Fractional-octave temperaments: Difference between revisions

(17 intermediate revisions by 7 users not shown)

Line 9:

The most common way to produce a fractional-octave temperament is through an excellent approximation of an interval relative to the size of the wireframe edo. For example, [[compton family]] tempers out the Pythagorean comma and maps 7 steps of 12edo to [[3/2]]. Likewise, a lot of 10th-octave temperaments have a [[13/8]] as 7\10, and 26th-octave temperaments often have a [[7/4]] for 21\26.

However, an equal division does not have to be harmonically decent to be a wireframe for a fractional-octave temperament. If an equal division has multiples which are high in consistency or are zeta equal divisions or otherwise harmonically strong, it can produce a lot of such ~~temperaments - notable~~ examples being [[20edo]] or [[32edo]]. Likewise, proximity of a step of equal division to a comma is often a source of these ~~temperaments - for~~ example [[56edo]]'s step being directly close to [[81/80]], and 44edo's step being extremely close to [[64/63]].

However, an equal division does not have to be harmonically decent to be a wireframe for a fractional-octave temperament. If an equal division has multiples which are high in consistency or are zeta equal divisions or otherwise harmonically strong, it can produce a lot of such temperaments—notable examples being [[20edo]] or [[32edo]]. Likewise, proximity of a step of equal division to a comma is often a source of these temperaments—for example [[56edo]]'s step being directly close to [[81/80]], and 44edo's step being extremely close to [[64/63]].

=== Disagreement between temperament catalog strategy and fractional-octave practice ===

Line 18:

== Individual pages of temperaments by subtending equal division ==

=== 2 to 40 ===

=== 2 to 100 ===

Many pages are yet to be created.

{| class="wikitable"

|+

|

|[[2nd-octave temperaments|2]]

| [[2nd-octave temperaments|2]]

|[[3rd-octave temperaments|3]]

| [[3rd-octave temperaments|3]]

|[[4th-octave temperaments|4]]

| [[4th-octave temperaments|4]]

|[[5th-octave temperaments|5]]

| [[5th-octave temperaments|5]]

|[[6th-octave temperaments|6]]

| [[6th-octave temperaments|6]]

|[[7th-octave temperaments|7]]

| [[7th-octave temperaments|7]]

|[[8th-octave temperaments|8]]

| [[8th-octave temperaments|8]]

|[[9th-octave temperaments|9]]

| [[9th-octave temperaments|9]]

|[[10th-octave temperaments|10]]

| [[10th-octave temperaments|10]]

|-

|[[11th-octave temperaments|11]]

| [[11th-octave temperaments|11]]

|[[12th-octave temperaments|12]]

| [[12th-octave temperaments|12]]

|[[13th-octave temperaments|13]]

| [[13th-octave temperaments|13]]

|[[14th-octave temperaments|14]]

| [[14th-octave temperaments|14]]

|[[15th-octave temperaments|15]]

| [[15th-octave temperaments|15]]

|[[16th-octave temperaments|16]]

| [[16th-octave temperaments|16]]

|[[17th-octave temperaments|17]]

| [[17th-octave temperaments|17]]

|[[18th-octave temperaments|18]]

| [[18th-octave temperaments|18]]

|[[19th-octave temperaments|19]]

| [[19th-octave temperaments|19]]

|[[20th-octave temperaments|20]]

| [[20th-octave temperaments|20]]

|-

|[[21st-octave temperaments|21]]

| [[21st-octave temperaments|21]]

|[[22nd-octave temperaments|22]]

| [[22nd-octave temperaments|22]]

|[[23rd-octave temperaments|23]]

| [[23rd-octave temperaments|23]]

|[[24th-octave temperaments|24]]

| [[24th-octave temperaments|24]]

|[[25th-octave temperaments|25]]

| [[25th-octave temperaments|25]]

|[[26th-octave temperaments|26]]

| [[26th-octave temperaments|26]]

|[[27th-octave temperaments|27]]

| [[27th-octave temperaments|27]]

|[[28th-octave temperaments|28]]

| [[28th-octave temperaments|28]]

|[[29th-octave temperaments|29]]

| [[29th-octave temperaments|29]]

|[[30th-octave temperaments|30]]

| [[30th-octave temperaments|30]]

|-

|[[31st-octave temperaments|31]]

| [[31st-octave temperaments|31]]

|[[32nd-octave temperaments|32]]

| [[32nd-octave temperaments|32]]

|[[33rd-octave temperaments|33]]

| [[33rd-octave temperaments|33]]

|[[34th-octave temperaments|34]]

| [[34th-octave temperaments|34]]

|[[35th-octave temperaments|35]]

| [[35th-octave temperaments|35]]

|[[36th-octave temperaments|36]]

| [[36th-octave temperaments|36]]

|[[37th-octave temperaments|37]]

| [[37th-octave temperaments|37]]

|[[38th-octave temperaments|38]]

| [[38th-octave temperaments|38]]

|[[39th-octave temperaments|39]]

| [[39th-octave temperaments|39]]

|[[40th-octave temperaments|40]]

| [[40th-octave temperaments|40]]

|-

| [[41st-octave temperaments|41]] / [[Countercomp family|C]]

| [[42nd-octave temperaments|42]]

| [[43rd-octave temperaments|43]]

| [[44th-octave temperaments|44]]

| [[45th-octave temperaments|45]]

| [[46th-octave temperaments|46]]

