Xenharmonic Wiki

Diasem: Difference between revisions

← Older editNewer edit →
VisualWikitext
Inthar (talk | contribs)
autopatrolled, emailconfirmed
15,004 edits
→Intervals: add 2.3.7 JI values
Inthar (talk | contribs)
autopatrolled, emailconfirmed
15,004 edits
→Intervals: Add 21edo to the interval table
Line 23: Line 23:
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 right-5"
{| class="wikitable right-2 right-3 right-4 right-5 right-6 right-7"
|+ Interval sizes in diasem
|+ Interval sizes in diasem
|-
|-
Line 29: Line 29:
! Sizes
! Sizes
! 2.3.7 JI
! 2.3.7 JI
! [[21edo]] (L:m:s = 3:2:1)
! [[31edo]] (L:m:s = 5:2:1)
! [[31edo]] (L:m:s = 5:2:1)
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
Line 35: Line 36:
|| s
|| s
| 64/63, 27.26¢
| 64/63, 27.26¢
| 1\21, 57.14¢
| 1\31, 38.71¢
| 1\31, 38.71¢
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
Line 40: Line 42:
| m
| m
| 28/27, 62.96¢
| 28/27, 62.96¢
| 2\21, 114.29¢
| 2\31, 77.42¢
| 2\31, 77.42¢
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
Line 45: Line 48:
| L
| L
| 9/8, 203.91¢
| 9/8, 203.91¢
| 3\21, 171.43¢
| 5\31, 193.55¢
| 5\31, 193.55¢
|-
|-
Line 51: Line 55:
| L + s
| L + s
| 8/7, 231.17¢
| 8/7, 231.17¢
| 4\21, 228.57¢
| 6\31, 232.26¢
| 6\31, 232.26¢
|-
|-
Line 56: Line 61:
| L + m
| L + m
| 7/6, 266.87¢
| 7/6, 266.87¢
| 5\21, 285.71¢
| 7\31, 270.97¢
| 7\31, 270.97¢
|-
|-
Line 61: Line 67:
| 2L
| 2L
| 81/64, 407.82¢
| 81/64, 407.82¢
| 6\21, 342.86¢
| 10\31, 387.10¢
| 10\31, 387.10¢
|-  bgcolor="#eaeaff"
|-  bgcolor="#eaeaff"
Line 67: Line 74:
| L + m + s
| L + m + s
| 32/27, 294.14¢
| 32/27, 294.14¢
| 6\21, 342.86¢
| 8\31, 309.68¢
| 8\31, 309.68¢
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
Line 72: Line 80:
| 2L + s
| 2L + s
| 9/7, 435.08¢
| 9/7, 435.08¢
| 7\21, 400.00¢
| 11\31, 425.81¢
| 11\31, 425.81¢
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
Line 77: Line 86:
| 2L + m
| 2L + m
| 21/16, 470.78¢
| 21/16, 470.78¢
| 8\21, 457.14¢
| 12\31, 464.52¢
| 12\31, 464.52¢
|-  
|-  
Line 83: Line 93:
| 2L + m + s
| 2L + m + s
| 4/3, 498.04¢
| 4/3, 498.04¢
| 9\21, 514.29¢
| 13\31, 503.23¢
| 13\31, 503.23¢
|-
|-
Line 88: Line 99:
| 3L + s
| 3L + s
| 81/56, 638.99¢
| 81/56, 638.99¢
| 10\21, 571.43¢
| 16\31, 619.35¢
| 16\31, 619.35¢
|-
|-
Line 93: Line 105:
| 3L + m
| 3L + m
| 189/128, 674.69¢
| 189/128, 674.69¢
| 11\21, 628.57¢
| 17\31, 658.06¢
| 17\31, 658.06¢
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
Line 99: Line 112:
| 2L + m + 2s
| 2L + m + 2s
| 256/189, 525.31¢
| 256/189, 525.31¢
| 10\21, 571.43¢
| 14\31, 541.94¢
| 14\31, 541.94¢
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
Line 104: Line 118:
| 2L + 2m + s
| 2L + 2m + s
| 112/81, 561.01¢
| 112/81, 561.01¢
| 11\21, 628.57¢
| 15\31, 580.65¢
| 15\31, 580.65¢
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
Line 109: Line 124:
| 3L + m + s
| 3L + m + s
| 3/2, 701.96¢
| 3/2, 701.96¢
| 12\21, 685.71¢
| 18\31, 696.77¢
| 18\31, 696.77¢
|-
|-
Line 115: Line 131:
| 3L + m + 2s
| 3L + m + 2s
| 32/21, 729.22¢
| 32/21, 729.22¢
| 13\21, 742.86¢
| 19\31, 735.48¢
| 19\31, 735.48¢
|-
|-
Line 120: Line 137:
| 3L + 2m + s
| 3L + 2m + s
| 14/9, 764.92¢
| 14/9, 764.92¢
| 14\21, 800.00¢
| 20\31, 774.19¢
| 20\31, 774.19¢
|-
|-
Line 125: Line 143:
| 4L + m + s
| 4L + m + s
| 27/16, 905.87¢
| 27/16, 905.87¢
| 15\21, 857.14¢
| 23\31, 890.32¢
| 23\31, 890.32¢
|-  bgcolor="#eaeaff"
|-  bgcolor="#eaeaff"
Line 131: Line 150:
| 3L + 2m + 2s
| 3L + 2m + 2s
| 128/81, 792.18¢
| 128/81, 792.18¢
| 15\21, 857.14¢
| 21\31, 812.90¢
| 21\31, 812.90¢
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
Line 136: Line 156:
| 4L + m + 2s
| 4L + m + 2s
| 12/7, 933.13¢
| 12/7, 933.13¢
| 16\21, 914.29¢
| 24\31, 929.03¢
| 24\31, 929.03¢
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
Line 141: Line 162:
| 4L + 2m + s
| 4L + 2m + s
| 7/4, 968.83¢
| 7/4, 968.83¢
| 17\21, 971.43¢
| 25\31, 967.74¢
| 25\31, 967.74¢
|-  
|-  
Line 147: Line 169:
| 4L + 2m + 2s
| 4L + 2m + 2s
| 16/9, 996.09¢
| 16/9, 996.09¢
| 18\21, 1028.57¢
| 26\31, 1006.45¢
| 26\31, 1006.45¢
|-
|-
Line 152: Line 175:
| 5L + m + 2s
| 5L + m + 2s
| 54/28, 1137.04¢
| 54/28, 1137.04¢
| 19\21, 1085.71¢
| 29\31, 1122.58¢
| 29\31, 1122.58¢
|-
|-
Line 157: Line 181:
| 5L + 2m + s
| 5L + 2m + s
| 63/32, 1172.74¢
| 63/32, 1172.74¢
| 20\21, 1142.86¢
| 30\31, 1161.29¢
| 30\31, 1161.29¢
|}
|}
Retrieved from "https://en.xen.wiki/w/Diasem"