Garibaldi temperament

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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
16/15 701.676
69\118 701.695
5/4 701.711
[0 -10 17> 701.728 (5 limit least squares)
6/5 701.738 (5 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 limit minimax)
[0 -95 -137 -129 167 143> 702.112 (15 limit least squares)
[0 -27 7 17> 702.114 (9 limit least squares)
55\94 702.12766
[0 -38 -80 -122 137 116> 702.12770 (13 limit least squares)
[0 -25 11 35> 702.140 (7 limit least squares)
[0 17 -52 -88 134> 702.183 (11 limit least squares)
9/7 702.193 (9 and 11 limit minimax)
7/6 702.209 (7 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