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38edo: Difference between revisions

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m →Theory: cleanup
m →Intervals: reduce to one decimal place for cent values, per discussion on Discord
Line 19: Line 19:
! Step
! Step
! Cents
! Cents
! 19-odd-limit ratios,<br />treated as 38df
! 19-odd-limit ratios,<br>in 38df val
! colspan="3" | [[Ups and Downs Notation]]*
! colspan="3" | [[Ups and downs notation]]*
|-
|-
| 0
| 0
| 0.0000
| 0.0
|
|
| Perfect 1sn
| Perfect 1sn
Line 30: Line 30:
|-
|-
| 1
| 1
| 31.5789
| 31.6
|
|
| Up 1sn
| Up 1sn
Line 37: Line 37:
|-
|-
| 2
| 2
| 63.1579
| 63.2
|
|
| Aug 1sn, dim 2nd
| Aug 1sn, dim 2nd
Line 44: Line 44:
|-
|-
| 3
| 3
| 94.7368
| 94.7
| [[20/19]], [[19/18]], [[18/17]], [[17/16]]
| [[20/19]], [[19/18]], [[18/17]], [[17/16]]
| Upaug 1sn, downminor 2nd
| Upaug 1sn, downminor 2nd
Line 51: Line 51:
|-
|-
| 4
| 4
| 126.3157
| 126.3
| [[16/15]], [[15/14]], [[14/13]], [[13/12]]
| [[16/15]], [[15/14]], [[14/13]], [[13/12]]
| Minor 2nd
| Minor 2nd
Line 58: Line 58:
|-
|-
| 5
| 5
| 157.8947
| 157.9
| [[12/11]], [[11/10]]
| [[12/11]], [[11/10]]
| Mid 2nd
| Mid 2nd
Line 65: Line 65:
|-
|-
| 6
| 6
| 189.4737
| 189.5
| [[10/9]], [[19/17]], [[9/8]]
| [[10/9]], [[19/17]], [[9/8]]
| Major 2nd
| Major 2nd
Line 72: Line 72:
|-
|-
| 7
| 7
| 221.0526
| 221.1
| [[17/15]]
| [[17/15]]
| Upmajor 2nd
| Upmajor 2nd
Line 79: Line 79:
|-
|-
| 8
| 8
| 252.6316
| 252.6
| [[8/7]], [[15/13]], [[22/19]], [[7/6]]
| [[8/7]], [[15/13]], [[22/19]], [[7/6]]
| Aug 2nd, Dim 3rd
| Aug 2nd, Dim 3rd
Line 86: Line 86:
|-
|-
| 9
| 9
| 284.2105
| 284.2
| [[20/17]], [[13/11]], [[19/16]]
| [[20/17]], [[13/11]], [[19/16]]
| Downminor 3rd
| Downminor 3rd
Line 93: Line 93:
|-
|-
| 10
| 10
| 315.7895
| 315.8
| [[6/5]]
| [[6/5]]
| Minor 3rd
| Minor 3rd
Line 100: Line 100:
|-
|-
| 11
| 11
| 347.3684
| 347.4
| [[17/14]], [[11/9]]
| [[17/14]], [[11/9]]
| Mid 3rd
| Mid 3rd
Line 107: Line 107:
|-
|-
| 12
| 12
| 378.9474
| 378.9
| [[16/13]], [[5/4]]
| [[16/13]], [[5/4]]
| Major 3rd
| Major 3rd
Line 114: Line 114:
|-
|-
| 13
| 13
| 410.5263
| 410.5
| [[24/19]], [[19/15]], [[14/11]]
| [[24/19]], [[19/15]], [[14/11]]
| Upmajor 3rd, Downdim 4th
| Upmajor 3rd, Downdim 4th
Line 121: Line 121:
|-
|-
| 14
| 14
| 442.1053
| 442.1
| [[9/7]], [[22/17]], [[13/10]]
| [[9/7]], [[22/17]], [[13/10]]
| Aug 3rd, dim 4th
| Aug 3rd, dim 4th
Line 128: Line 128:
|-
|-
| 15
| 15
| 473.6843
| 473.7
| [[17/13]]
| [[17/13]]
| Down 4th
| Down 4th
Line 135: Line 135:
|-
|-
| 16
| 16
| 505.2632
| 505.3
| [[4/3]]
| [[4/3]]
| Perfect 4th
| Perfect 4th
Line 142: Line 142:
|-
|-
| 17
| 17
| 536.8421
| 536.8
| [[19/14]], [[15/11]], [[26/19]], [[11/8]]
| [[19/14]], [[15/11]], [[26/19]], [[11/8]]
| Up 4th
| Up 4th
Line 149: Line 149:
|-
|-
| 18
| 18
| 568.4211
| 568.4
| [[18/13]], [[7/5]]
| [[18/13]], [[7/5]]
| Aug 4th
| Aug 4th
Line 156: Line 156:
|-
|-
| 19
