Garibaldi

Garibaldi is a 7-limit (and higher) temperament of the schismatic family. It is an extension of helmholtz temperament beyond the 5 limit but with the same simple chain-of-fifths structure (so that standard notation may be used). As in helmholtz temperament, 5/4 is mapped to the diminished fourth (e.g. A-Db), and the new mapping specific to garibaldi is that 7/4 is mapped to the double diminished octave (e.g. A-Abb). This makes garibaldi a marvel temperament.

Spectrum of garibaldi tunings by eigenmonzos

Eigenmonzo	Fifth	Comments
16/15	701.676
(69\118)	701.695
5/4	701.711
[0 -10 17⟩	701.728	5-odd-limit least squares
6/5	701.738	5-odd-limit minimax
100\171	701.754
10/9	701.760
(31\53)	701.887
15/13	701.9355
13/10	701.9362
4/3	701.955
16/13	702.026
13/12	702.030
18/13	702.034
86\147	702.041
11/10	702.097
15/11	702.102
14/13	702.109	13- and 15-odd-limit minimax
[0 -95 -137 -129 167 143⟩	702.112	15-odd-limit least squares
[0 -27 7 17⟩	702.114	9-odd-limit least squares
(55\94)	702.12766
[0 -38 -80 -122 137 116⟩	702.12770	13-odd-limit least squares
[0 -25 11 35⟩	702.140	7-odd-limit least squares
[0 17 -52 -88 134⟩	702.183	11-odd-limit least squares
9/7	702.193	9- and 11-odd-limit minimax
7/6	702.209	7-odd-limit minimax
(79\135)	702.222
8/7	702.227
14/11	702.230
11/8	702.231
12/11	702.244
11/9	702.258
(24\41)	702.439
15/14	702.778
7/5	702.915
(17\29)	703.448
13/11	703.597