Meantone: Difference between revisions

Formula to calculate n-comma meantone: improvement and converse derivation
Prime-optimized tunings: update terminlogyy
Line 72: Line 72:
! Weight-skew\Order !! Euclidean
! Weight-skew\Order !! Euclidean
|-
|-
| Tenney || CTE<br>~3/2 = 697.2143¢
| Tenney || CTE: ~3/2 = 697.2143¢
|-
|-
| Tenney-Weil || CTWE<br>~3/2 = 696.6512¢
| Weil || CWE: ~3/2 = 696.6512¢
|-
|-
| Equilateral || CEE<br>~3/2 = 696.8947¢<br>[[Eigenmonzo basis|Eigenmonzo (unchanged-interval) basis]]: 2.1875 (4/17-comma tuning)
| Equilateral || CEE: ~3/2 = 696.8947¢<br>[[Eigenmonzo basis|Eigenmonzo (unchanged-interval) basis]]: 2.1875 (4/17-comma tuning)
|-
|-
| Equilateral-Weil || CEWE<br>~3/2 = 696.4534¢<br>Eigenmonzo (unchanged-interval) basis: 2.48828125/3 (11/43-comma tuning)
| Skewed-equilateral || CSEE: ~3/2 = 696.4534¢<br>Eigenmonzo (unchanged-interval) basis: 2.48828125/3 (11/43-comma tuning)
|-
|-
| Benedetti || CBE<br>~3/2 = 697.3738¢<br>Eigenmonzo (unchanged-interval) basis: 2.{{monzo| 0 25 36 }} (36/169-comma tuning)
| Benedetti/Wilson || CBE: ~3/2 = 697.3738¢<br>Eigenmonzo (unchanged-interval) basis: 2.{{monzo| 0 25 36 }} (36/169-comma tuning)
|-
|-
| Benedetti-Weil || CBWE<br>~3/2 = 696.7868¢<br>Eigenmonzo (unchanged-interval) basis: 2.{{monzo| 0 5 31 }} (31/129-comma tuning)
| Skewed-Benedetti/Wilson || CSBE: ~3/2 = 696.7868¢<br>Eigenmonzo (unchanged-interval) basis: 2.{{monzo| 0 5 31 }} (31/129-comma tuning)
|}
|}


Line 90: Line 90:
! Weight-skew\Order !! Euclidean
! Weight-skew\Order !! Euclidean
|-
|-
| Tenney || CTE<br>~3/2 = 696.9521¢
| Tenney || CTE: ~3/2 = 696.9521¢
|-
|-
| Tenney-Weil || CTWE<br>~3/2 = 696.6562¢
| Weil || CWE: ~3/2 = 696.6562¢
|-
|-
| Equilateral || CEE<br>~3/2 = 696.8843¢<br>Eigenmonzo (unchanged-interval) basis: 2.{{monzo| 0 1 4 10 }}
| Equilateral || CEE: ~3/2 = 696.8843¢<br>Eigenmonzo (unchanged-interval) basis: 2.{{monzo| 0 1 4 10 }}
|-
|-
| Equilateral-Weil || CEWE<br>~3/2 = 696.7248¢<br>Eigenmonzo (unchanged-interval) basis: 2.4117715/9
| Skewed-equilateral || CSEE: ~3/2 = 696.7248¢<br>Eigenmonzo (unchanged-interval) basis: 2.4117715/9
|-
|-
| Benedetti || CBE<br>~3/2 = 697.0147¢<br>Eigenmonzo (unchanged-interval) basis: 2.{{monzo| 0 1225 1764 2250 }}
| Benedetti/Wilson || CBE: ~3/2 = 697.0147¢<br>Eigenmonzo (unchanged-interval) basis: 2.{{monzo| 0 1225 1764 2250 }}
|-
|-
| Benedetti-Weil || CBWE<br>~3/2 = 696.6306¢<br>Eigenmonzo (unchanged-interval) basis: 2.{{monzo| 0 -3290 3171 7215 }}
| Skewed-Benedetti/Wilson || CSBE: ~3/2 = 696.6306¢<br>Eigenmonzo (unchanged-interval) basis: 2.{{monzo| 0 -3290 3171 7215 }}
|}
|}