Xenharmonic Wiki

55edo: Difference between revisions

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VisualWikitext
+subsets and supersets
Correct many entries in the interval table
Line 34: Line 34:
| 1
| 1
| 21.8
| 21.8
| 128/125, 64/63, 65/64, 78/77,<br>91/90, 99/98, ''81/80''
| 65/64, 78/77, 99/98, ''128/125''
| ^1
| ^1
| up 1sn
| up 1sn
Line 41: Line 41:
| 2
| 2
| 43.6
| 43.6
| 36/35
| 36/35, ''64/63''
| ^^1
| ^^1
| dup 1sn
| dup 1sn
Line 48: Line 48:
| 3
| 3
| 65.5
| 65.5
| 28/27, ''25/24''
| 28/27
| vvm2
| vvm2
| dudminor 2nd
| dudminor 2nd
Line 55: Line 55:
| 4
| 4
| 87.3
| 87.3
| 25/24, 21/20
| 21/20, ''18/17'', ''25/24''
| vm2
| vm2
| downminor 2nd
| downminor 2nd
Line 62: Line 62:
| 5
| 5
| 109.1
| 109.1
| 16/15
| 16/15, 17/16
| m2
| m2
| minor 2nd
| minor 2nd
Line 69: Line 69:
| 6
| 6
| 130.9
| 130.9
| 14/13, ''13/12''
| 13/12, 14/13
| ^m2
| ^m2
| upminor 2nd
| upminor 2nd
Line 76: Line 76:
| 7
| 7
| 152.7
| 152.7
| 13/12, 12/11, ''11/10''
| 12/11, ''11/10''
| ~2
| ~2
| mid 2nd
| mid 2nd
Line 83: Line 83:
| 8
| 8
| 174.5
| 174.5
| ''10/9''
|  
| vM2
| vM2
| downmajor 2nd
| downmajor 2nd
Line 90: Line 90:
| 9
| 9
| 196.4
| 196.4
| 9/8, 10/9
| 9/8, ''10/9''
| M2
| M2
| major 2nd
| major 2nd
Line 104: Line 104:
| 11
| 11
| 240.0
| 240.0
| 8/7, 15/13
| 8/7
| ^^M2
| ^^M2
| dupmajor 2nd
| dupmajor 2nd
Line 125: Line 125:
| 14
| 14
| 305.5
| 305.5
| 6/5-
| 6/5
| m3
| m3
| minor 3rd
| minor 3rd
Line 132: Line 132:
| 15
| 15
| 327.3
| 327.3
| 6/5+
|  
| ^m3
| ^m3
| upminor 3rd
| upminor 3rd
Line 146: Line 146:
| 17
| 17
| 370.9
| 370.9
| 16/13
| 26/21, ''16/13''
| vM3
| vM3
| downmajor 3rd
| downmajor 3rd
Line 174: Line 174:
| 21
| 21
| 458.2
| 458.2
| 13/10
| ''21/16''
| vv4
| vv4
| dud 4th
| dud 4th
Line 181: Line 181:
| 22
| 22
| 480.0
| 480.0
| 21/16
|  
| v4
| v4
| down 4th
| down 4th
Line 188: Line 188:
| 23
| 23
| 501.8
| 501.8
| 4/3, 27/20
| 4/3, ''27/20''
| P4
| P4
| perfect 4th
| perfect 4th
Line 195: Line 195:
| 24
| 24
| 523.6
| 523.6
| ''27/20''
|  
| ^4
| ^4
| up 4th
| up 4th
Line 202: Line 202:
| 25
| 25
| 545.5
| 545.5
| 11/8
| 11/8, 15/11
| ~4
| ~4
| mid 4th
| mid 4th
Line 209: Line 209:
| 26
| 26
| 567.3
| 567.3
| 18/13, 25/18
| 18/13
| vA4
| vA4
| downaug 4th
| downaug 4th
Line 216: Line 216:
| 27
| 27
| 589.1
| 589.1
| 7/5
| 7/5, 24/17
| A4, vd5
| A4, vd5
| aug 4th, downdim 5th
| aug 4th, downdim 5th
Line 223: Line 223:
| 28
| 28
| 610.9
| 610.9
| 10/7
| 10/7, 17/12
| ^A4, d5
| ^A4, d5
| upaug 4th, dim 5th
| upaug 4th, dim 5th
Line 230: Line 230:
| 29
| 29
| 632.7
| 632.7
| 13/9, 36/25
| 13/9
| ^d5
| ^d5
| updim 5th
| updim 5th
Line 237: Line 237:
| 30
| 30
| 654.5
| 654.5
| 16/11
| 16/11, 22/15
| ~5
| ~5
| mid 5th
| mid 5th
Line 244: Line 244:
| 31
| 31
| 676.4
| 676.4
| ''40/27''
|  
