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385edo: Difference between revisions

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Doesn't support septimal pental so the limit must be specified
Rework; cleanup; clarify the title row of the rank-2 temp table
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== Theory ==
== Theory ==
385et tempers out following commas:
385edo has a reasonable approximation to the 11-limit, and perhaps beyond. The equal temperament [[tempering out|tempers out]] [[19683/19600]], [[589824/588245]], and [[703125/702464]] in the 7-limit; [[540/539]], [[8019/8000]], 43923/43904, 151263/151250, 160083/160000, 166698/166375, and 172032/171875 in the 11-limit. It [[support]]s [[hemipental]] and provides the [[optimal patent val]] for the 7-limit version thereof. Using the [[patent val]], it tempers out [[1575/1573]], [[1716/1715]], [[2200/2197]], [[4096/4095]], [[6656/665]] and [[10648/10647]] in the 13-limit; and [[936/935]], [[1275/1274]], 1377/1375, and [[2601/2600]] in the 17-limit.
 
7-limit commas: 589824/588245, 134217728/133984375, [[703125/702464]], 1959552/1953125, 5250987/5242880, 200120949/200000000
 
11-limit commas: 1073741824/1071794405, 161280/161051, 25165824/25109315, 234375/234256, 2097152/2096325, 1366875/1362944, 166698/166375, 496125/495616, 151263/151250, 104857600/104825259, [[540/539]], 172032/171875, 369140625/369098752, 825000/823543, 180224/180075, [[8019/8000]], 160083/160000, 539055/537824, 766656/765625, 202397184/201768035, 43923/43904, 20614528/20588575, 39135393/39062500, 781258401/781250000


=== Prime harmonics ===
=== Prime harmonics ===
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=== Subsets and supersets ===
=== Subsets and supersets ===
385 factors into 5 x 7 x 11, with subset edos {{EDOs| 5, 7, 11, 35, 55, and 77 }}.
Since 385 factors into {{factorization|385}}, 385edo has subset edos {{EDOs| 5, 7, 11, 35, 55, and 77 }}.


== Regular temperament properties ==
== Regular temperament properties ==
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| 2.3
| 2.3
| {{monzo| -122 77 }}
| {{monzo| -122 77 }}
| {{val| 385 610 }}
| {{mapping| 385 610 }}
| +0.2070
| +0.2070
| 0.2071
| 0.2071
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| 2.3.5
| 2.3.5
| {{monzo| -28 25 -5 }}, {{monzo| 38 -2 -15 }}
| {{monzo| -28 25 -5 }}, {{monzo| 38 -2 -15 }}
| {{val| 385 610 894 }}
| {{mapping| 385 610 894 }}
| +0.1122
| +0.1122
| 0.2158
| 0.2158
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| 2.3.5.7
| 2.3.5.7
| 19683/19600, 589824/588245, 703125/702464
| 19683/19600, 589824/588245, 703125/702464
| {{val| 385 610 894 1081 }}
| {{mapping| 385 610 894 1081 }}
| +0.0374
| +0.0374
| 0.2274
| 0.2274
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|-
|-
| 2.3.5.7.11
| 2.3.5.7.11
| 540/539, 8019/8000, 496125/495616, 172032/171875
| 540/539, 8019/8000, 151263/151250, 172032/171875
| {{val| 385 610 894 1081 1332 }}
| {{mapping| 385 610 894 1081 1332 }}
| +0.0085
| +0.0085
| 0.2114
| 0.2114
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|-
|-
| 2.3.5.7.11.13
| 2.3.5.7.11.13
| 540/539, 1716/1715, 8019/8000, 4096/4095, 81675/81536
| 540/539, 1575/1573, 2200/2197, 4096/4095, 8019/8000
| {{val| 385 610 894 1081 1332 1425 }}
| {{mapping| 385 610 894 1081 1332 1425 }}
| -0.0394
| -0.0394
| 0.2207
| 0.2207
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|-
|-
| 2.3.5.7.11.13.17
| 2.3.5.7.11.13.17
| 540/539, 936/935, 1377/1375, 1716/1715, 4096/4095, 13365/13328
| 540/539, 936/935, 1377/1375, 1575/1573, 2200/2197, 4096/4095
| {{val| 385 610 894 1081 1332 1425 1574 }}
| {{mapping| 385 610 894 1081 1332 1425 1574 }}
| -0.0693
| -0.0693
| 0.2171
| 0.2171
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|+Table of rank-2 temperaments by generator
|+Table of rank-2 temperaments by generator
! Periods<br>per 8ve
! Periods<br>per 8ve
! Generator<br>(Reduced)
! Generator*
! Cents<br>(Reduced)
! Cents*
! Associated<br>Ratio
! Associated<br>Ratio*
! Temperaments
! Temperaments
|-
|-
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| [[Pental]] (5-limit)
| [[Pental]] (5-limit)
|}
|}
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct


{{Todo| review }}
[[Category:Hemipental]]
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