Pontiac: Difference between revisions

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'''Pontiac''' is a 7-limit (and higher) [[temperament]] of the [[Schismatic family #Pontiac|schismatic family]]. It is an extension of [[Helmholtz (temperament)|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. 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]].

{{Infobox regtemp

| Title = Pontiac

| Subgroups = 2.3.5.7

| Comma basis = [[32805/32768]], [[4375/4374]]

| Generator = 3/2

| Mapping = 1; 1 -8 39

| Pergen = (P8, P5)

| Edo join 1 = 53 | Edo join 2 = 65

| Optimization method = CWE

| Generator tuning = 701.758

| MOS scales = [[12L 17s]], [[12L 29s]], [[12L 41s]], [[53L 12s]]

| Odd limit 1 = 9 | Mistuning 1 = 0.401 | Complexity 1 = 53

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

}}

'''Pontiac''' is a 7-limit (and higher) [[temperament]] of the [[Schismatic family #Pontiac|schismatic family]]. It is an extension of [[Helmholtz (temperament)|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. 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]]es of size 12, 17, 29, 41, 53, 65, and 118 are available.

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.

Pontiac was named by [[Gene Ward Smith]] in 2004<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10729.html Yahoo! Tuning Group | Beep, orwell, and schismic]</ref>.

Pontiac was named by [[Gene Ward Smith]] in 2004<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10729.html Yahoo! Tuning Group | Beep, orwell, and schismic]</ref>. For technical data see [[Schismatic family#Pontiac]].

== Interval chain ==

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-'''Pontiac''' is a 7-limit (and higher) [[temperament]] of the [[Schismatic family #Pontiac|schismatic family]]. It is an extension of [[Helmholtz (temperament)|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. 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]].
+{{Infobox regtemp
+| Title = Pontiac
+| Subgroups = 2.3.5.7
+| Comma basis = [[32805/32768]], [[4375/4374]]
+| Generator = 3/2
+| Mapping = 1; 1 -8 39
+| Pergen = (P8, P5)
+| Edo join 1 = 53 | Edo join 2 = 65
+| Optimization method = CWE
+| Generator tuning = 701.758
+| MOS scales = [[12L&nbsp;17s]], [[12L&nbsp;29s]], [[12L&nbsp;41s]], [[53L&nbsp;12s]]
+| Odd limit 1 = 9 | Mistuning 1 = 0.401 | Complexity 1 = 53
+| Odd limit 2 = (7-limit) 63 | Mistuning 2 = 0.716 | Complexity 2 = 118
+}}
+'''Pontiac''' is a 7-limit (and higher) [[temperament]] of the [[Schismatic family #Pontiac|schismatic family]]. It is an extension of [[Helmholtz (temperament)|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. 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]]es of size 12, 17, 29, 41, 53, 65, and 118 are available.
 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.
-Pontiac was named by [[Gene Ward Smith]] in 2004<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10729.html Yahoo! Tuning Group | Beep, orwell, and schismic]</ref>.
+Pontiac was named by [[Gene Ward Smith]] in 2004<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10729.html Yahoo! Tuning Group | Beep, orwell, and schismic]</ref>. For technical data see [[Schismatic family#Pontiac]].
 == Interval chain ==