| v5
| v5
| down 5th
| down 5th
Line 251: Line 251:
| 32
| 32
| 698.2
| 698.2
| 3/2, 40/27
| 3/2, ''40/27''
| P5
| P5
| perfect 5th
| perfect 5th
Line 258: Line 258:
| 33
| 33
| 720.0
| 720.0
| 32/21
|  
| ^5
| ^5
| up 5th
| up 5th
Line 265: Line 265:
| 34
| 34
| 741.8
| 741.8
| 20/13
| ''32/21''
| ^^5
| ^^5
| dup 5th
| dup 5th
Line 293: Line 293:
| 38
| 38
| 829.1
| 829.1
| 13/8
| 21/13, ''13/8''
| ^m6
| ^m6
| upminor 6th
| upminor 6th
Line 307: Line 307:
| 40
| 40
| 872.7
| 872.7
| 5/3-
|  
| vM6
| vM6
| downmajor 6th
| downmajor 6th
Line 314: Line 314:
| 41
| 41
| 894.5
| 894.5
| 5/3+
| 5/3
| M6
| M6
| major 6th
| major 6th
Line 335: Line 335:
| 44
| 44
| 960.0
| 960.0
| 7/4, 26/15
| 7/4
| vvm7
| vvm7
| dudminor 7th
| dudminor 7th
Line 349: Line 349:
| 46
| 46
| 1003.6
| 1003.6
| 16/9, 9/5
| 16/9, ''9/5''
| m7
| m7
| minor 7th
| minor 7th
Line 356: Line 356:
| 47
| 47
| 1025.5
| 1025.5
| ''9/5''
|  
| ^m7
| ^m7
| upminor 7th
| upminor 7th
Line 363: Line 363:
| 48
| 48
| 1047.3
| 1047.3
| ''20/11'', 11/6, 24/13
| 11/6, ''20/11''
| ~7
| ~7
| mid 7th
| mid 7th
Line 370: Line 370:
| 49
| 49
| 1069.1
| 1069.1
| ''24/13'', 13/7
| 13/7, 24/13
| vM7
| vM7
| downmajor 7th
| downmajor 7th
Line 377: Line 377:
| 50
| 50
| 1090.9
| 1090.9
| 15/8
| 15/8, ''32/17''
| M7
| M7
| major 7th
| major 7th
Line 384: Line 384:
| 51
| 51
| 1112.7
| 1112.7
| 40/21, 48/25
| 40/21, ''17/9'', ''48/25''
| ^M7
| ^M7
| upmajor 7th
| upmajor 7th
Line 391: Line 391:
| 52
| 52
| 1134.5
| 1134.5
| 56/27, ''48/25''
| 56/27
| ^^M7
| ^^M7
| dupmajor 7th
| dupmajor 7th
Line 398: Line 398:
| 53
| 53
| 1156.4
| 1156.4
| 35/18
| 35/18, ''63/32''
| vv8
| vv8
| dud 8ve
| dud 8ve
Line 405: Line 405:
| 54
| 54
| 1178.2
| 1178.2
| 125/64, 63/32, 128/65, 77/39,<br>180/91, 196/99, ''160/81''
| 128/65, 77/39, 196/99, ''125/64''
| v8
| v8
| down 8ve
| down 8ve
Line 417: Line 417:
| D
| D
|}
|}
<nowiki>*</nowiki> 55f val (tending flat), inconsistent intervals labeled in ''italic''


== Selected just intervals by error ==
== Approximation to JI ==
=== Selected just intervals by error ===
The following table shows how [[15-odd-limit]] just intervals are represented in 55edo (ordered by absolute error).
The following table shows how [[15-odd-limit]] just intervals are represented in 55edo (ordered by absolute error).
{{15-odd-limit|55}}
{{15-odd-limit|55}}
Line 424: Line 426:
== 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|-87 55}}
| {{monzo| -87 55 }}
|{{mapping|55 87}}
| {{mapping| 55 87 }}
| +1.1903
| +1.1903
| 1.1915
| 1.1915
| 5.46
| 5.46
|-
|-
|2.3.5
| 2.3.5
|81/80, 6442450944/6103515625
| 81/80, 6442450944/6103515625
|{{mapping|55 87 128}}
| {{mapping| 55 87 128 }}
| -0.1309
| -0.1309
| 2.1012
| 2.1012
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