Pontiac: Difference between revisions

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| Odd limit 2 = (7-limit) 63 | Mistuning 2 = 0.716 | Complexity 2 = 118

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'''Pontiac''' is a [[7-limit]] (and higher) [[regular temperament|temperament]] of the [[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 standard notation may be used). As in helmholtz temperament, [[5/4]] is mapped to the diminished fourth (e.g. C–F♭), and the new mapping specific to pontiac is that [[7/4]] is mapped to the quintuple-augmented third (e.g. C–Exx#). This makes pontiac a [[ragismic microtemperaments|ragismic temperament]]. An excellent tuning for pontiac is [[171edo]], and [[mos scale]]s of size 12, 17, 29, 41, 53, 65, and 118 are available.

'''Pontiac''' is a [[7-limit]] (and higher) [[regular temperament|temperament]] of the [[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 standard notation may be used). As in helmholtz temperament, [[5/4]] is mapped to the diminished fourth (e.g. C–F♭), and the new mapping specific to pontiac is that [[7/4]] is mapped to the quintuple-augmented third (e.g. C–Exx#). This makes pontiac a [[ragismic microtemperaments|ragismic temperament]]. An excellent tuning for pontiac is [[171edo]], with a perfect fifth generator 100\171, and [[mos scale]]s of size 12, 17, 29, 41, 53, 65, and 118 are available.

Immediate 11-limit extensions include helenoid ({{nowrap| 53 & 65 }}), mapping 11/8 to -30 fifths, ''ponta'' ({{nowrap| 171 & 224 }}), mapping 11/8 to -83 fifths, and ''pontic'' ({{nowrap| 118 & 171 }}), mapping 11/8 to +88 fifths.

@@ Line 13: / Line 13: @@
 | Odd limit 2 = (7-limit) 63 | Mistuning 2 = 0.716 | Complexity 2 = 118
 }}
-'''Pontiac''' is a [[7-limit]] (and higher) [[regular temperament|temperament]] of the [[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 standard notation may be used). As in helmholtz temperament, [[5/4]] is mapped to the diminished fourth (e.g. C–F♭), and the new mapping specific to pontiac is that [[7/4]] is mapped to the quintuple-augmented third (e.g. C–Exx#). This makes pontiac a [[ragismic microtemperaments|ragismic temperament]]. An excellent tuning for pontiac is [[171edo]], and [[mos scale]]s of size 12, 17, 29, 41, 53, 65, and 118 are available.
+'''Pontiac''' is a [[7-limit]] (and higher) [[regular temperament|temperament]] of the [[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 standard notation may be used). As in helmholtz temperament, [[5/4]] is mapped to the diminished fourth (e.g. C–F♭), and the new mapping specific to pontiac is that [[7/4]] is mapped to the quintuple-augmented third (e.g. C–Exx#). This makes pontiac a [[ragismic microtemperaments|ragismic temperament]]. An excellent tuning for pontiac is [[171edo]], with a perfect fifth generator 100\171, and [[mos scale]]s of size 12, 17, 29, 41, 53, 65, and 118 are available.
 Immediate 11-limit extensions include helenoid ({{nowrap| 53 & 65 }}), mapping 11/8 to -30 fifths, ''ponta'' ({{nowrap| 171 & 224 }}), mapping 11/8 to -83 fifths, and ''pontic'' ({{nowrap| 118 & 171 }}), mapping 11/8 to +88 fifths.