| 19
| 600.0000
| 600.0
| [[24/17]], [[17/12]]
| [[24/17]], [[17/12]]
| Upaug 4th, downdim 5th
| Upaug 4th, downdim 5th
Line 163: Line 163:
|-
|-
| 20
| 20
| 631.5789
| 631.6
| [[10/7]], [[13/9]]
| [[10/7]], [[13/9]]
| Dim 5th
| Dim 5th
Line 170: Line 170:
|-
|-
| 21
| 21
| 663.1579
| 663.2
| [[16/11]], [[19/13]], [[22/15]], [[28/19]]
| [[16/11]], [[19/13]], [[22/15]], [[28/19]]
| Down 5th
| Down 5th
Line 177: Line 177:
|-
|-
| 22
| 22
| 694.7368
| 694.7
| [[3/2]]
| [[3/2]]
| Perfect 5th
| Perfect 5th
Line 184: Line 184:
|-
|-
| 23
| 23
| 726.3157
| 726.3
| [[26/17]]
| [[26/17]]
| Up 5th
| Up 5th
Line 191: Line 191:
|-
|-
| 24
| 24
| 757.8947
| 757.9
| [[20/13]], [[17/11]], [[14/9]]
| [[20/13]], [[17/11]], [[14/9]]
| Aug 5th, dim 6th
| Aug 5th, dim 6th
Line 198: Line 198:
|-
|-
| 25
| 25
| 789.4737
| 789.5
| [[11/7]], [[30/19]], [[19/12]]
| [[11/7]], [[30/19]], [[19/12]]
| Upaug 5th, downminor 6th
| Upaug 5th, downminor 6th
Line 205: Line 205:
|-
|-
| 26
| 26
| 821.0526
| 821.1
| [[8/5]], [[13/8]]
| [[8/5]], [[13/8]]
| Minor 6th
| Minor 6th
Line 212: Line 212:
|-
|-
| 27
| 27
| 852.6316
| 852.6
| [[18/11]], [[28/17]]
| [[18/11]], [[28/17]]
| Mid 6th
| Mid 6th
Line 219: Line 219:
|-
|-
| 28
| 28
| 884.2105
| 884.2
| [[5/3]]
| [[5/3]]
| Major 6th
| Major 6th
Line 226: Line 226:
|-
|-
| 29
| 29
| 915.7895
| 915.8
| [[32/19]], [[22/13]], [[17/10]]
| [[32/19]], [[22/13]], [[17/10]]
| Upmajor 6th
| Upmajor 6th
Line 233: Line 233:
|-
|-
| 30
| 30
| 947.3684
| 947.4
| [[12/7]], [[19/11]], [[26/15]], [[7/4]]
| [[12/7]], [[19/11]], [[26/15]], [[7/4]]
| Aug 6th, dim 7th
| Aug 6th, dim 7th
Line 240: Line 240:
|-
|-
| 31
| 31
| 978.9474
| 978.9
| [[30/17]]
| [[30/17]]
| Downminor 7th
| Downminor 7th
Line 247: Line 247:
|-
|-
| 32
| 32
| 1010.5263
| 1010.5
| [[16/9]], [[34/19]], [[9/5]]
| [[16/9]], [[34/19]], [[9/5]]
| Minor 7th
| Minor 7th
Line 254: Line 254:
|-
|-
| 33
| 33
| 1042.1053
| 1042.1
| [[20/11]], [[11/6]]
| [[20/11]], [[11/6]]
| Mid 7th
| Mid 7th
Line 261: Line 261:
|-
|-
| 34
| 34
| 1073.6843
| 1073.7
| [[24/13]], [[13/7]], [[28/15]], [[15/8]]
| [[24/13]], [[13/7]], [[28/15]], [[15/8]]
| Major 7th
| Major 7th
Line 268: Line 268:
|-
|-
| 35
| 35
| 1105.2632
| 1105.3
| [[32/17]], [[17/9]], [[36/19]], [[19/10]]
| [[32/17]], [[17/9]], [[36/19]], [[19/10]]
| Upmajor 7th, Downdim 8ve
| Upmajor 7th, Downdim 8ve
Line 275: Line 275:
|-
|-
| 36
| 36
| 1136.8421
| 1136.8
|
|
| Aug 7th, dim 8ve
| Aug 7th, dim 8ve
Line 282: Line 282:
|-
|-
| 37
| 37
| 1168.4211
| 1168.4
|
|
| Down 8ve
| Down 8ve
Line 289: Line 289:
|-
|-
| 38
| 38
| 1200.0000
| 1200.0
|
|
| Perfect 8ve
| Perfect 8ve
Line 295: Line 295:
| D
| D
|}
|}
<nowiki />* Ups and downs may be substituted with semi-sharps and semi-flats, respectively
<nowiki/>* Ups and downs may be substituted with semi-sharps and semi-flats, respectively


== Notation ==
== Notation ==
Retrieved from "https://en.xen.wiki/w/38edo"