Meantone family: Difference between revisions

← Older edit Newer edit →

VisualWikitext

@@ Line 798: / Line 798: @@
 {{Main| Flattone }}
-In flattone tunings, the fifth is typically even flatter than that of [[19edo]]. Here, 9 fourths get to the interval class for 7, so that [[7/4]] is a diminished seventh (C–B𝄫), [[7/6]] is a diminished third (C–E𝄫), and [[7/5]] is a double-diminished fifth (C–G𝄫). In general, septimal subminor intervals are diminished and septimal supermajor intervals are augmented, which makes it quite easy to learn flattone notation. Good tunings for flattone are [[45edo]], [[64edo]], and [[71edo]].
+In flattone, 9 fourths get to the interval class for 7, so that [[7/4]] is a diminished seventh (C–B𝄫), [[7/6]] is a diminished third (C–E𝄫), and [[7/5]] is a double-diminished fifth (C–G𝄫). In general, septimal subminor intervals are diminished and septimal supermajor intervals are augmented, which makes it quite easy to learn flattone notation. The fifth in flattone is typically flatter than that of [[19edo]]. Good tunings for flattone include [[45edo]], [[64edo]], and [[71edo]].
 [[Subgroup]]: 2.3.5.7
@@ Line 870: / Line 870: @@
 Badness (Sintel): 0.920
-== Flattertone ==
-Flattertone tunings are typically at least as flat as [[26edo]]. Here, 17 fifths get to the interval class for 7, so that [[7/4]] is a double-augmented sixth (C–Ax). [[26edo]] and [[33edo|33cd-edo]] are the two primary flattertone tunings. [[1/2-comma meantone]] is also encompassed within flattertone's range. Any flatter than this, the meantone mapping for 5/4 is too inaccurate (it becomes more of a [[16/13]] or [[27/22]]), and [[deeptone]] temperament's mapping is more logical.
-[[Subgroup]]: 2.3.5.7
-[[Comma list]]: 81/80, 1875/1792
-{{Mapping|legend=1| 1 0 -4 -24 | 0 1 4 17 }}
-: mapping generators: ~2, ~3
-[[Optimal tuning]]s:
-* [[WE]]: ~2 = 1204.4511{{c}}, ~3/2 = 694.3258{{c}}
-: [[error map]]: {{val| +4.451 -3.178 -9.011 +3.554 }}
-* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 692.0479{{c}}
-: error map: {{val| 0.000 -9.907 -18.122 -4.012 }}
-{{Optimal ET sequence|legend=1| 7d, 19d, 26, 59bcd, 85bccd }}
-[[Badness]] (Sintel): 2.43
-==== 11-limit ====
-Subgroup: 2.3.5.7.11
-Comma list: 45/44, 81/80, 1375/1344
-Mapping: {{mapping| 1 0 -4 -24 -6 | 0 1 4 17 6 }}
-Optimal tunings:
-* WE: ~2 = 1203.4653{{c}}, ~3/2 = 693.8144{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 692.0422{{c}}
-{{Optimal ET sequence|legend=0| 7d, 19d, 26 }}
-Badness (Sintel): 1.53
-; Music
-* [https://youtu.be/scCuGXnj5IY ''Music in 33EDO (33-Tone Equal Temperament) - Feb 2024''] by [[Budjarn Lambeth]] (2024)
 == Dominant ==
@@ Line 1,051: / Line 1,012: @@
 Badness (Sintel): 0.864
+== Flattertone ==
+In flattertone, 17 fifths get to the interval class for 7, so that [[7/4]] is a double-augmented sixth (C–Ax). The fifth in flattertone is typically at least as flat as [[26edo]]. Here, 26edo and [[33edo|33cd-edo]] are the two primary flattertone tunings. [[1/2-comma meantone]] is also encompassed within flattertone's range. Any flatter than this, the meantone mapping for 5/4 is too inaccurate (it becomes more of a [[16/13]] or [[27/22]]), and [[deeptone]] temperament's mapping is more logical.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 81/80, 1875/1792
+{{Mapping|legend=1| 1 0 -4 -24 | 0 1 4 17 }}
+: mapping generators: ~2, ~3
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1204.4511{{c}}, ~3/2 = 694.3258{{c}}
+: [[error map]]: {{val| +4.451 -3.178 -9.011 +3.554 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 692.0479{{c}}
+: error map: {{val| 0.000 -9.907 -18.122 -4.012 }}
+{{Optimal ET sequence|legend=1| 7d, 19d, 26, 59bcd, 85bccd }}
+[[Badness]] (Sintel): 2.43
+==== 11-limit ====
+Subgroup: 2.3.5.7.11
+Comma list: 45/44, 81/80, 1375/1344
+Mapping: {{mapping| 1 0 -4 -24 -6 | 0 1 4 17 6 }}
+Optimal tunings:
+* WE: ~2 = 1203.4653{{c}}, ~3/2 = 693.8144{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 692.0422{{c}}
+{{Optimal ET sequence|legend=0| 7d, 19d, 26 }}
+Badness (Sintel): 1.53
+; Music
+* [https://youtu.be/scCuGXnj5IY ''Music in 33EDO (33-Tone Equal Temperament) - Feb 2024''] by [[Budjarn Lambeth]] (2024)
 == Sharptone ==