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 pontiac is that [[7/4]] is mapped to the quintuple augmented third (e.g. A-~~Cxxx~~). This makes pontiac a [[Ragismic microtemperaments|ragismic temperament]].

'''Pontiac''' 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. 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]].

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.

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.

== Interval chain ==

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

! rowspan="3" | ~~Fifth generator~~

! rowspan="3" | #

! rowspan="3" | Cents*

! colspan="4" | Approximate Ratios

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

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

Gencom mapping: {{mapping| 1 2 -1 19 -9 -10 29 | 0 -1 8 -39 30 33 -60 }}

{| class="wikitable center-~~all~~"

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

|-

! [[~~eigenmonzo~~|~~eigenmonzo~~ (~~unchanged~~-interval]])

! [[Eigenmonzo|Eigenmonzo (Unchanged-interval)]]

! ~~fifth~~ (¢)

! Generator (¢)

! ~~comments~~

! Comments

|-

| 11/10

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Gencom: [2 4/3; 375/374 540/539 625/624 729/728 2200/2197]

Gencom mapping: [{{~~val~~|1 2 -1 19 -31 -10 29~~}}, {{val~~|0 -1 8 -39 83 33 -60}}]

Gencom mapping: {{mapping| 1 2 -1 19 -31 -10 29 | 0 -1 8 -39 83 33 -60 }}

{| class="wikitable center-~~all~~"

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

|-

! ~~eigenmonzo~~ (~~unchanged~~-interval)

! Eigenmonzo (Unchanged-interval)

! ~~fifth~~ (¢)

! Generator (¢)

! ~~comments~~

! Comments

|-

| 16/15

Line 1,176:

Gencom: [2 4/3; 441/440 595/594 625/624 729/728 2880/2873]

Gencom mapping: [{{~~val~~|1 2 -1 19 40 -10 29~~}}, {{val~~|0 -1 8 -39 -88 33 -60}}]

Gencom mapping: {{mapping| 1 2 -1 19 40 -10 29 | 0 -1 8 -39 -88 33 -60 }}

{| class="wikitable center-~~all~~"

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

|-

! ~~eigenmonzo~~ (~~unchanged~~-interval)

! Eigenmonzo (Unchanged-interval)

! ~~fifth~~ (¢)

! Generator (¢)

! ~~comments~~

! Comments

|-

| 22/17

Line 1,309:

|}

[[Category:Pontiac| ]]

[[Category:Temperaments]]

[[Category:Schismatic family]]

[[Category:Ragismic microtemperaments]]

[[Category:~~Schismatic family]]~~

[[Category:Horwell temperaments]]

~~[[Category:Temperaments~~]]

@@ Line 1: / Line 1: @@
-'''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]].
+'''Pontiac''' 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. 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]].
-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.
+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.
 == Interval chain ==
 {| class="wikitable center-1 right-2"
-! rowspan="3" | Fifth <br>generator
+! rowspan="3" | #
 ! rowspan="3" | Cents*
 ! colspan="4" | Approximate Ratios
@@ Line 904: / Line 904: @@
 Gencom: [2 4/3; 352/351 385/384 561/560 625/624 729/728]
-Gencom mapping: [{{val|1 2 -1 19 -9 -10 29}}, {{val|0 -1 8 -39 30 33 -60}}]
+Gencom mapping: {{mapping| 1 2 -1 19 -9 -10 29 | 0 -1 8 -39 30 33 -60 }}
-{| class="wikitable center-all"
+{| class="wikitable center-1 center-2"
 |-
-! [[eigenmonzo|eigenmonzo<br>(unchanged-interval]])
+! [[Eigenmonzo|Eigenmonzo<br>(Unchanged-interval)]]
-! fifth<br>(¢)
+! Generator<br>(¢)
-! comments
+! Comments
 |-
 | 11/10
@@ Line 1,040: / Line 1,040: @@
 Gencom: [2 4/3; 375/374 540/539 625/624 729/728 2200/2197]
-Gencom mapping: [{{val|1 2 -1 19 -31 -10 29}}, {{val|0 -1 8 -39 83 33 -60}}]
+Gencom mapping: {{mapping| 1 2 -1 19 -31 -10 29 | 0 -1 8 -39 83 33 -60 }}
-{| class="wikitable center-all"
+{| class="wikitable center-1 center-2"
 |-
-! eigenmonzo<br>(unchanged-interval)
+! Eigenmonzo<br>(Unchanged-interval)
-! fifth<br>(¢)
+! Generator<br>(¢)
-! comments
+! Comments
 |-
 | 16/15
@@ Line 1,176: / Line 1,176: @@
 Gencom: [2 4/3; 441/440 595/594 625/624 729/728 2880/2873]
-Gencom mapping: [{{val|1 2 -1 19 40 -10 29}}, {{val|0 -1 8 -39 -88 33 -60}}]
+Gencom mapping: {{mapping| 1 2 -1 19 40 -10 29 | 0 -1 8 -39 -88 33 -60 }}
-{| class="wikitable center-all"
+{| class="wikitable center-1 center-2"
 |-
-! eigenmonzo<br>(unchanged-interval)
+! Eigenmonzo<br>(Unchanged-interval)
-! fifth<br>(¢)
+! Generator<br>(¢)
-! comments
+! Comments
 |-
 | 22/17
@@ Line 1,309: / Line 1,309: @@
 |}
+[[Category:Pontiac| ]] <!-- main article -->
+[[Category:Temperaments]]
+[[Category:Schismatic family]]
 [[Category:Ragismic microtemperaments]]
-[[Category:Schismatic family]]
+[[Category:Horwell temperaments]]
-[[Category:Temperaments]]