Pontiac: Difference between revisions

Line 11:

| 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♭; 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.

@@ Line 11: / Line 11: @@
 | 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♭; 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.