Garibaldi: Difference between revisions

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{{Infobox regtemp

| Title = Garibaldi, Garibaldi Nestoria

| Subgroups = 2.3.5.7, 2.3.5.7.19

| Comma basis = [[225/224]], [[3125/3087]] (7-limit);

[[225/224]], [[361/360]], [[400/399]] (2.3.5.7.19)

| Generator = 3/2

| Mapping = 1; 1 -8 -14 -3

| Pergen = (P8, P5)

| Edo join 1 = 41 | Edo join 2 = 53

| Optimization method = CWE

| Generator tuning = 702.077

| MOS scales = [[5L 2s]], [[5L 7s]], [[12L 5s]], [[12L 17s]]

| Odd limit 1 = 9 | Mistuning 1 = 4.33 | Complexity 1 = 41

| Odd limit 2 = (L11.19) 21 | Mistuning 2 = 4.65 | Complexity 2 = 41

}}

'''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.

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+{{Infobox regtemp
+| Title = Garibaldi, Garibaldi Nestoria
+| Subgroups = 2.3.5.7, 2.3.5.7.19
+| Comma basis = [[225/224]], [[3125/3087]] (7-limit);
+[[225/224]], [[361/360]], [[400/399]] (2.3.5.7.19)
+| Generator = 3/2
+| Mapping = 1; 1 -8 -14 -3
+| Pergen = (P8, P5)
+| Edo join 1 = 41 | Edo join 2 = 53
+| Optimization method = CWE
+| Generator tuning = 702.077
+| MOS scales = [[5L&nbsp;2s]], [[5L&nbsp;7s]], [[12L&nbsp;5s]], [[12L 17s]]
+| Odd limit 1 = 9 | Mistuning 1 = 4.33 | Complexity 1 = 41
+| Odd limit 2 = (L11.19) 21 | Mistuning 2 = 4.65 | Complexity 2 = 41
+}}
 '''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.