Lemba

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)
12\62	232.258
129140163/1500625	232.418 (9 limit least squares)
18/13	232.676
7/6	233.282
9/7	233.583
4/3	233.985
21/17	234.274
17/16	234.985
14/13	235.851
15/14	239.814
16/13	240.528
16/15	244.134
15/13	247.741
11/9	252.592

Music

Lemba Suite (Prelude, Aria & Fugue) by Claudi Meneghin

In 8/7 eigenmonzo tuning