385edo: Difference between revisions

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Created page because the category already existed
 
Doesn't support septimal pental so the limit must be specified
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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
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 ===
{{Harmonics in equal|385}}
{{Harmonics in equal|385}}


===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}}.
385 factors into 5 x 7 x 11, with subset edos {{EDOs| 5, 7, 11, 35, 55, and 77 }}.


==Regular temperament properties==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" |[[Subgroup]]
! rowspan="2" | [[Subgroup]]
! rowspan="2" |[[Comma list|Comma List]]
! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" |[[Mapping]]
! rowspan="2" | [[Mapping]]
! rowspan="2" |Optimal<br>8ve Stretch (¢)
! rowspan="2" | Optimal<br>8ve Stretch (¢)
! colspan="2" |Tuning Error
! colspan="2" | Tuning Error
|-
|-
![[TE error|Absolute]] (¢)
! [[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
! [[TE simple badness|Relative]] (%)
|-
|-
|2.3
| 2.3
|{{monzo|-122 77}}
| {{monzo| -122 77 }}
|{{val|385 610}}
| {{val| 385 610 }}
| +0.2070
| +0.2070
| 0.2071
| 0.2071
| 6.64
| 6.64
|-
|-
|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}}
| {{val| 385 610 894 }}
| +0.1122
| +0.1122
| 0.2158
| 0.2158
| 6.92
| 6.92
|-
|-
|2.3.5.7
| 2.3.5.7
|19683/19600, 703125/702464, 589824/588245
| 19683/19600, 589824/588245, 703125/702464
|{{val|385 610 894 1081}}
| {{val| 385 610 894 1081 }}
| +0.0374
| +0.0374
| 0.2274
| 0.2274
| 7.30
| 7.30
|-
|-
|2.3.5.7.11
| 2.3.5.7.11
|540/539, 8019/8000, 496125/495616, 172032/171875
| 540/539, 8019/8000, 496125/495616, 172032/171875
|{{val|385 610 894 1081 1332}}
| {{val| 385 610 894 1081 1332 }}
| +0.0085
| +0.0085
| 0.2114
| 0.2114
| 6.78
| 6.78
|-
|-
|2.3.5.7.11.13
| 2.3.5.7.11.13
|540/539, 1716/1715, 8019/8000, 4096/4095, 81675/81536
| 540/539, 1716/1715, 8019/8000, 4096/4095, 81675/81536
|{{val|385 610 894 1081 1332 1425}}
| {{val| 385 610 894 1081 1332 1425 }}
| -0.0394
| -0.0394
| 0.2207
| 0.2207
| 7.08
| 7.08
|-
|-
|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, 1716/1715, 4096/4095, 13365/13328
|{{val|385 610 894 1081 1332 1425 1574}}
| {{val| 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<br>(Reduced)
! Cents<br>(reduced)
! Cents<br>(Reduced)
! Associated<br>ratio
! Associated<br>Ratio
! Temperaments
! Temperaments
|-
|-
|1
| 1
|62\385
| 62\385
|193.247
| 193.247
|4096/3645
| 4096/3645
|[[Luna]]
| [[Luna]]
|-
|-
|1
| 1
|162/385
| 162/385
|504.935
| 504.935
|4/3
| 4/3
|[[Countermeantone]]
| [[Countermeantone]]
|-
|-
|5
| 5
|160\385<br>(6\385)
| 160\385<br>(6\385)
|498.701<br>(18.701)
| 498.701<br>(18.701)
|4/3<br>(81/80)
| 4/3<br>(81/80)
|[[Pental]]
| [[Pental]] (5-limit)
|}
|}
{{Todo| review }}

Revision as of 14:20, 16 May 2023

← 384edo 385edo 386edo →
Prime factorization 5 × 7 × 11
Step size 3.11688 ¢ 
Fifth 225\385 (701.299 ¢) (→ 45\77)
Semitones (A1:m2) 35:30 (109.1 ¢ : 93.51 ¢)
Consistency limit 7
Distinct consistency limit 7

Template:EDO intro

Theory

385et tempers out following commas:

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

Approximation of prime harmonics in 385edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 -0.66 +0.18 +0.52 +0.37 +1.03 +1.02 -1.41 +1.34 -1.01 -1.14
Relative (%) +0.0 -21.1 +5.8 +16.8 +11.9 +33.1 +32.7 -45.2 +42.9 -32.3 -36.6
Steps
(reduced) 		385
(0) 		610
(225) 		894
(124) 		1081
(311) 		1332
(177) 		1425
(270) 		1574
(34) 		1635
(95) 		1742
(202) 		1870
(330) 		1907
(367)

Subsets and supersets

385 factors into 5 x 7 x 11, with subset edos 5, 7, 11, 35, 55, and 77.

Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢) 		Tuning Error
Absolute (¢) Relative (%)
2.3 [-122 77⟩ ⟨385 610] +0.2070 0.2071 6.64
2.3.5 [-28 25 -5⟩, [38 -2 -15⟩ ⟨385 610 894] +0.1122 0.2158 6.92
2.3.5.7 19683/19600, 589824/588245, 703125/702464 ⟨385 610 894 1081] +0.0374 0.2274 7.30
2.3.5.7.11 540/539, 8019/8000, 496125/495616, 172032/171875 ⟨385 610 894 1081 1332] +0.0085 0.2114 6.78
2.3.5.7.11.13 540/539, 1716/1715, 8019/8000, 4096/4095, 81675/81536 ⟨385 610 894 1081 1332 1425] -0.0394 0.2207 7.08
2.3.5.7.11.13.17 540/539, 936/935, 1377/1375, 1716/1715, 4096/4095, 13365/13328 ⟨385 610 894 1081 1332 1425 1574] -0.0693 0.2171 6.97

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve 		Generator
(Reduced) 		Cents
(Reduced) 		Associated
Ratio 		Temperaments
1 62\385 193.247 4096/3645 Luna
1 162/385 504.935 4/3 Countermeantone
5 160\385
(6\385) 		498.701
(18.701) 		4/3
(81/80) 		Pental (5-limit)
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