21edt: Difference between revisions
m Add table of harmonics |
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{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! Degrees | |||
! Cents | |||
! | ! Hekts | ||
| Approximate Ratio | |||
|- | |- | ||
! colspan="3" | 0 | ! colspan="3" | 0 | ||
| [[1/1|1/1]] | |||
|- | |- | ||
| 1 | |||
| 90.569 | |||
|61.905 | | 61.905 | ||
| [[21/20|21/20]], [[135/128|135/128]] | |||
|- | |- | ||
| 2 | |||
| 181.139 | |||
|123.81 | | 123.81 | ||
| [[10/9|10/9]] | |||
|- | |- | ||
| 3 | |||
| 271.708 | |||
|185.714 | | 185.714 | ||
| [[7/6|7/6]] | |||
|- | |- | ||
| 4 | |||
| 362.277 | |||
|247.619 | | 247.619 | ||
| [[16/13|16/13]] | |||
|- | |- | ||
| 5 | |||
| 452.846 | |||
|309.524 | | 309.524 | ||
| [[13/10|13/10]] | |||
|- | |- | ||
| 6 | |||
| 543.416 | |||
|371.429 | | 371.429 | ||
| [[15/11|15/11]], [[11/8|11/8]] | |||
|- | |- | ||
| 7 | |||
| 633.985 | |||
|433.333 | | 433.333 | ||
| [[13/9|13/9]] | |||
|- | |- | ||
| 8 | |||
| 724.554 | |||
|495.238 | | 495.238 | ||
| 35/23 | |||
|- | |- | ||
| 9 | |||
| 815.124 | |||
|557.143 | | 557.143 | ||
| [[8/5|8/5]] | |||
|- | |- | ||
| 10 | |||
| 905.693 | |||
|619.048 | | 619.048 | ||
| 27/16 | |||
|- | |- | ||
| 11 | |||
| 996.262 | |||
|680.952 | | 680.952 | ||
| 16/9 | |||
|- | |- | ||
| 12 | |||
| 1086.831 | |||
|742.857 | | 742.857 | ||
| [[15/8|15/8]] | |||
|- | |- | ||
| 13 | |||
| 1177.401 | |||
|804.762 | | 804.762 | ||
| 69/35 | |||
|- | |- | ||
| 14 | |||
| 1267.97 | |||
|866.667 | | 866.667 | ||
| 27/13 | |||
|- | |- | ||
| 15 | |||
| 1358.539 | |||
|928.571 | | 928.571 | ||
| 11/5 ([[11/10|11/10]] plus an octave), 24/11 (12/11 plus an octave) | |||
|- | |- | ||
| 16 | |||
| 1449.109 | |||
|990.476 | | 990.476 | ||
| 30/13 ([[15/13|15/13]] plus an octave) | |||
|- | |- | ||
| 17 | |||
| 1539.678 | |||
|1052.381 | | 1052.381 | ||
| 39/16 | |||
|- | |- | ||
| 18 | |||
| 1630.247 | |||
|1114.286 | | 1114.286 | ||
| 18/7 ([[9/7|9/7]] plus an octave) | |||
|- | |- | ||
| 19 | |||
| 1720.816 | |||
|1076.19 | | 1076.19 | ||
| 27/10 | |||
|- | |- | ||
| 20 | |||
| 1811.386 | |||
|1238.095 | | 1238.095 | ||
| 20/7, 128/45 | |||
|- | |- | ||
| 21 | |||
| 1901.955 | |||
|1300 | | 1300 | ||
| 3/1 | |||
|} | |} | ||
| Line 126: | Line 126: | ||
== Harmonics== | == Harmonics== | ||
Not the best approximations but all within 20 cents: it has 5th (+ | Not the best approximations but all within 20 cents: it has 5th (+20¢), 7th (−16¢), 10th (+2¢), 11th (+15¢), 13th (−3¢), 17th (−14¢), 23rd (+6¢), and 37th (−2¢) harmonics. For a lower division of the tritave that's quite a constellation! The chord is a little out of tune but it works, you can really sink into it. | ||
{{Harmonics in equal | {{Harmonics in equal | ||