Garibaldi: Difference between revisions

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'''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 Pythagorean major third), and the new mapping specific to garibaldi is that [[7/4]] is mapped to the doubly-diminished octave (e.g. C–C𝄫; a comma-flat Pythagorean minor seventh). This makes garibaldi a [[marvel temperaments|marvel temperament]].

'''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 Pythagorean major third), and the new mapping specific to garibaldi is that [[7/4]] is mapped to the doubly-diminished octave (e.g. C–C𝄫; a comma-flat Pythagorean minor seventh). This makes garibaldi a [[marvel temperaments|marvel temperament]].

Immediate 11-limit extensions include ''cassandra'' {{nowrap|(41 & 53)}}, mapping 11/8 to +23 fifths, ''andromeda'' {{nowrap|(29 & 41)}}, mapping 11/8 to −18 fifths, and ''helenus'' {{nowrap|(53 & 65d)}}, mapping 11/8 to −30 fifths. Garibaldi is most naturally a 2.3.5.7.19 [[subgroup]] temperament due to its immediate availability of [[19/16]] at the minor third (C–E♭). This is sometimes known as ''garibaldi nestoria''.

Revision as of 15:44, 16 April 2025 view source Nick Vuci (talk \| contribs) autopatrolled, emailconfirmed 388 edits m Edited Helmholtz redirect ← Older edit		Revision as of 02:29, 17 April 2025 view source Lériendil (talk \| contribs) 8,044 edits m Text replacement - "[[Helmholtz temperament\|" to "[[Helmholtz (temperament)\|" Newer edit →
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	'''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 Pythagorean major third), and the new mapping specific to garibaldi is that [[7/4]] is mapped to the doubly-diminished octave (e.g. C–C𝄫; a comma-flat Pythagorean minor seventh). This makes garibaldi a [[marvel temperaments\|marvel temperament]].		'''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 Pythagorean major third), and the new mapping specific to garibaldi is that [[7/4]] is mapped to the doubly-diminished octave (e.g. C–C𝄫; a comma-flat Pythagorean minor seventh). This makes garibaldi a [[marvel temperaments\|marvel temperament]].

	Immediate 11-limit extensions include ''cassandra'' {{nowrap\|(41 & 53)}}, mapping 11/8 to +23 fifths, ''andromeda'' {{nowrap\|(29 & 41)}}, mapping 11/8 to −18 fifths, and ''helenus'' {{nowrap\|(53 & 65d)}}, mapping 11/8 to −30 fifths. Garibaldi is most naturally a 2.3.5.7.19 [[subgroup]] temperament due to its immediate availability of [[19/16]] at the minor third (C–E♭). This is sometimes known as ''garibaldi nestoria''.		Immediate 11-limit extensions include ''cassandra'' {{nowrap\|(41 & 53)}}, mapping 11/8 to +23 fifths, ''andromeda'' {{nowrap\|(29 & 41)}}, mapping 11/8 to −18 fifths, and ''helenus'' {{nowrap\|(53 & 65d)}}, mapping 11/8 to −30 fifths. Garibaldi is most naturally a 2.3.5.7.19 [[subgroup]] temperament due to its immediate availability of [[19/16]] at the minor third (C–E♭). This is sometimes known as ''garibaldi nestoria''.