Pontiac: Difference between revisions

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| Subgroups = 2.3.5.7

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

| ~~Generator~~ = 3/2

| Edo join 1 = 53 | Edo join 2 = 171

| Mapping = 1; 1 -8 39

| Generators = 3/2

| Generators tuning = 701.758

| Optimization method = CWE

| Pergen = (P8, P5)

~~| Edo join 1 = 53 | Edo join 2 = 171~~

~~| 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

| Odd limit 2 = 7-limit 81 | Mistuning 2 = 0.884 | 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]], with a perfect fifth generator 100\171, 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♭; a comma-flat major third), and the new mapping specific to pontiac is that [[7/4]] is mapped to the quintuple-augmented third (e.g. C–Exx#; a three-comma-sharp major sixth). 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.

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]].

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== Interval chain ==

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

@@ Line 3: / Line 3: @@
 | Subgroups = 2.3.5.7
 | Comma basis = [[4375/4374]], [[32805/32768]]
-| Generator = 3/2
+| Edo join 1 = 53 | Edo join 2 = 171
 | Mapping = 1; 1 -8 39
+| Generators = 3/2
+| Generators tuning = 701.758
+| Optimization method = CWE
 | Pergen = (P8, P5)
-| Edo join 1 = 53 | Edo join 2 = 171
-| 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
+| Odd limit 2 = 7-limit 81 | Mistuning 2 = 0.884 | 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]], with a perfect fifth generator 100\171, 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♭; a comma-flat major third), and the new mapping specific to pontiac is that [[7/4]] is mapped to the quintuple-augmented third (e.g. C–Exx#; a three-comma-sharp major sixth). 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.
 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]].
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+{{Clear}}
 == Interval chain ==
 {| class="wikitable center-1 right-2"