Pontiac - Revision history

FloraC: Cleanup on infobox

2026-02-09T09:58:53Z

Cleanup on infobox

← Older revision		Revision as of 09:58, 9 February 2026
Line 3:		Line 3:
	\| Subgroups = 2.3.5.7		\| Subgroups = 2.3.5.7
	\| Comma basis = [[4375/4374]], [[32805/32768]]		\| Comma basis = [[4375/4374]], [[32805/32768]]
	\| ~~Generator~~ = 3/2		\| Edo join 1 = 53 \| Edo join 2 = 171
	\| Mapping = 1; 1 -8 39		\| Mapping = 1; 1 -8 39
			\| Generators = 3/2
			\| Generators tuning = 701.758
			\| Optimization method = CWE
	\| Pergen = (P8, P5)		\| 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]]		\| MOS scales = [[12L 17s]], [[12L 29s]], [[12L 41s]], [[53L 12s]]
	\| Odd limit 1 = 9 \| Mistuning 1 = 0.401 \| Complexity 1 = 53		\| Odd limit 1 = 9 \| Mistuning 1 = 0.401 \| Complexity 1 = 53

Overthink: expand second odd limit to 81

2026-02-08T19:08:56Z

expand second odd limit to 81

← Older revision		Revision as of 19:08, 8 February 2026
Line 11:		Line 11:
	\| MOS scales = [[12L 17s]], [[12L 29s]], [[12L 41s]], [[53L 12s]]		\| MOS scales = [[12L 17s]], [[12L 29s]], [[12L 41s]], [[53L 12s]]
	\| Odd limit 1 = 9 \| Mistuning 1 = 0.401 \| Complexity 1 = 53		\| 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.		'''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.

Overthink: formatting

2025-12-22T21:22:39Z

formatting

← Older revision		Revision as of 21:22, 22 December 2025
Line 18:		Line 18:

	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]].		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]].
			__TOC__
			{{Clear}}
	== Interval chain ==		== Interval chain ==
	{\| class="wikitable center-1 right-2"		{\| class="wikitable center-1 right-2"

FloraC: Explain the intervals in terms of commatic inflections

2025-12-16T12:37:30Z

Explain the intervals in terms of commatic inflections

← Older revision		Revision as of 12:37, 16 December 2025
Line 13:		Line 13:
	\| Odd limit 2 = (7-limit) 63 \| Mistuning 2 = 0.716 \| Complexity 2 = 118		\| 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]], 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.		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.

FloraC: /* Notation */ focus on the 7-limit part

2025-12-16T12:34:55Z

Notation: focus on the 7-limit part

← Older revision		Revision as of 12:34, 16 December 2025
Line 917:		Line 917:

	== Notation ==		== Notation ==
	~~Using pontiac can be a challenge because it defies the tradition of tertian harmony~~ in [[~~chain-of-fifths notation~~]]~~. The just major triad on C~~ is ~~C–Fb–G, for example. One may want~~ to adopt an additional module of accidentals such as arrows to represent the comma step~~, allowing them to write the chord above as C–vE–G~~.		Like in [[schismic]], it is recommended to adopt an additional module of accidentals such as arrows to represent the comma step.

	However, that which is considered sufficient to notate [[garibaldi #Notation\|garibaldi]] may not be sufficient for pontiac when it comes to septimal and undecimal harmony, as 7/4 is a triple-up major sixth (C–^<sup>3</sup>A), which is still a lot of stacks of bending. The interval is often notated as a down-minor seventh such as in [[FJS]] and [[HEJI]]. Combination of these reasons suggests that another set of accidentals to represent [[64/63]], the septimal comma, or [[5120/5103]], the amount by which the septimal comma exceeds the syntonic comma, may be desired. Ponta, one notable extension to the 11-limit, identifies the undecimal quartertone of [[33/32]] by a stack of two septimal commas, and can benefit considerably from this new set of accidentals.		However, that which is considered sufficient to notate [[garibaldi #Notation\|garibaldi]] may not be sufficient for pontiac when it comes to septimal and undecimal harmony, as 7/4 is a triple-up major sixth (C–^<sup>3</sup>A), which is still a lot of stacks of bending. The interval is often notated as a down-minor seventh such as in [[FJS]] and [[HEJI]]. Combination of these reasons suggests that another set of accidentals to represent [[64/63]], the septimal comma, or [[5120/5103]], the amount by which the septimal comma exceeds the syntonic comma, may be desired. Ponta, one notable extension to the 11-limit, identifies the undecimal quartertone of [[33/32]] by a stack of two septimal commas, and can benefit considerably from this new set of accidentals.

	== Tuning spectra ==		== Tuning spectra ==

Overthink: + generator

2025-12-14T05:04:51Z

+ generator

← Older revision		Revision as of 05:04, 14 December 2025
Line 13:		Line 13:
	\| Odd limit 2 = (7-limit) 63 \| Mistuning 2 = 0.716 \| Complexity 2 = 118		\| 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.		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.

