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Blackdye: Difference between revisions

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The following is a table of blackdye 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 blackdye using the following expressions.  
The following is a table of blackdye 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 blackdye using the following expressions.  


{| class="wikitable center-2 center-3"
{| class="wikitable right-2 right-3 right-4"
|+ Interval sizes in blackdye
|+ Interval sizes in blackdye
|-
|-
! | Interval class
! | Interval class
! Sizes
! Sizes
! In [[34edo]] (L:m:s = 5:3:1)
! [[5-limit]] JI
! [[34edo]] (L:m:s = 5:3:1)
|-
|-
!|[[TAMNAMS|1-step]]
!|[[TAMNAMS|1-step]]
| s<br/>m<br/>L || 1\34, 35.29¢<br/>3\34, 105.88¢<br/>5\34, 176.47¢
| s<br/>m<br/>L  
| 81/80, 21.51¢<br/>16/15, 111.73¢<br/>10/9, 182.40¢
| 1\34, 35.29¢<br/>3\34, 105.88¢<br/>5\34, 176.47¢
|-
|-
!|[[TAMNAMS|2-step]]
!|[[TAMNAMS|2-step]]
| L + s<br/>L + m || 6\34, 211.77¢<br/>8\34, 282.35¢
| L + s<br/>L + m  
| 9/8, 203.91¢<br/>32/27, 294.14¢
| 6\34, 211.77¢<br/>8\34, 282.35¢
|-  
|-  
!|[[TAMNAMS|3-step]]
!|[[TAMNAMS|3-step]]
| L + 2s<br/>L + m + s<br/>2L + s<br/>2L + m
| L + 2s<br/>L + m + s<br/>2L + s<br/>2L + m
| 729/640‚ 225.42¢<br/>6/5, 315.64¢<br/>5/4, 386.31¢<br/>320/243, 476.54¢
| 7\34, 247.06¢<br/>9\34, 317.65¢<br/>11\34, 388.24¢<br/>13\34, 458.82¢
| 7\34, 247.06¢<br/>9\34, 317.65¢<br/>11\34, 388.24¢<br/>13\34, 458.82¢
|-  
|-  
!|[[TAMNAMS|4-step]]
!|[[TAMNAMS|4-step]]
| 2L + 2s<br/>2L + m + s
| 2L + 2s<br/>2L + m + s
| 81/64, 407.82¢<br/>4/3, 498.04¢
| 12\34, 423.53¢<br/>14\34, 494.12¢
| 12\34, 423.53¢<br/>14\34, 494.12¢
|-
|-
!|[[TAMNAMS|5-step]]
!|[[TAMNAMS|5-step]]
| 2L + m + 2s<br/>2L + 2m + s<br/>3L + 2s<br/>3L + m + s
| 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¢
| 27/20, 519.55¢<br/>64/45, 609.78¢<br/>45/32, 590.22¢<br/>40/27, 680.45¢
| 15\34, 529.41¢<br/>17\34, 600.00¢<br/>17\34, 600.00¢<br/>19\34, 670.59¢
|-
|-
!|[[TAMNAMS|6-step]]
!|[[TAMNAMS|6-step]]
| 3L + m + 2s<br/>3L + 2m + s
| 3L + m + 2s<br/>3L + 2m + s
| 3/2, 701.96¢<br/>128/81, 792.18¢
| 20\34, 705.88¢<br/>22\34, 776.47¢
| 20\34, 705.88¢<br/>22\34, 776.47¢
|-  
|-  
!|[[TAMNAMS|7-step]]
!|[[TAMNAMS|7-step]]
| 3L + m + 3s<br/>3L + 2m + 2s<br/>4L + m + 2s<br/>4L + 2m + s
| 3L + m + 3s<br/>3L + 2m + 2s<br/>4L + m + 2s<br/>4L + 2m + s
| 243/160, 723.46¢<br/>8/5, 813.69¢<br/>5/3, 884.36¢<br/>1280/729, 974.58¢
| 21\34, 741.18¢<br/>23\34, 811.77¢<br/>25\34, 882.35¢<br/>27\34, 952.94¢
| 21\34, 741.18¢<br/>23\34, 811.77¢<br/>25\34, 882.35¢<br/>27\34, 952.94¢
|-  
|-  
!|[[TAMNAMS|8-step]]
!|[[TAMNAMS|8-step]]
| 4L + m + 3s<br/>4L + 2m + 2s
| 4L + m + 3s<br/>4L + 2m + 2s
| 27/16, 905.87¢<br/>16/9, 996.09¢
| 26\34, 917.65¢<br/>28\34, 988.24¢
| 26\34, 917.65¢<br/>28\34, 988.24¢
|-
|-
!|[[TAMNAMS|9-step]]
!|[[TAMNAMS|9-step]]
| 5L + 2m + s<br/>5L + m + 2s<br/>4L + 2m + 2s
| 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¢
| 9/5, 1017.60¢<br/>15/8, 1088.27¢<br/>160/81, 1178.49¢
| 29\34, 1023.53¢<br/>31\34, 1094.12¢<br/>33\34, 1164.71¢
|}
|}
The octave in blackdye can be called the "perfect 10-step" in TAMNAMS.
The octave in blackdye can be called the "perfect 10-step" in TAMNAMS.
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