30edt: Difference between revisions
No edit summary |
No edit summary |
||
| Line 11: | Line 11: | ||
|Hekts | |Hekts | ||
| | Approximate Ratios | | | Approximate Ratios | ||
|Lambda scale name | |||
| | Sigma scale name | | | Sigma scale name | ||
|- | |- | ||
| colspan="3"| 0 | |||
| colspan=" | |||
| | <span style="color: #660000;">[[1/1|1/1]]</span> | | | <span style="color: #660000;">[[1/1|1/1]]</span> | ||
| | C | | colspan="2" |C | ||
|- | |- | ||
| | 1 | | | 1 | ||
| Line 22: | Line 22: | ||
|43.333 | |43.333 | ||
| | 28/27, 27/26 | | | 28/27, 27/26 | ||
|C^/Dbv | |||
| | C#/Dbb | | | C#/Dbb | ||
|- | |- | ||
| Line 28: | Line 29: | ||
|86.667 | |86.667 | ||
| | [[14/13|14/13]], [[15/14|15/14]], [[16/15|16/15]], 29/27 | | | [[14/13|14/13]], [[15/14|15/14]], [[16/15|16/15]], 29/27 | ||
|Db | |||
| | Cx/Db | | | Cx/Db | ||
|- | |- | ||
| Line 34: | Line 36: | ||
|130 | |130 | ||
| | 10/9~9/8 | | | 10/9~9/8 | ||
|C# | |||
| | D | | | D | ||
|- | |- | ||
| Line 40: | Line 43: | ||
|173.333 | |173.333 | ||
| | [[15/13|15/13]] | | | [[15/13|15/13]] | ||
|C#^/Dv | |||
| | D#/Ebb | | | D#/Ebb | ||
|- | |- | ||
| Line 46: | Line 50: | ||
|216.667 | |216.667 | ||
| | 6/5 | | | 6/5 | ||
|D | |||
| | Dx/Eb | | | Dx/Eb | ||
|- | |- | ||
| Line 52: | Line 57: | ||
|260 | |260 | ||
| | <span style="color: #660000;">[[5/4|5/4]]</span> | | | <span style="color: #660000;">[[5/4|5/4]]</span> | ||
|D^/Ev | |||
| | E | | | E | ||
|- | |- | ||
| Line 58: | Line 64: | ||
|303.333 | |303.333 | ||
| | 9/7 | | | 9/7 | ||
|E | |||
| | E#/Fbb | | | E#/Fbb | ||
|- | |- | ||
| Line 64: | Line 71: | ||
|346.667 | |346.667 | ||
| | [[4/3|4/3]] | | | [[4/3|4/3]] | ||
|E^/Fbv | |||
| | Ex/Fb | | | Ex/Fb | ||
|- | |- | ||
| Line 70: | Line 78: | ||
|390 | |390 | ||
| | 7/5 | | | 7/5 | ||
|Fb | |||
| | F | | | F | ||
|- | |- | ||
| Line 76: | Line 85: | ||
|433.333 | |433.333 | ||
| | [[13/9|13/9]] | | | [[13/9|13/9]] | ||
|E# | |||
| | F#/Gb | | | F#/Gb | ||
|- | |- | ||
| Line 82: | Line 92: | ||
|476.667 | |476.667 | ||
| | 3/2 | | | 3/2 | ||
|E#^/Fv | |||
| | G | | | G | ||
|- | |- | ||
| Line 88: | Line 99: | ||
|520 | |520 | ||
| | <span style="color: #660000;">[[14/9|14/9]]</span> | | | <span style="color: #660000;">[[14/9|14/9]]</span> | ||
|F | |||
| | G#/Hbb | | | G#/Hbb | ||
|- | |- | ||
| Line 94: | Line 106: | ||
|563.333 | |563.333 | ||
| | 8/5 | | | 8/5 | ||
|F^/Gv | |||
| | Gx/Hb | | | Gx/Hb | ||
|- | |- | ||
| Line 100: | Line 113: | ||
|606.667 | |606.667 | ||
| | [[5/3|5/3]] | | | [[5/3|5/3]] | ||
|G | |||
| | H | | | H | ||
|- | |- | ||
| Line 106: | Line 120: | ||
|650 | |650 | ||
| | 19/11 | | | 19/11 | ||
|G^/Hbv | |||
| | H#/Jbb | | | H#/Jbb | ||
|- | |- | ||
