@@ Line 5: / Line 5: @@
 * ''[[Pelogic]]'', {21/20, 135/128} → [[Pelogic family #Pelogic|Pelogic family]]
 * ''[[August]]'', {36/35, 128/125} → [[Augmented family #August|Augmented family]]
+* [[Negri]], {49/48, 225/224} → [[Slendro clan #Negri|Slendro clan]]
 * [[Pajara]], {50/49, 64/63} → [[Diaschismic family #Pajara|Diaschismic family]]
 * [[Meantone]], {81/80, 126/125} → [[Meantone family #Septimal meantone|Meantone family]]
@@ Line 28: / Line 29: @@
 * ''[[Gammy]]'', {225/224, 94143178827/91913281250} → [[Gammic family #Gammy|Gammic family]]
-Considered below are negri, wizard, tritonic, septimin, slender, triton, merman, marvolo, amavil, enneaportent, submajor, alphorn, tertiosec, gwazy, and gracecordial.
+Considered below are wizard, tritonic, septimin, slender, triton, merman, marvolo, amavil, enneaportent, submajor, alphorn, tertiosec, gwazy, and gracecordial.
 Since (5/4)<sup>2</sup> = 225/224 × 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess a version of the augmented triad where each third approximates either 5/4 or 9/7. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before 12edo established itself as the standard tuning, it is arguably more authentic to tune it as two stacked major thirds and a diminished fourth, which is what it is in meantone, than as the modern version of three stacked very sharp major thirds.
@@ Line 35: / Line 36: @@
 Marvel tempering allows for a tritone substitution whereby the dominant seventh chord formed by adding 16/9 above the root shares its tritone with a 4:5:6:7 tetrad. (The tritone of the dominant seventh is (16/9)/(5/4) = 64/45. Setting this equal to 10/7 gives (10/7)/(64/45) = 225/224.)
-== Negri ==
-{{main| Negri }}
-Negri tempers out the [[negri comma]] in the 5-limit, [[49/48]] and [[225/224]] in the 7-limit. It can be extended naturally to the 2.3.5.7.13 subgroup by adding [[91/90]] to the comma list; this will be discussed below under the title of negra.
-Subgroup: 2.3.5
-[[Comma list]]: 16875/16384
-[[Mapping]]: [{{val| 1 2 2 }}, {{val| 0 -4 3 }}]
-{{Multival|legend=1| 4 -3 -14 }}
-[[POTE generator]]: ~16/15 = 125.7549
-{{Optimal ET sequence|legend=1| 9, 10, 19, 67c, 86c, 105c }}
-[[Badness]]: 0.086856
-=== 7-limit ===
-Subgroup: 2.3.5.7
-[[Comma list]]: 49/48, 225/224
-[[Mapping]]: [{{val| 1 2 2 3 }}, {{val| 0 -4 3 -2 }}]
-{{Multival|legend=1| 4 -3 2 -14 -8 13 }}
-[[POTE generator]]: ~15/14 = 125.608
-{{Optimal ET sequence|legend=1| 9, 10, 19, 48d, 67cdd, 86cdd }}
-[[Badness]]: 0.026483
-==== Negra ====
-This is the 2.3.5.7.13 extension of negri.
