Garibaldi: Difference between revisions
m make notation consistent |
m Cleanup on infobox |
||
| Line 3: | Line 3: | ||
| Subgroups = 2.3.5.7, 2.3.5.7.19 | | Subgroups = 2.3.5.7, 2.3.5.7.19 | ||
| Comma basis = [[225/224]], [[3125/3087]] (7-limit); <br>[[190/189]], [[225/224]], [[361/360]] (2.3.5.7.19) | | Comma basis = [[225/224]], [[3125/3087]] (7-limit); <br>[[190/189]], [[225/224]], [[361/360]] (2.3.5.7.19) | ||
| Mapping = 1; 1 -8 -14 -3 | | Mapping = 1; 1 -8 -14 -3 | ||
| Edo join 1 = 41 | Edo join 2 = 53 | | Edo join 1 = 41 | Edo join 2 = 53 | ||
| Generators = 3/2 | |||
| Generators tuning = 702.10 | |||
| Optimization method = CWE | | Optimization method = CWE | ||
| | | Pergen = (P8, P5) | ||
| MOS scales = [[5L 2s]], [[5L 7s]], [[12L 5s]], [[12L 17s]] | | MOS scales = [[5L 2s]], [[5L 7s]], [[12L 5s]], [[12L 17s]] | ||
| Odd limit 1 = 9 | Mistuning 1 = 4.33 | Complexity 1 = 17 | | Odd limit 1 = 9 | Mistuning 1 = 4.33 | Complexity 1 = 17 | ||
| Odd limit 2 = | | Odd limit 2 = 2.3.5.7.19 21 | Mistuning 2 = 4.65 | Complexity 2 = 17 | ||
}} | }} | ||
'''Garibaldi''' is a [[7-limit]] (and higher) [[regular temperament|temperament]] of the [[schismatic family #Garibaldi|schismatic family]]. It is an [[extension]] of [[helmholtz (temperament)|helmholtz]] temperament beyond the 5-limit but with the same simple [[chain of fifths|chain-of-fifths]] structure (so that [[chain-of-fifths notation|standard notation]] may be used). The garibaldi temperament tempers together the Pythagorean, syntonic, and archytas commas into a singular generalized "comma", which can be used to reach intervals of 3, 5, and 7. As in helmholtz temperament, [[5/4]] is mapped to the diminished fourth (e.g. C–F♭; a comma-flat major third), and the new mapping specific to garibaldi is that [[7/4]] is mapped to the double-diminished octave (e.g. C–C𝄫; a comma-flat minor seventh). This makes garibaldi a [[marvel temperaments|marvel temperament]] and a [[hemifamity temperaments|hemifamity temperament]]. Tuning the fifth a fraction of a cent sharp gives the best tunings. | '''Garibaldi''' is a [[7-limit]] (and higher) [[regular temperament|temperament]] of the [[schismatic family #Garibaldi|schismatic family]]. It is an [[extension]] of [[helmholtz (temperament)|helmholtz]] temperament beyond the 5-limit but with the same simple [[chain of fifths|chain-of-fifths]] structure (so that [[chain-of-fifths notation|standard notation]] may be used). The garibaldi temperament tempers together the Pythagorean, syntonic, and archytas commas into a singular generalized "comma", which can be used to reach intervals of 3, 5, and 7. As in helmholtz temperament, [[5/4]] is mapped to the diminished fourth (e.g. C–F♭; a comma-flat major third), and the new mapping specific to garibaldi is that [[7/4]] is mapped to the double-diminished octave (e.g. C–C𝄫; a comma-flat minor seventh). This makes garibaldi a [[marvel temperaments|marvel temperament]] and a [[hemifamity temperaments|hemifamity temperament]]. Tuning the fifth a fraction of a cent sharp gives the best tunings. | ||