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Diasem: Difference between revisions

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→Intervals: add 2.3.7 JI values
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The following is a table of diasem intervals and their abstract sizes in terms of L, m and s. Given concrete sizes of L, m and s in edo steps or cents, you can compute the concrete size of any interval in diasem using the following expressions.
The following is a table of diasem intervals and their abstract sizes in terms of L, m and s. Given concrete sizes of L, m and s in edo steps or cents, you can compute the concrete size of any interval in diasem using the following expressions.


{| class="wikitable right-2 right-3 right-4 "
{| class="wikitable right-2 right-3 right-4 right-5"
|+ Interval sizes in diasem
|+ Interval sizes in diasem
|-
|-
!colspan=2|Interval class
!colspan=2|Interval class
! Sizes
! Sizes
! In [[31edo]] (L:m:s = 5:2:1)
! 2.3.7 JI
! [[31edo]] (L:m:s = 5:2:1)
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
!rowspan=3|[[TAMNAMS|1-step]]
!rowspan=3|[[TAMNAMS|1-step]]
!| <small>small</small>
!| <small>small</small>
|| s
|| s
| 64/63, 27.26¢
| 1\31, 38.71¢
| 1\31, 38.71¢
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
!|<small>medium</small>
!|<small>medium</small>
| m
| m
| 28/27, 62.96¢
| 2\31, 77.42¢
| 2\31, 77.42¢
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
!|<small>large</small>
!|<small>large</small>
| L
| L
| 9/8, 203.91¢
| 5\31, 193.55¢
| 5\31, 193.55¢
|-
|-
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!|<small>small</small>
!|<small>small</small>
| L + s
| L + s
| 8/7, 231.17¢
| 6\31, 232.26¢
| 6\31, 232.26¢
|-
|-
!|<small>medium</small>
!|<small>medium</small>
| L + m
| L + m
| 7/6, 266.87¢
| 7\31, 270.97¢
| 7\31, 270.97¢
|-
|-
!|<small>large</small>
!|<small>large</small>
| 2L
| 2L
| 81/64, 407.82¢
| 10\31, 387.10¢
| 10\31, 387.10¢
|-  bgcolor="#eaeaff"
|-  bgcolor="#eaeaff"
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!|<small>small</small>
!|<small>small</small>
| L + m + s
| L + m + s
| 32/27, 294.14¢
| 8\31, 309.68¢
| 8\31, 309.68¢
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
!|<small>medium</small>
!|<small>medium</small>
| 2L + s
| 2L + s
| 9/7, 435.08¢
| 11\31, 425.81¢
| 11\31, 425.81¢
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
!|<small>large</small>
!|<small>large</small>
| 2L + m
| 2L + m
| 21/16, 470.78¢
| 12\31, 464.52¢
| 12\31, 464.52¢
|-  
|-  
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!|<small>small</small>
!|<small>small</small>
| 2L + m + s
| 2L + m + s
| 4/3, 498.04¢
| 13\31, 503.23¢
| 13\31, 503.23¢
|-
|-
!|<small>medium</small>
!|<small>medium</small>
| 3L + s
| 3L + s
| 81/56, 638.99¢
| 16\31, 619.35¢
| 16\31, 619.35¢
|-
|-
!|<small>large</small>
!|<small>large</small>
| 3L + m
| 3L + m
| 189/128, 674.69¢
| 17\31, 658.06¢
| 17\31, 658.06¢
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
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!|<small>small</small>
!|<small>small</small>
| 2L + m + 2s
| 2L + m + 2s
| 256/189, 525.31¢
| 14\31, 541.94¢
| 14\31, 541.94¢
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
!|<small>medium</small>
!|<small>medium</small>
| 2L + 2m + s
| 2L + 2m + s
| 112/81, 561.01¢
| 15\31, 580.65¢
| 15\31, 580.65¢
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
!|<small>large</small>
!|<small>large</small>
| 3L + m + s
| 3L + m + s
| 3/2, 701.96¢
| 18\31, 696.77¢
| 18\31, 696.77¢
|-
|-
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!|<small>small</small>
!|<small>small</small>
| 3L + m + 2s
| 3L + m + 2s
| 32/21, 729.22¢
| 19\31, 735.48¢
| 19\31, 735.48¢
|-
|-
!|<small>medium</small>
!|<small>medium</small>
| 3L + 2m + s
| 3L + 2m + s
| 14/9, 764.92¢
| 20\31, 774.19¢
| 20\31, 774.19¢
|-
|-
!|<small>large</small>
!|<small>large</small>
| 4L + m + s
| 4L + m + s
| 27/16, 905.87¢
| 23\31, 890.32¢
| 23\31, 890.32¢
|-  bgcolor="#eaeaff"
|-  bgcolor="#eaeaff"
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!|<small>small</small>
!|<small>small</small>
| 3L + 2m + 2s
| 3L + 2m + 2s
| 128/81, 792.18¢
| 21\31, 812.90¢
| 21\31, 812.90¢
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
!|<small>medium</small>
!|<small>medium</small>
| 4L + m + 2s
| 4L + m + 2s
| 12/7, 933.13¢
| 24\31, 929.03¢
| 24\31, 929.03¢
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
!|<small>large</small>
!|<small>large</small>
| 4L + 2m + s
| 4L + 2m + s
| 7/4, 968.83¢
| 25\31, 967.74¢
| 25\31, 967.74¢
|-  
|-  
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!|<small>small</small>
!|<small>small</small>
| 4L + 2m + 2s
| 4L + 2m + 2s
| 16/9, 996.09¢
| 26\31, 1006.45¢
| 26\31, 1006.45¢
|-
|-
!|<small>medium</small>
!|<small>medium</small>
| 5L + m + 2s
| 5L + m + 2s
| 54/28, 1137.04¢
| 29\31, 1122.58¢
| 29\31, 1122.58¢
|-
|-
!|<small>large</small>
!|<small>large</small>
| 5L + 2m + s
| 5L + 2m + s
| 63/32, 1172.74¢
| 30\31, 1161.29¢
| 30\31, 1161.29¢
|}
|}
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