-Subgroup: 2.3.5.7.13
-[[Comma list]]: 49/48, 65/64, 91/90
-[[Sval]] [[mapping]]: [{{val| 1 2 2 3 4 }}, {{val| 0 -4 3 -2 -3 }}]
-[[Gencom]] [[mapping]]: [{{val| 1 2 2 3 0 4 }}, {{val| 0 -4 3 -2 0 -3 }}]
-[[Gencom]]: [2 14/13; 49/48 65/64 91/90]
-[[POTE generator]]: ~14/13 = 125.567
-{{Optimal ET sequence|legend=1| 9, 10, 19, 48df, 67cddf, 86cddff }}
-=== 11-limit ===
-Subgroup: 2.3.5.7.11
-Comma list: 45/44, 49/48, 56/55
-Mapping: [{{val| 1 2 2 3 4 }}, {{val| 0 -4 3 -2 -5 }}]
-POTE generator: ~15/14 = 126.474
-{{Optimal ET sequence|legend=1| 9, 10, 19 }}
-Badness: 0.026190
-==== 13-limit ====
-Subgroup: 2.3.5.7.11.13
-Comma list: 45/44, 49/48, 56/55, 78/77
-Mapping: [{{val| 1 2 2 3 4 4 }}, {{val| 0 -4 3 -2 -5 -3 }}]
-POTE generator: ~14/13 = 126.431
-{{Optimal ET sequence|legend=1| 9, 10, 19 }}
-Badness: 0.017833
-=== Negril ===
-Subgroup: 2.3.5.7.11
-Comma list: 49/48, 100/99, 225/224
-Mapping: [{{val| 1 2 2 3 2 }}, {{val| 0 -4 3 -2 14 }}]
-POTE generator: ~15/14 = 124.767
-{{Optimal ET sequence|legend=1| 19, 29, 48d, 77cdd }}
-Badness: 0.038679
-==== 13-limit ====
-Subgroup: 2.3.5.7.11.13
-Comma list: 49/48, 65/64, 91/90, 875/858
-Mapping: [{{val| 1 2 2 3 2 4 }}, {{val| 0 -4 3 -2 14 -3 }}]
-POTE generator: ~14/13 = 124.716
-{{Optimal ET sequence|legend=1| 19, 29, 48df, 77cddf }}
-Badness: 0.024383
-=== Negric ===
-Subgroup: 2.3.5.7.11
-Comma list: 33/32, 49/48, 77/75
-Mapping: [{{val| 1 2 2 3 3 }}, {{val| 0 -4 3 -2 4 }}]
-POTE generator: ~15/14 = 127.039
-{{Optimal ET sequence|legend=1| 9, 19e }}
-Badness: 0.030617
-==== 13-limit ====
-Subgroup: 2.3.5.7.11.13
-Comma list: 33/32, 49/48, 65/64, 91/90
-Mapping: [{{val| 1 2 2 3 3 4 }}, {{val| 0 -4 3 -2 4 -3 }}]
-POTE generator: ~14/13 = 127.039
-{{Optimal ET sequence|legend=1| 9, 19e }}
-Badness: 0.020205
-=== Negroni ===
-Subgroup: 2.3.5.7.11
-Comma list: 49/48, 55/54, 225/224
-Mapping: [{{val| 1 2 2 3 5 }}, {{val| 0 -4 3 -2 -15 }}]
-POTE generator: ~15/14 = 124.539
-{{Optimal ET sequence|legend=1| 10, 19e, 29, 77cddee }}
-Badness: 0.035296
-==== 13-limit ====
-Subgroup: 2.3.5.7.11.13
-Comma list: 49/48, 55/54, 65/64, 91/90
-Mapping: [{{val| 1 2 2 3 5 4 }}, {{val| 0 -4 3 -2 -15 -3 }}]
-POTE generator: ~14/13 = 124.545
-{{Optimal ET sequence|legend=1| 10, 19e, 29, 77cddeef }}
-Badness: 0.021559
-=== Wilsec ===
-Subgroup: 2.3.5.7.11
-Comma list: 49/48, 121/120, 225/224
-Mapping: [{{val| 1 6 -1 5 4 }}, {{val| 0 -8 6 -4 -1 }}]
-POTE generator: ~11/8 = 537.186
-{{Optimal ET sequence|legend=1| 9, 20, 29, 38d, 67cdde }}
-Badness: 0.041886
-==== 13-limit ====
-Subgroup: 2.3.5.7.11.13
-Comma list: 49/48, 65/64, 91/90, 121/120
-Mapping: [{{val| 1 6 -1 5 4 7 }}, {{val| 0 -8 6 -4 -1 -6 }}]
-POTE generator: ~11/8 = 537.208
-{{Optimal ET sequence|legend=1| 9, 20, 29, 38df, 67cddef }}
-Badness: 0.025192
-==== 17-limit ====
-Subgroup: 2.3.5.7.11.13.17
-Comma list: 49/48, 65/64, 91/90, 121/120, 154/153
-Mapping: [{{val| 1 6 -1 5 4 7 -2 }}, {{val| 0 -8 6 -4 -1 -6 11 }}]
-POTE generator: ~11/8 = 537.230
-{{Optimal ET sequence|legend=1| 9, 20g, 29g, 38df, 67cddefg }}
-Badness: 0.021778
-==== 19-limit ====
-Subgroup: 2.3.5.7.11.13.17.19
-Comma list: 49/48, 65/64, 77/76, 91/90, 121/120, 154/153
-Mapping: [{{val| 1 6 -1 5 4 7 -2 7 }}, {{val| 0 -8 6 -4 -1 -6 11 -5 }}]
-POTE generator: ~11/8 = 537.214
-{{Optimal ET sequence|legend=1| 9, 20g, 29g, 38df, 67cddefgh }}
-Badness: 0.016828
 == Wizard ==

Marvel temperaments: Difference between revisions