| Line 112: | Line 127: | ||
|693.333 | |693.333 | ||
| | [[9/5|9/5]] | | | [[9/5|9/5]] | ||
|Hb | |||
| | Hx/Jb | | | Hx/Jb | ||
|- | |- | ||
| Line 118: | Line 134: | ||
|736.667 | |736.667 | ||
| | 13/7 | | | 13/7 | ||
|G# | |||
| | J | | | J | ||
|- | |- | ||
| Line 124: | Line 141: | ||
|780 | |780 | ||
| | <span style="color: #660000;">[[27/14|27/14]]</span> | | | <span style="color: #660000;">[[27/14|27/14]]</span> | ||
|G#^/Hv | |||
| | J#/Kbb | | | J#/Kbb | ||
|- | |- | ||
| Line 130: | Line 148: | ||
|823.333 | |823.333 | ||
| | 2/1 | | | 2/1 | ||
|H | |||
| | Jx/Kb | | | Jx/Kb | ||
|- | |- | ||
| Line 136: | Line 155: | ||
|866.667 | |866.667 | ||
| | [[27/13|27/13]] | | | [[27/13|27/13]] | ||
|H^/Jv | |||
| | K | | | K | ||
|- | |- | ||
| Line 142: | Line 162: | ||
|910 | |910 | ||
| | 28/13 | | | 28/13 | ||
|J | |||
| | K#/Lb | | | K#/Lb | ||
|- | |- | ||
| Line 148: | Line 169: | ||
|953.333 | |953.333 | ||
| | [[9/4|9/4]] ([[9/8|9/8]] plus an octave) | | | [[9/4|9/4]] ([[9/8|9/8]] plus an octave) | ||
|J^/Av | |||
| | L | | | L | ||
|- | |- | ||
| Line 154: | Line 176: | ||
|996.667 | |996.667 | ||
| | 7/3 | | | 7/3 | ||
|A | |||
| | L#/Abb | | | L#/Abb | ||
|- | |- | ||
| Line 160: | Line 183: | ||
|1040 | |1040 | ||
| | [[12/5|12/5]] (<span style="color: #660000;">[[6/5|6/5]]</span> plus an octave) | | | [[12/5|12/5]] (<span style="color: #660000;">[[6/5|6/5]]</span> plus an octave) | ||
|A^/Bbv | |||
| | Lx/Ab | | | Lx/Ab | ||
|- | |- | ||
| Line 166: | Line 190: | ||
|1083.333 | |1083.333 | ||
| | 5/2 | | | 5/2 | ||
|Bb | |||
| | A | | | A | ||
|- | |- | ||
| Line 172: | Line 197: | ||
|1126.667 | |1126.667 | ||
| | [[13/5|13/5]] ([[13/10|13/10]] plus an octave) | | | [[13/5|13/5]] ([[13/10|13/10]] plus an octave) | ||
|A# | |||
| | A#/Bbb | | | A#/Bbb | ||
|- | |- | ||
| Line 178: | Line 204: | ||
|1170 | |1170 | ||
| | 8/3 | | | 8/3 | ||
|A#^/Bv | |||
| | Ax/Bb | | | Ax/Bb | ||
|- | |- | ||
| Line 184: | Line 211: | ||
|1213.333 | |1213.333 | ||
| | [[14/5|14/5]] ([[7/5|7/5]] plus an octave) | | | [[14/5|14/5]] ([[7/5|7/5]] plus an octave) | ||
| | B | | colspan="2" |B | ||
|- | |- | ||
| | 29 | | | 29 | ||
| Line 190: | Line 217: | ||
|1256.667 | |1256.667 | ||
| | 26/9 | | | 26/9 | ||
|B^/Cv | |||
| | B#/Cb | | | B#/Cb | ||
|- | |- | ||
| Line 196: | Line 224: | ||
|1300 | |1300 | ||
| | [[3/1|3/1]] | | | [[3/1|3/1]] | ||
| | C | | colspan="2" |C | ||
|} | |} | ||
Revision as of 20:44, 7 July 2019
Division of the third harmonic into 30 equal parts (30edt) is related to 19 edo, but with the 3/1 rather than the 2/1 being just. The octave is about 4.5715 cents stretched and the step size is about 63.3985 cents. It is consistent to the 10-integer-limit.