FloraC: 53 & 171 is a better edo join. - gencom (irrelevant). Misc. cleanup and style improvements

2025-11-04T09:27:18Z

53 & 171 is a better edo join. - gencom (irrelevant). Misc. cleanup and style improvements

← Older revision		Revision as of 09:27, 4 November 2025
Line 2:		Line 2:
	\| Title = Pontiac		\| Title = Pontiac
	\| Subgroups = 2.3.5.7		\| Subgroups = 2.3.5.7
	\| Comma basis = [[~~32805~~/~~32768~~]], [[~~4375~~/~~4374~~]]		\| Comma basis = [[4375/4374]], [[32805/32768]]
	\| Generator = 3/2		\| Generator = 3/2
	\| Mapping = 1; 1 -8 39		\| Mapping = 1; 1 -8 39
	\| Pergen = (P8, P5)		\| Pergen = (P8, P5)
	\| Edo join 1 = 53 \| Edo join 2 = 65		\| Edo join 1 = 53 \| Edo join 2 = 171
	\| Optimization method = CWE		\| Optimization method = CWE
	\| Generator tuning = 701.758		\| Generator tuning = 701.758
Line 13:		Line 13:
	\| Odd limit 2 = (7-limit) 63 \| Mistuning 2 = 0.716 \| Complexity 2 = 118		\| 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.		'''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.

	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 ({{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]].		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]].
Line 23:		Line 23:
	! rowspan="3" \| #		! rowspan="3" \| #
	! rowspan="3" \| Cents*		! rowspan="3" \| Cents*
	! colspan="4" \| Approximate ~~Ratios~~		! colspan="4" \| Approximate ratios
	\|-		\|-
	! rowspan="2" \| 7-limit		! rowspan="2" \| 7-limit
	! colspan="3" \| 17-limit ~~Extension~~		! colspan="3" \| 17-limit extension
	\|-		\|-
	! Helenoid		! Helenoid
Line 917:		Line 917:

	== Notation ==		== Notation ==
	Using pontiac can be a challenge because it defies the tradition of tertian harmony in [[~~circle~~-of-fifths notation]]. The just major triad on C is ~~C-Fb-G~~, for example. One may want to adopt an additional module of accidentals such as arrows to represent the comma step, allowing them to write the chord above as ~~C-vE-G~~.		Using pontiac can be a challenge because it defies the tradition of tertian harmony in [[chain-of-fifths notation]]. The just major triad on C is C–Fb–G, for example. One may want to adopt an additional module of accidentals such as arrows to represent the comma step, allowing them to write the chord above as C–vE–G.

	However, that which is considered sufficient to notate [[~~Garibaldi~~ #Notation\|garibaldi]] may not be sufficient for pontiac when it comes to septimal and undecimal harmony, as 7/4 is a triple-up major sixth (C-^<sup>3</sup>A), which is still a lot of stacks of bending. The interval is often notated as a down-minor seventh such as in [[FJS]] and [[HEJI]]. Combination of these reasons suggests that another set of accidentals to represent [[64/63]], the septimal comma, or [[5120/5103]], the amount by which the septimal comma exceeds the syntonic comma, may be desired. Ponta, one notable extension to the 11-limit, identifies the undecimal quartertone of [[33/32]] by a stack of two septimal commas, and can benefit considerably from this new set of accidentals.		However, that which is considered sufficient to notate [[garibaldi #Notation\|garibaldi]] may not be sufficient for pontiac when it comes to septimal and undecimal harmony, as 7/4 is a triple-up major sixth (C–^<sup>3</sup>A), which is still a lot of stacks of bending. The interval is often notated as a down-minor seventh such as in [[FJS]] and [[HEJI]]. Combination of these reasons suggests that another set of accidentals to represent [[64/63]], the septimal comma, or [[5120/5103]], the amount by which the septimal comma exceeds the syntonic comma, may be desired. Ponta, one notable extension to the 11-limit, identifies the undecimal quartertone of [[33/32]] by a stack of two septimal commas, and can benefit considerably from this new set of accidentals.

	== Tuning spectra ==		== Tuning spectra ==
	=== Helenoid ===		=== Helenoid ===
	~~Gencom: [2 4/3; 352/351 385/384 561/560 625/624 729/728]~~

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

	{\| class="wikitable center-1 center-2"		{\| class="wikitable center-1 center-2"
	\|-		\|-
Line 1,059:		Line 1,055:

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

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

	{\| class="wikitable center-1 center-2"		{\| class="wikitable center-1 center-2"
	\|-		\|-
Line 1,195:		Line 1,187:

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

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

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

Overthink: Expanded intro

2025-11-04T00:42:06Z

Expanded intro

← Older revision		Revision as of 00:42, 4 November 2025
Line 1:		Line 1:
	'''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.		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 ==		== Interval chain ==

FloraC: - parent category

2025-04-28T14:33:54Z

- parent category

← Older revision		Revision as of 14:33, 28 April 2025
Line 1,319:		Line 1,319:

	[[Category:Pontiac\| ]] <!-- main article -->		[[Category:Pontiac\| ]] <!-- main article -->
	~~[[Category:Temperaments]]~~
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
	[[Category:Schismatic family]]		[[Category:Schismatic family]]
	[[Category:Ragismic microtemperaments]]		[[Category:Ragismic microtemperaments]]
	[[Category:Horwell temperaments]]		[[Category:Horwell temperaments]]

Lériendil at 23:37, 19 April 2025

2025-04-19T23:37:29Z

← Older revision		Revision as of 23:37, 19 April 2025
Line 1,320:		Line 1,320:
	[[Category:Pontiac\| ]] <!-- main article -->		[[Category:Pontiac\| ]] <!-- main article -->
	[[Category:Temperaments]]		[[Category:Temperaments]]
			[[Category:Rank-2 temperaments]]
	[[Category:Schismatic family]]		[[Category:Schismatic family]]
	[[Category:Ragismic microtemperaments]]		[[Category:Ragismic microtemperaments]]
	[[Category:Horwell temperaments]]		[[Category:Horwell temperaments]]