Lemba: Difference between revisions
m Add & fix a few more table entries |
m More fibonacci eigenmonzos, substitute +4 generator mapping for 11/9 rather than -1 that doesn't completely throw the tuning of everything else off. |
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| [0 66 -17 -23 25 -7> | | [0 66 -17 -23 25 -7> | ||
| 231.399 (15 limit least squares) | | 231.399 (15 limit least squares) | ||
|- | |||
| 17/13 | |||
| 232.213 | |||
|- | |- | ||
| 12\62 | | 12\62 | ||
| Line 101: | Line 104: | ||
| 17/16 | | 17/16 | ||
| 234.985 | | 234.985 | ||
|- | |||
| 21/16 | |||
| 235.390 | |||
|- | |||
| 11\56 | |||
| 235.714 | |||
|- | |- | ||
| 14/13 | | 14/13 | ||
| 235.851 | | 235.851 | ||
|- | |||
| 11/9 | |||
| 236.851 | |||
|- | |- | ||
| 16/15 | | 16/15 | ||
| Line 116: | Line 128: | ||
| 15/13 | | 15/13 | ||
| 247.741 | | 247.741 | ||
|} | |} | ||
Revision as of 15:50, 2 February 2021
Lemba as a regular temperament is the intersection of the Jubilismic clan and the Gamelismic clan. This means that the perfect fifth is split into three equal parts, each approximately an 8/7. It also means the period is half an octave, and repeats precisely a tritone apart, tempering out 50/49. A generator plus a period comes very close to the golden ratio phi, which means ratios in the sequence 8:13:21:34:55 etc are also well approximated, and any one of these can be made just by choosing the right eigenmonzo. The combination of these factors means many composite ratios in the 2.3.5.7.13.17 subgroup are both well approximated and accessible with a relatively small gamut, giving you a strong selection of chords to choose from. It forms mode of symmetry scales that are always double a fibonacci sequence number, at 4, 6, 10, 16, 26, etc, which means L/s ratios remain evenly mixed and clearly distinct many iterations down.
Spectrum of Lemba Tunings by Eigenmonzos
Gencom: [7/5 8/7; 45/44 50/49 65/64 78/77]
Gencom map: [<2 2 5 6 5 7|,[<0 3 -1 -1 5 1|]
| Eigenmonzo | Supermajor Second |
|---|---|
| 5/4 | 213.686 |
| 15/11 | 221.016 |
| 12/11 | 224.681 |
| 3\16 | 225.000 |
| 13/10 | 227.107 |
| 11/10 | 227.501 |
| 13/11 | 227.698 |
| 8\42b | 228.571 |
| 6/5 | 228.910 |
| 21/13 | 230.253 |
| 11/8 | 230.264 |
| 14/11 | 230.415 (15 limit minimax) |
| 13/12 | 230.714 |
| 5\26 | 230.769 |
| 10/9 | 231.085 (9, 11 and 13 limit minimax) |
| 8/7 | 231.174 (7 limit minimax) |
| [0 63 -20 -20 22 -6> | 231.250 (13 limit least squares) |
| [0 17 -6 -6 6> | 231.294 (11 limit least squares) |
| 52521875/177147 | 231.298 (7 limit least squares) |
| [0 66 -17 -23 25 -7> | 231.399 (15 limit least squares) |
| 17/13 | 232.213 |
| 12\62 | 232.258 |
| 129140163/1500625 | 232.418 (9 limit least squares) |
| 18/13 | 232.676 |
| 7/6 | 233.282 |
| 7\36 | 233.333 |
| 9/7 | 233.583 |
| 4/3 | 233.985 |
| 21/17 | 234.274 |
| 9\46 | 234.783 |
| 17/16 | 234.985 |
| 21/16 | 235.390 |
| 11\56 | 235.714 |
| 14/13 | 235.851 |
| 11/9 | 236.851 |
| 16/15 | 237.243 |
| 15/14 | 239.814 |
| 16/13 | 240.528 |
| 15/13 | 247.741 |
Music
Lemba Suite (Prelude, Aria & Fugue) by Claudi Meneghin
In 8/7 eigenmonzo tuning