Pontiac: Difference between revisions

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'''Pontiac temperament''' is a 7-limit (and higher) temperament of the [[Schismatic family #Pontiac|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-D♭), and the new mapping specific to ~~garibaldi~~ is that [[7/4]] is mapped to the quintuple augmented third (e.g. A-Cxxx). This makes pontiac a [[Ragismic microtemperaments|ragismic temperament]].

'''Pontiac temperament''' is a 7-limit (and higher) temperament of the [[Schismatic family #Pontiac|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-D♭), and the new mapping specific to pontiac is that [[7/4]] is mapped to the quintuple augmented third (e.g. A-Cxxx). This makes pontiac a [[Ragismic microtemperaments|ragismic temperament]].

Immediate 11-limit extensions include ''helenoid'' (53&65), mapping 11/8 to -30 fifths, ''ponta'' (53&171), mapping 11/8 to -83 fifths, and ''pontic'' (118&171), mapping 11/8 to +88 fifths.

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== Spectrum of pontiac tunings by eigenmonzos ==

=== Helenoid mapping ===

Gencom: [2 4/3; 352/351 385/384 625/624 729/728]

Gencom: [2 4/3; 352/351 385/384 561/560 625/624 729/728]

Gencom map: [{{val|1 2 -1 19 -9 -10}}, {{val|0 -1 8 -39 30 33}}]

Gencom map: [{{val|1 2 -1 19 -9 -10 29}}, {{val|0 -1 8 -39 30 33 -60}}]

{| class="wikitable center-1 right-2"

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-'''Pontiac temperament''' is a 7-limit (and higher) temperament of the [[Schismatic family #Pontiac|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-D♭), and the new mapping specific to garibaldi is that [[7/4]] is mapped to the quintuple augmented third (e.g. A-Cxxx). This makes pontiac a [[Ragismic microtemperaments|ragismic temperament]].
+'''Pontiac temperament''' is a 7-limit (and higher) temperament of the [[Schismatic family #Pontiac|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-D♭), and the new mapping specific to pontiac is that [[7/4]] is mapped to the quintuple augmented third (e.g. A-Cxxx). This makes pontiac a [[Ragismic microtemperaments|ragismic temperament]].
 Immediate 11-limit extensions include ''helenoid'' (53&amp;65), mapping 11/8 to -30 fifths, ''ponta'' (53&amp;171), mapping 11/8 to -83 fifths, and ''pontic'' (118&amp;171), mapping 11/8 to +88 fifths.
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 == Spectrum of pontiac tunings by eigenmonzos ==
 === Helenoid mapping ===
-Gencom: [2 4/3; 352/351 385/384 625/624 729/728]
+Gencom: [2 4/3; 352/351 385/384 561/560 625/624 729/728]
-Gencom map: [{{val|1 2 -1 19 -9 -10}}, {{val|0 -1 8 -39 30 33}}]
+Gencom map: [{{val|1 2 -1 19 -9 -10 29}}, {{val|0 -1 8 -39 30 33 -60}}]
 {| class="wikitable center-1 right-2"