Blackdye: Difference between revisions

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@@ Line 8: / Line 8: @@
 "Blackdye" is a name given by [[User:ks26|ks26]]. The name is a pun on "blackwood" and "diatonic" since its step sizes are intermediate between that of [[diatonic]] (5L 2s) and [[blackwood]][10] ([[5L 5s]]).
+== Intervals ==
+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 center-2 center-3"
+|+ Interval sizes in blackdye
+|-
+! | Interval class
+! Sizes
+! In [[34edo]] (L:m:s = 5:3:1)
+|-
+!|[[TAMNAMS|1-step]]
+| s<br/>m<br/>L || 1\34, 35.29¢<br/>3\34, 105.88¢<br/>5\34, 176.47¢
+|-
+!|[[TAMNAMS|2-step]]
+| L + s<br/>L + m || 6\34, 211.77¢<br/>8\34, 282.35¢
+|-
+!|[[TAMNAMS|3-step]]
+| L + 2s<br/>L + m + s<br/>2L + s<br/>2L + m
+| 7\34, 247.06¢<br/>9\34, 317.65¢<br/>11\34, 388.24¢<br/>13\34, 458.82¢
+|-
+!|[[TAMNAMS|4-step]]
+| 2L + 2s<br/>2L + m + s
+| 12\34, 423.53¢<br/>14\34, 494.12¢
+|-
+!|[[TAMNAMS|5-step]]
+| 2L + m + 2s<br/>2L + 2m + s<br/>3L + 2s<br/>3L + m + s
+| 15\34, 529.412¢<br/>17\34, 600.00¢<br/>17\34, 600.00¢<br/>19\34, 670.59¢
+|-
+!|[[TAMNAMS|6-step]]
+| 3L + m + 2s<br/>3L + 2m + s
+| 20\34, 705.88¢<br/>22\34, 776.47¢
+|-
+!|[[TAMNAMS|7-step]]
+| 3L + m + 3s<br/>3L + 2m + 2s<br/>4L + m + 2s<br/>4L + 2m + s
+| 21\34, 741.18¢<br/>23\34, 811.77¢<br/>25\34, 882.35¢<br/>27\34, 952.94¢
+|-
+!|[[TAMNAMS|8-step]]
+| 4L + m + 3s<br/>4L + 2m + 2s
+| 26\34, 917.65¢<br/>28\34, 988.24¢
+|-
+!|[[TAMNAMS|9-step]]
+| 5L + 2m + s<br/>5L + m + 2s<br/>4L + 2m + 2s
+| 29\34,1023.53¢<br/>31\34, 1094.12<br/>33\34, 1164.71¢
+|}
 == Modes ==
 The modes arranged in cyclic order: (Note: The mode names are based on the 5-limit JI interpretation; modes in a less JI-like tuning may differ greatly from what these names suggest.)