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In [[Wart notation|38df]], all primes are flat from 3 to 19.  
In [[Wart notation|38df]], all primes are flat from 3 to 19.  


In 38df, the mapping of all [[19-odd-limit]] intervals is identical to their direct mapping of 38edo, excepting, of course, for 7/4 and 13/8, as well as their octave complements 8/7 and 16/13, which are mapped to their second-best steps within 38df.  
In 38df, the mapping of all [[19-odd-limit]] intervals is identical to their direct best approximation in 38edo, excepting, of course, for 7/4 and 13/8, as well as their octave complements 8/7 and 16/13, which are mapped to their second-best steps within 38df.  
   
   
{{Harmonics in equal|38}}
{{Harmonics in equal|38}}
Line 19: Line 19:
!19-limit ratios,
!19-limit ratios,
treated as 38df
treated as 38df
!19-limit ratios,
by direct mapping
! colspan="3" | [[Ups and Downs Notation]]*
! colspan="3" | [[Ups and Downs Notation]]*
|-
|-
| 0
| 0
| 0.0000
| 0.0000
|
|
|
| Perfect 1sn
| Perfect 1sn
Line 33: Line 30:
| 1
| 1
| 31.5789
| 31.5789
|
|
|
| Up 1sn
| Up 1sn
Line 41: Line 37:
| 2
| 2
| 63.1579
| 63.1579
|
|
|
| Aug 1sn, dim 2nd
| Aug 1sn, dim 2nd
Line 49: Line 44:
| 3
| 3
| 94.7368
| 94.7368
|[[20/19]], [[19/18]], [[18/17]], [[17/16]]
|[[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 57: Line 51:
| 4
| 4
| 126.3157
| 126.3157
|[[16/15]], [[15/14]], [[14/13]], [[13/12]]
|[[16/15]], [[15/14]], [[14/13]], [[13/12]]
|[[16/15]], [[15/14]], [[14/13]], [[13/12]]
| Minor 2nd
| Minor 2nd
Line 65: Line 58:
| 5
| 5
| 157.8947
| 157.8947
|[[12/11]], [[11/10]]
|[[12/11]], [[11/10]]
|[[12/11]], [[11/10]]
| Mid 2nd
| Mid 2nd
Line 73: Line 65:
| 6
| 6
| 189.4737
| 189.4737
|[[10/9]], [[19/17]], [[9/8]]
|[[10/9]], [[19/17]], [[9/8]]
|[[10/9]], [[19/17]], [[9/8]]
| Major 2nd
| Major 2nd
Line 82: Line 73:
| 221.0526
| 221.0526
|[[17/15]]
|[[17/15]]
|[[17/15]], [[8/7]]
| Upmajor 2nd
| Upmajor 2nd
| ^M2
| ^M2
Line 90: Line 80:
| 252.6316
| 252.6316
|[[8/7]], [[15/13]], [[22/19]], [[7/6]]
|[[8/7]], [[15/13]], [[22/19]], [[7/6]]
|[[15/13]], [[22/19]], [[7/6]]
| Aug 2nd, Dim 3rd
| Aug 2nd, Dim 3rd
| A2, d3
| A2, d3
Line 97: Line 86:
| 9
| 9
| 284.2105
| 284.2105
|[[20/17]], [[13/11]], [[19/16]]
|[[20/17]], [[13/11]], [[19/16]]
|[[20/17]], [[13/11]], [[19/16]]
| Downminor 3rd
| Downminor 3rd
Line 105: Line 93:
| 10
| 10
| 315.7895
| 315.7895
|[[6/5]]
|[[6/5]]
|[[6/5]]
| Minor 3rd
| Minor 3rd
Line 114: Line 101:
| 347.3684
| 347.3684
|[[17/14]], [[11/9]]
|[[17/14]], [[11/9]]
|[[17/14]], [[11/9]], [[16/13]]
| Mid 3rd
| Mid 3rd
| ~3
| ~3
Line 122: Line 108:
| 378.9474
| 378.9474
|[[16/13]], [[5/4]]
|[[16/13]], [[5/4]]
|[[5/4]]
| Major 3rd
| Major 3rd
| M3
| M3
Line 129: Line 114:
| 13
| 13
| 410.5263
| 410.5263
|[[24/19]], [[19/15]], [[14/11]]
|[[24/19]], [[19/15]], [[14/11]]
|[[24/19]], [[19/15]], [[14/11]]
| Upmajor 3rd, Downdim 4th
| Upmajor 3rd, Downdim 4th
Line 137: Line 121:
| 14
| 14
| 442.1053
| 442.1053
|[[9/7]], [[22/17]], [[13/10]]
|[[9/7]], [[22/17]], [[13/10]]
|[[9/7]], [[22/17]], [[13/10]]
| Aug 3rd, dim 4th
| Aug 3rd, dim 4th
Line 145: Line 128:
| 15
| 15
| 473.6843
| 473.6843
|[[17/13]]
|[[17/13]]
|[[17/13]]
| Down 4th
| Down 4th
Line 153: Line 135:
| 16
| 16
| 505.2632
| 505.2632
|[[4/3]]
|[[4/3]]
|[[4/3]]
| Perfect 4th