Because 19edo has the 3rd, 5th, 7th, and 13th harmonics all flat (the latter two very flat), it benefits greatly from octave stretching. 30edt is one possible alternative; at the cost of sharpening the octave, it achieves much better matches to the odd harmonics; the 3 (tritave) is by definition just, the 5 slightly sharp, and the 7 and 13 slightly flat.
Intervals of 30edt
| Degrees | Cents | Hekts | Approximate Ratios | Lambda scale name | Sigma scale name |
| 0 | 1/1 | C | |||
| 1 | 63.3985 | 43.333 | 28/27, 27/26 | C^/Dbv | C#/Dbb |
| 2 | 126.797 | 86.667 | 14/13, 15/14, 16/15, 29/27 | Db | Cx/Db |
| 3 | 190.1955 | 130 | 10/9~9/8 | C# | D |
| 4 | 253.594 | 173.333 | 15/13 | C#^/Dv | D#/Ebb |
| 5 | 316.9925 | 216.667 | 6/5 | D | Dx/Eb |
| 6 | 380.391 | 260 | 5/4 | D^/Ev | E |
| 7 | 443.7895 | 303.333 | 9/7 | E | E#/Fbb |
| 8 | 507.188 | 346.667 | 4/3 | E^/Fbv | Ex/Fb |
| 9 | 570.5865 | 390 | 7/5 | Fb | F |
| 10 | 633.985 | 433.333 | 13/9 | E# | F#/Gb |
| 11 | 697.3835 | 476.667 | 3/2 | E#^/Fv | G |
| 12 | 760.782 | 520 | 14/9 | F | G#/Hbb |
| 13 | 824.1805 | 563.333 | 8/5 | F^/Gv | Gx/Hb |
| 14 | 887.579 | 606.667 | 5/3 | G | H |
| 15 | 950.9775 | 650 | 19/11 | G^/Hbv | H#/Jbb |
| 16 | 1014.376 | 693.333 | 9/5 | Hb | Hx/Jb |
| 17 | 1077.7745 | 736.667 | 13/7 | G# | J |
| 18 | 1141.173 | 780 | 27/14 | G#^/Hv | J#/Kbb |
| 19 | 1204.5715 | 823.333 | 2/1 | H | Jx/Kb |
| 20 | 1267.97 | 866.667 | 27/13 | H^/Jv | K |
| 21 | 1331.3685 | 910 | 28/13 | J | K#/Lb |
| 22 | 1394.767 | 953.333 | 9/4 (9/8 plus an octave) | J^/Av | L |
| 23 | 1458.1655 | 996.667 | 7/3 | A | L#/Abb |
| 24 | 1521.564 | 1040 | 12/5 (6/5 plus an octave) | A^/Bbv | Lx/Ab |
| 25 | 1584.9625 | 1083.333 | 5/2 | Bb | A |
| 26 | 1648.361 | 1126.667 | 13/5 (13/10 plus an octave) | A# | A#/Bbb |
| 27 | 1711.7595 | 1170 | 8/3 | A#^/Bv | Ax/Bb |
| 28 | 1775.158 | 1213.333 | 14/5 (7/5 plus an octave) | B | |
| 29 | 1838.5565 | 1256.667 | 26/9 | B^/Cv | B#/Cb |
| 30 | 1901.955 | 1300 | 3/1 | C | |
30edt contains all 19edo intervals within 3/1, all temepered progressively sharper. The accumulation of the .241 cent sharpening of the unit step relative to 19edo leads to the excellent 6edt approximations of 6/5 and 5/2. Non-redundantly with simpler edts, the 41 degree ~9/2 is only .6615 cents flatter than that in 6edo.
30edt also contains all the MOS contained in 15edt, being the double of this equal division. Being even, 30edt introduces
MOS with an even number of periods per tritave such as a 6L 6s similar to Hexe Dodecatonic. This MOS has a period of 1/6 of the tritave and the generator is a single or double step. The major scale is sLsLsLsLsLsL, and the minor scale is LsLsLsLsLsLs. Being a "real" 3/2, the interval of 11 degrees generates an unfair Sigma scale of 8L 3s and the major scale is LLLsLLLsLLs. The sharp 9/7 of 7 degrees, in addition to generating a Lambda MOS will generate a 4L 9s unfair Superlambda MOS which does not border on being atonal as the 17edt rendition does.
Compositions in 30edt
- "Room Full Of Steam", Mason Green. In the key of "Eb subminor".