Very low accuracy temperaments: Difference between revisions

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 [[Badness]] (Sintel): 1.22
+== Sept ==
+Sept preserves the 2.3.7-subgroup of mapping of 7edo, and harmonic 5 is mapped to an independent generator. As harmonic 5 is way more accurately approximated than 7 by 7edo, this temperament provides little improvement to 7edo'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 5-limit structure of 7edo and give prime 7 an independent generator instead, which is exactly what [[jamesbond]] does.
+This temperament used to be known as ''mujannab''.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 54/49, 64/63
+{{Mapping|legend=1| 7 11 0 20 | 0 0 1 0 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~9/8 = 170.823{{c}}, ~5/4 = 393.792{{c}} (~15/14 = 52.145{{c}})
+: [[error map]]: {{val| -4.236 -22.898 -0.994 +47.642 }}
+* [[CWE]]: ~9/8 = 171.429{{c}}, ~5/4 = 392.719{{c}} (~15/14 = 49.862{{c}})
+: error map: {{val| 0.000 -16.241 +6.406 +59.746 }}
+{{Optimal ET sequence|legend=1| 7, 14d }}
+[[Badness]] (Sintel): 2.68
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 45/44, 54/49, 64/63
+Mapping: {{mapping| 7 11 0 20 8 | 0 0 1 0 1 }}
+Optimal tunings:
+* WE: ~11/10 = 170.817{{c}}, ~5/4 = 393.252{{c}} (~33/32 = 51.619{{c}})
+* CWE: ~11/10 = 171.429{{c}}, ~5/4 = 391.840{{c}} (~33/32 = 48.983{{c}})
+{{Optimal ET sequence|legend=0| 7, 14de }}
+Badness (Sintel): 2.02
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 27/26, 45/44, 52/49, 64/63
+Mapping: {{mapping| 7 11 0 20 8 26 | 0 0 1 0 1 0 }}
+Optimal tunings:
+* WE: ~11/10 = 170.795{{c}}, ~5/4 = 393.611{{c}} (~33/32 = 52.021{{c}})
+* CWE: ~11/10 = 171.429{{c}}, ~5/4 = 392.725{{c}} (~33/32 = 49.868{{c}})
+{{Optimal ET sequence|legend=0| 7, 14de }}
+Badness (Sintel): 1.77
 == Geryon ==
@@ Line 446: / Line 497: @@
 == Plutus ==
+{{Distinguish| Pluto }}
 {{See also| Meantone family }}