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[edit]
| 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 |