Sensamagic clan: Difference between revisions
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The ''sensamagic clan'' tempers out the [[sensamagic family|sensamagic comma]], [[245/243]], a [[ | The '''sensamagic clan''' tempers out the [[sensamagic family|sensamagic comma]], [[245/243]], a triprime [[comma]] with no factors of 2, {{val| 0 -5 1 2 }} to be exact. There are a number of [[Regular Temperaments|linear temperament]]s in the [[Regular Temperaments|clan]] (magic, father, sensi, godzilla, superpyth, octacot, rodan, hedgehog, clyde, shrutar, sidi) but they've mostly been discussed elsewhere. Tempering out 245/243 alone leads to a [[Planar temperament|rank three temperament]] for which [[283edo]] is the [[optimal patent val]]. | ||
=Bohpier= | = Bohpier = | ||
Comma: 1220703125/1162261467 | Comma: 1220703125/1162261467 | ||
Line 12: | Line 12: | ||
Badness: 0.8605 | Badness: 0.8605 | ||
==7-limit== | == 7-limit == | ||
[[Comma]]s: 245/243, 3125/3087 | [[Comma]]s: 245/243, 3125/3087 | ||
Line 27: | Line 27: | ||
[[Badness]]: 0.0682 | [[Badness]]: 0.0682 | ||
==11-limit== | == 11-limit == | ||
Commas: 100/99, 245/243, 1344/1331 | Commas: 100/99, 245/243, 1344/1331 | ||
Line 38: | Line 38: | ||
Badness: 0.0339 | Badness: 0.0339 | ||
==13-limit== | == 13-limit == | ||
Commas: 100/99, 144/143, 196/195, 275/273 | Commas: 100/99, 144/143, 196/195, 275/273 | ||
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Badness: 0.0249 | Badness: 0.0249 | ||
==Music== | == Music == | ||
by [[Chris Vaisvil]]: | by [[Chris Vaisvil]]: | ||
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* [http://micro.soonlabel.com/bophier/bophier-12equal-six-octaves.mp3 bophier-12equal-six-octaves.mp3] | * [http://micro.soonlabel.com/bophier/bophier-12equal-six-octaves.mp3 bophier-12equal-six-octaves.mp3] | ||
=Sensa (Escaped)= | = Sensa (Escaped) = | ||
{{see also| Escapade family #Escaped }} | |||
Commas: 245/243, 65625/65536 | Commas: 245/243, 65625/65536 | ||
Line 68: | Line 70: | ||
Badness: 0.0887 | Badness: 0.0887 | ||
==11-limit== | == 11-limit == | ||
Commas: 245/243, 385/384, 4000/3993 | Commas: 245/243, 385/384, 4000/3993 | ||
Line 79: | Line 81: | ||
Badness: 0.0358 | Badness: 0.0358 | ||
==13-limit== | == 13-limit == | ||
Commas: 245/243, 352/351, 385/384, 625/624 | Commas: 245/243, 352/351, 385/384, 625/624 | ||
Line 90: | Line 92: | ||
Badness: 0.0317 | Badness: 0.0317 | ||
=Salsa= | = Salsa = | ||
{{see also| Schismatic family }} | |||
Commas: 245/243, 32805/32768 | Commas: 245/243, 32805/32768 | ||
Line 103: | Line 107: | ||
Badness: 0.08015 | Badness: 0.08015 | ||
==11-limit== | == 11-limit == | ||
Commas: 243/242, 245/242, 385/384 | Commas: 243/242, 245/242, 385/384 | ||
Line 114: | Line 118: | ||
Badness: 0.0394 | Badness: 0.0394 | ||
==13-limit== | == 13-limit == | ||
Commas: 105/104, 144/143, 243/242, 245/242 | Commas: 105/104, 144/143, 243/242, 245/242 | ||
Line 125: | Line 129: | ||
Badness: 0.0310 | Badness: 0.0310 | ||
=Pycnic= | = Pycnic = | ||
