: ~6/5 = 236.416, ~7/4 = 1002.701 (~28/27 = 57.038) ~~~~

* [[WE]]: ~6/5 = 236.416{{c}}, ~7/4 = 1002.701{{c}} (~28/27 = 57.038{{c}})

: [[error map]]: {{val| -17.921 -10.628 +50.676 -1.966 }}

* [[CWE]]: ~6/5 = 240.000, ~7/4 = 1005.135 (~28/27 = 45.135)

* [[CWE]]: ~6/5 = 240.000{{c}}, ~7/4 = 1005.135{{c}} (~28/27 = 45.135{{c}})

: error map: {{val| 0.000 +18.045 +93.686 +36.309 }}

[[Badness]] (Sintel): 1.22

@@ Line 313: / Line 313: @@
 == Quint ==
-Quint preserves the 5-limit mapping of 5edo, and harmonic 7 is mapped to an independent generator. As harmonic 7 is way more accurately approximated than 5 by 5edo, this temperament provides little improvement to 5edo's 7-limit tuning, so in what way this temperament is useful remains unexplained. It would make much more sense to, for example, preserve the 2.3.7-subgroup structure of 5edo and give prime 5 an independent generator instead, which is exactly what [[blackwood]] does.
+Quint preserves the 5-limit mapping of 5edo, and harmonic 7 is mapped to an independent generator. As harmonic 7 is already quite accurately approximated by 5edo for its size, this temperament provides little improvement, so it is only provided below for bookkeeping purposes. It would make much more sense to, for example, preserve the 2.3.7-subgroup structure of 5edo and give prime 5 an independent generator instead, which is exactly what [[blackwood]] does.
 [[Subgroup]]: 2.3.5.7
@@ Line 320: / Line 320: @@
 {{Mapping|legend=1| 5 8 12 0 | 0 0 0 1 }}
 : Mapping generators: ~6/5, ~7
 [[Optimal tuning]]s:
-* [[WE]]: ~6/5 = 236.416, ~7/4 = 1002.701 (~28/27 = 57.038) <!-- Please review, last digit may be wrong -->
+* [[WE]]: ~6/5 = 236.416{{c}}, ~7/4 = 1002.701{{c}} (~28/27 = 57.038{{c}})
 : [[error map]]: {{val| -17.921 -10.628 +50.676 -1.966 }}
-* [[CWE]]: ~6/5 = 240.000, ~7/4 = 1005.135 (~28/27 = 45.135)
+* [[CWE]]: ~6/5 = 240.000{{c}}, ~7/4 = 1005.135{{c}} (~28/27 = 45.135{{c}})
 : error map: {{val| 0.000 +18.045 +93.686 +36.309 }}
-{{Optimal ET sequence|legend=1| 5, 15ccd }}
+{{Optimal ET sequence|legend=1| 5, 15ccd, 20cccd }}
 [[Badness]] (Sintel): 1.22