Ragismic microtemperaments: Difference between revisions

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== Supermajor ==

The generator for supermajor temperament is a supermajor third, 9/7, tuned about 0.002 cents flat. 37 of these give (215~~)/3~~, 46 give (219~~)/5~~, and 75 give (230~~)/7~~. This is clearly quite a complex temperament; it makes up for it, to the extent it does, with extreme accuracy: ~~1106~~ or ~~1277~~ can be used as tunings, leading to accuracy even greater than that of ennealimmal. The 80-note ~~mos~~ is presumably the place to start, and if that is not enough notes for you, there is always the 171-note ~~mos~~.

The generator for supermajor temperament is a supermajor third, [[9/7]], tuned about 0.002 cents flat. Note that in the data that follow, the generator is given as its [[octave complement]]. 37 of these give 3/222, 46 give 5/227, and 75 give 7/245. This is clearly quite a complex temperament; it makes up for it, to the extent it does, with extreme accuracy: [[1106edo]] or [[1277edo]] can be used as tunings, leading to accuracy even greater than that of [[ennealimmal]]. The 80-note generator chain is presumably the place to start, and if that is not enough notes for you, there is always the 171-note generator chain.

[[Subgroup]]: 2.3.5.7

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[[Comma list]]: 4375/4374, 52734375/52706752

: mapping generators: ~2, ~14/9

[[Optimal tuning]] ([[~~POTE~~]]): ~2 = 1200.~~000~~{{c}}, ~9/7 = ~~435~~.~~082~~{{c}}

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1200.0067{{c}}, ~14/9 = 764.9222{{c}}

: [[error map]]: {{val| +0.007 +0.019 -0.074 +0.037 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~14/9 = 764.9181{{c}}

: error map: {{val| 0.000 +0.013 -0.083 +0.029 }}

{{Optimal ET sequence|legend=1| ~~11,~~ 80, 171, 764, 935, 1106, 1277, 3660, 4937, 6214 }}

{{Optimal ET sequence|legend=1| 80, 171, 764, 935, 1106, 1277, 3660, 4937, 6214 }}

[[Badness]] (Sintel): 0.274

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Comma list: 3025/3024, 4375/4374, 35156250/35153041

Mapping: {{mapping| 2 ~~30 38 60 41~~ | 0 -37 -46 -75 -47 }}

Mapping: {{mapping| 2 -7 -8 -15 -6 | 0 37 46 75 47 }}

: mapping generators: ~99/70, ~11/10

Optimal ~~tuning (POTE)~~: ~99/70 = 600.~~000~~{{c}}, ~9/7 = ~~435~~.~~082~~{{c}}

Optimal tunings:

* WE: ~99/70 = 600.0103{{c}}, ~11/10 = 164.9205{{c}}

* CWE: ~99/70 = 600.0000{{c}}, ~11/10 = 164.9180{{c}}

{{Optimal ET sequence|legend=0| 80, 342, 764, 1106, 1448, 2554, ~~4002f~~, ~~6556cf~~ }}

{{Optimal ET sequence|legend=0| 80, 262d, 342, 764, 1106, 1448, 2554, 4002e, 6556cee }}

Badness (Sintel): 0.422

@@ Line 32: / Line 32: @@
 == Supermajor ==
-The generator for supermajor temperament is a supermajor third, 9/7, tuned about 0.002 cents flat. 37 of these give (2<sup>15</sup>)/3, 46 give (2<sup>19</sup>)/5, and 75 give (2<sup>30</sup>)/7. This is clearly quite a complex temperament; it makes up for it, to the extent it does, with extreme accuracy: 1106 or 1277 can be used as tunings, leading to accuracy even greater than that of ennealimmal. The 80-note mos is presumably the place to start, and if that is not enough notes for you, there is always the 171-note mos.
+The generator for supermajor temperament is a supermajor third, [[9/7]], tuned about 0.002 cents flat. Note that in the data that follow, the generator is given as its [[octave complement]]. 37 of these give 3/2<sup>22</sup>, 46 give 5/2<sup>27</sup>, and 75 give 7/2<sup>45</sup>. This is clearly quite a complex temperament; it makes up for it, to the extent it does, with extreme accuracy: [[1106edo]] or [[1277edo]] can be used as tunings, leading to accuracy even greater than that of [[ennealimmal]]. The 80-note generator chain is presumably the place to start, and if that is not enough notes for you, there is always the 171-note generator chain.
 [[Subgroup]]: 2.3.5.7
@@ Line 38: / Line 38: @@
 [[Comma list]]: 4375/4374, 52734375/52706752
-{{Mapping|legend=1| 1 15 19 30 | 0 -37 -46 -75 }}
+{{Mapping|legend=1| 1 -22 -27 -45 | 0 37 46 75 }}
+: mapping generators: ~2, ~14/9
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~9/7 = 435.082{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.0067{{c}}, ~14/9 = 764.9222{{c}}
+: [[error map]]: {{val| +0.007 +0.019 -0.074 +0.037 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~14/9 = 764.9181{{c}}
+: error map: {{val| 0.000 +0.013 -0.083 +0.029 }}
-{{Optimal ET sequence|legend=1| 11, 80, 171, 764, 935, 1106, 1277, 3660, 4937, 6214 }}
+{{Optimal ET sequence|legend=1| 80, 171, 764, 935, 1106, 1277, 3660, 4937, 6214 }}
 [[Badness]] (Sintel): 0.274
@@ Line 51: / Line 56: @@
 Comma list: 3025/3024, 4375/4374, 35156250/35153041
-Mapping: {{mapping| 2 30 38 60 41 | 0 -37 -46 -75 -47 }}
+Mapping: {{mapping| 2 -7 -8 -15 -6 | 0 37 46 75 47 }}
+: mapping generators: ~99/70, ~11/10
-Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~9/7 = 435.082{{c}}
+Optimal tunings:
+* WE: ~99/70 = 600.0103{{c}}, ~11/10 = 164.9205{{c}}
+* CWE: ~99/70 = 600.0000{{c}}, ~11/10 = 164.9180{{c}}
-{{Optimal ET sequence|legend=0| 80, 342, 764, 1106, 1448, 2554, 4002f, 6556cf }}
+{{Optimal ET sequence|legend=0| 80, 262d, 342, 764, 1106, 1448, 2554, 4002e, 6556cee }}
 Badness (Sintel): 0.422