The fifth of pycnic in size is a meantone fifth, but four of them are not used to reach 5. This has the effect of making the Pythagorean major third, nominally 81/64, very close to 5/4 in tuning, being a cent sharp of it in the POTE tuning for instance. Pycnic has MOS of size 9, 11, 13, 15, 17... which contain these alternative thirds, leading to two kinds of major triads, an official one and a nominally Pythagorean one which is actually in better tune. | The fifth of pycnic in size is a meantone fifth, but four of them are not used to reach 5. This has the effect of making the Pythagorean major third, nominally 81/64, very close to 5/4 in tuning, being a cent sharp of it in the POTE tuning for instance. Pycnic has MOS of size 9, 11, 13, 15, 17... which contain these alternative thirds, leading to two kinds of major triads, an official one and a nominally Pythagorean one which is actually in better tune. | ||
Line 140: | Line 144: | ||
Badness: 0.0737 | Badness: 0.0737 | ||
=Cohemiripple= | = Cohemiripple = | ||
{{see also| Mint temperaments #Ripple }} | |||
Commas: 245/243, 1323/1250 | Commas: 245/243, 1323/1250 | ||
Line 153: | Line 159: | ||
Badness: 0.1902 | Badness: 0.1902 | ||
==11-limit== | == 11-limit == | ||
Commas: 77/75, 243/242, 245/242 | Commas: 77/75, 243/242, 245/242 | ||
Line 164: | Line 170: | ||
Badness: 0.0827 | Badness: 0.0827 | ||
==13-limit== | == 13-limit == | ||
Commas: 66/65, 77/75, 147/143, 243/242 | Commas: 66/65, 77/75, 147/143, 243/242 | ||
Line 175: | Line 181: | ||
Badness: 0.0499 | Badness: 0.0499 | ||
=Superthird= | = Superthird = | ||
Commas: 245/243, 78125/76832 | Commas: 245/243, 78125/76832 | ||
Line 188: | Line 194: | ||
Badness: 0.1394 | Badness: 0.1394 | ||
==11-limit== | == 11-limit == | ||
Commas: 100/99, 245/243, 78125/76832 | Commas: 100/99, 245/243, 78125/76832 | ||
Line 199: | Line 205: | ||
Badness: 0.0709 | Badness: 0.0709 | ||
==13-limit== | == 13-limit == | ||
Commas: 100/99, 144/143, 196/195, 1375/1352 | Commas: 100/99, 144/143, 196/195, 1375/1352 | ||
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Badness: 0.0528 | Badness: 0.0528 | ||
=Magus= | = Magus = | ||
Commas: 50331648/48828125 | Commas: 50331648/48828125 | ||
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Badness: 0.3602 | Badness: 0.3602 | ||
==7-limit== | == 7-limit == | ||
Commas: 245/243, 28672/28125 | Commas: 245/243, 28672/28125 | ||
Line 234: | Line 240: | ||
Badness: 0.1084 | Badness: 0.1084 | ||
==11-limit== | == 11-limit == | ||
Commas: 176/175, 245/243, 1331/1323 | Commas: 176/175, 245/243, 1331/1323 | ||
Line 245: | Line 251: | ||
Badness: 0.0451 | Badness: 0.0451 | ||
==13-limit== | == 13-limit == | ||
Commas: 91/90, 176/175, 245/243, 1331/1323 | Commas: 91/90, 176/175, 245/243, 1331/1323 | ||
Line 256: | Line 262: | ||
Badness: 0.0430 | Badness: 0.0430 | ||
=Leapweek= | = Leapweek = | ||
Commas: 245/243, 2097152/2066715 | Commas: 245/243, 2097152/2066715 | ||
Line 267: | Line 273: | ||
Badness: 0.14058 | Badness: 0.14058 | ||
==11-limit== | == 11-limit == | ||
Commas: 245/243, 385/384, 1331/1323 | Commas: 245/243, 385/384, 1331/1323 | ||
Line 278: | Line 284: | ||
Badness: 0.0507 | Badness: 0.0507 | ||
==13-limit== | == 13-limit == | ||
Commas: 169/168, 245/243, 352/351, 364/363 | Commas: 169/168, 245/243, 352/351, 364/363 | ||
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[[Category:Temperament clan]] | [[Category:Temperament clan]] | ||
[[Category:Sensamagic]] | [[Category:Sensamagic]] | ||
[[Category:Rank 2]] | |||
[[Category:Listen]] | [[Category:Listen]] |