| Perfect 4th
Line 161: Line 142:
| 17
| 17
| 536.8421
| 536.8421
|[[19/14]], [[15/11]], [[26/19]], [[11/8]]
|[[19/14]], [[15/11]], [[26/19]], [[11/8]]
|[[19/14]], [[15/11]], [[26/19]], [[11/8]]
| Up 4th
| Up 4th
Line 169: Line 149:
| 18
| 18
| 568.4211
| 568.4211
|[[18/13]], [[7/5]]
|[[18/13]], [[7/5]]
|[[18/13]], [[7/5]]
| Aug 4th
| Aug 4th
Line 177: Line 156:
| 19
| 19
| 600.0000
| 600.0000
|[[24/17]], [[17/12]]
|[[24/17]], [[17/12]]
|[[24/17]], [[17/12]]
| Upaug 4th, downdim 5th
| Upaug 4th, downdim 5th
Line 185: Line 163:
| 20
| 20
| 631.5789
| 631.5789
|[[10/7]], [[13/9]]
|[[10/7]], [[13/9]]
|[[10/7]], [[13/9]]
| Dim 5th
| Dim 5th
Line 193: Line 170:
| 21
| 21
| 663.1579
| 663.1579
|[[16/11]], [[19/13]], [[22/15]], [[28/19]]
|[[16/11]], [[19/13]], [[22/15]], [[28/19]]
|[[16/11]], [[19/13]], [[22/15]], [[28/19]]
| Down 5th
| Down 5th
Line 201: Line 177:
| 22
| 22
| 694.7368
| 694.7368
|[[3/2]]
|[[3/2]]
|[[3/2]]
| Perfect 5th
| Perfect 5th
Line 209: Line 184:
| 23
| 23
| 726.3157
| 726.3157
|[[26/17]]
|[[26/17]]
|[[26/17]]
| Up 5th
| Up 5th
Line 217: Line 191:
| 24
| 24
| 757.8947
| 757.8947
|[[20/13]], [[17/11]], [[14/9]]
|[[20/13]], [[17/11]], [[14/9]]
|[[20/13]], [[17/11]], [[14/9]]
| Aug 5th, dim 6th
| Aug 5th, dim 6th
Line 225: Line 198:
| 25
| 25
| 789.4737
| 789.4737
|[[11/7]], [[30/19]], [[19/12]]
|[[11/7]], [[30/19]], [[19/12]]
|[[11/7]], [[30/19]], [[19/12]]
| Upaug 5th, downminor 6th
| Upaug 5th, downminor 6th
Line 234: Line 206:
| 821.0526
| 821.0526
|[[8/5]], [[13/8]]
|[[8/5]], [[13/8]]
|[[8/5]]
| Minor 6th
| Minor 6th
| m6
| m6
Line 242: Line 213:
| 852.6316
| 852.6316
|[[18/11]], [[28/17]]
|[[18/11]], [[28/17]]
|[[13/8]], [[18/11]], [[28/17]]
| Mid 6th
| Mid 6th
| ~6
| ~6
Line 249: Line 219:
| 28
| 28
| 884.2105
| 884.2105
|[[5/3]]
|[[5/3]]
|[[5/3]]
| Major 6th
| Major 6th
Line 257: Line 226:
| 29
| 29
| 915.7895
| 915.7895
|[[32/19]], [[22/13]], [[17/10]]
|[[32/19]], [[22/13]], [[17/10]]
|[[32/19]], [[22/13]], [[17/10]]
| Upmajor 6th
| Upmajor 6th
Line 266: Line 234:
| 947.3684
| 947.3684
|[[12/7]], [[19/11]], [[26/15]], [[7/4]]
|[[12/7]], [[19/11]], [[26/15]], [[7/4]]
|[[12/7]], [[19/11]], [[26/15]]
| Aug 6th, dim 7th
| Aug 6th, dim 7th
| A6, d7
| A6, d7
Line 274: Line 241:
| 978.9474
| 978.9474
|[[30/17]]
|[[30/17]]
|[[7/4]], [[30/17]]
| Downminor 7th
| Downminor 7th
| vm7
| vm7
Line 281: Line 247:
| 32
| 32
| 1010.5263
| 1010.5263
|[[16/9]], [[34/19]], [[9/5]]
|[[16/9]], [[34/19]], [[9/5]]
|[[16/9]], [[34/19]], [[9/5]]
| Minor 7th
| Minor 7th
Line 289: Line 254:
| 33
| 33
| 1042.1053
| 1042.1053
|[[20/11]], [[11/6]]
|[[20/11]], [[11/6]]
|[[20/11]], [[11/6]]
| Mid 7th
| Mid 7th
Line 297: Line 261:
| 34
| 34
| 1073.6843
| 1073.6843
|[[24/13]], [[13/7]], [[28/15]], [[15/8]]
|[[24/13]], [[13/7]], [[28/15]], [[15/8]]
|[[24/13]], [[13/7]], [[28/15]], [[15/8]]
| Major 7th
| Major 7th
Line 305: Line 268:
| 35
| 35
| 1105.2632
| 1105.2632
|[[32/17]], [[17/9]], [[36/19]], [[19/10]]
|[[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 313: Line 275:
| 36
| 36
| 1136.8421
| 1136.8421
|
|
|
| Aug 7th, dim 8ve
| Aug 7th, dim 8ve
Line 321: Line 282:
| 37
| 37
| 1168.4211
| 1168.4211
|
|
|
| Down 8ve
| Down 8ve
Line 329: Line 289:
| 38
| 38
| 1200.0000
| 1200.0000
|
|
|
| Perfect 8ve
| Perfect 8ve
Retrieved from "https://en.xen.wiki/w/38edo"