| [[47th-octave temperaments|47]]

| [[48th-octave temperaments|48]]

| [[49th-octave temperaments|49]]

| [[50th-octave temperaments|50]]

|-

| [[51st-octave temperaments|51]]

| [[52nd-octave temperaments|52]]

| [[53rd-octave temperaments|53]] / [[Mercator family|M]]

| [[54th-octave temperaments|54]]

| [[55th-octave temperaments|55]]

| [[56th-octave temperaments|56]]

| [[57th-octave temperaments|57]]

| [[58th-octave temperaments|58]]

| [[59th-octave temperaments|59]]

| [[60th-octave temperaments|60]]

|-

| [[61st-octave temperaments|61]]

| [[62nd-octave temperaments|62]]

| [[63rd-octave temperaments|63]]

| [[64th-octave temperaments|64]]

| [[65th-octave temperaments|65]]

| [[66th-octave temperaments|66]]

| [[67th-octave temperaments|67]]

| [[68th-octave temperaments|68]]

| [[69th-octave temperaments|69]]

| [[70th-octave temperaments|70]]

|-

| [[71st-octave temperaments|71]]

| [[72nd-octave temperaments|72]]

| [[73rd-octave temperaments|73]]

| [[74th-octave temperaments|74]]

| [[75th-octave temperaments|75]]

| [[76th-octave temperaments|76]]

| [[77th-octave temperaments|77]]

| [[78th-octave temperaments|78]]

| [[79th-octave temperaments|79]]

| [[80th-octave temperaments|80]]

|-

| [[81st-octave temperaments|81]]

| [[82nd-octave temperaments|82]]

| [[83rd-octave temperaments|83]]

| [[84th-octave temperaments|84]]

| [[85th-octave temperaments|85]]

| [[86th-octave temperaments|86]]

| [[87th-octave temperaments|87]]

| [[88th-octave temperaments|88]]

| [[89th-octave temperaments|89]]

| [[90th-octave temperaments|90]]

|-

| [[91st-octave temperaments|91]]

| [[92nd-octave temperaments|92]]

| [[93rd-octave temperaments|93]]

| [[94th-octave temperaments|94]]

| [[95th-octave temperaments|95]]

| [[96th-octave temperaments|96]]

| [[97th-octave temperaments|97]]

| [[98th-octave temperaments|98]]

| [[99th-octave temperaments|99]]

| [[100th-octave temperaments|100]]

|}

=== 40 and up ===

=== 101 and up ===

~~<nowiki>*</nowiki>~~ Countercomp family

C = Countercomp family

~~<nowiki>**</nowiki>~~ Mercator family equated with 53rd-octave temperaments until otherwise discovered, also contains 106th-octave temperaments

M = Mercator family equated with 53rd-octave temperaments until otherwise discovered, also contains 106th-octave temperaments

== Temperaments discussed elsewhere ==

Line 78:

Line 145:

* 1\2 period temperaments

**[[Diaschismic family|Diaschismic temperaments]]

** [[Diaschismic family|Diaschismic temperaments]]

** [[Vishnuzmic family|Vishnuzmic temperaments]]

** [[Jubilismic clan|Jubilismic temperaments]]

Line 89:

Line 156:

** [[Landscape microtemperaments|Landscape temperaments]]

* 1\4 period temperaments

** [[~~Dimipent~~ family|Diminished temperaments]]

** [[Diminished family|Diminished temperaments]]

** [[Undim family|Undim temperaments]]

* 1\5 period temperaments

** [[~~Pental~~ family|~~Pental~~ temperaments]]

** [[Quintile family|Quintile temperaments]]

** [[Quintosec family|Quintosec temperaments]]

** [[Trisedodge family|Trisedodge temperaments]]

Line 102:

Line 169:

** [[Stearnsmic clan #Stearnscape|Stearnscape]]

* [[Akjaysma|Akjaysmic temperaments]] (1\7 period)

**[[Ragismic microtemperaments #Brahmagupta|Brahmagupta]]

** [[Ragismic microtemperaments #Brahmagupta|Brahmagupta]]

** [[Schismatic family #Septant|Septant]]

** [[~~Apotome~~ family #Whitewood|Whitewood]]

** [[Whitewood family #Whitewood|Whitewood temperaments]]

** [[Keemic temperaments #Sevond|Sevond]]

** [[Mistismic temperaments #Neutron|Neutron]]

* [[Ragismic microtemperaments #Octoid|Octoid]], [[Schismatic family #Octant|octant]] (1\8 period)

* [[~~Tritrizo~~ clan|~~Tritrizo~~ temperaments]] (1\9 period)

* [[Septiennealimmal clan|Septiennealimmal temperaments]] (1\9 period)

** [[Ragismic microtemperaments #Ennealimmal|Ennealimmal]]

** [[Augmented family #Niner|Niner]]

** [[Marvel temperaments #Enneaportent|Enneaportent]]

** [[Kleismic family #Novemkleismic|Novemkleismic]]

* [[~~15/14 equal-step tuning|~~Linus ~~temperaments~~]] (1\10 period)

* [[Linus]] temperaments (1\10 period)

** [[Breedsmic temperaments #Decoid|Decoid]]

** [[Ragismic microtemperaments #Deca|Deca]]

** [[Cloudy clan #Decic|Decic]]

** [[Stearnsmic clan #Decistearn|Decistearn]]

** [[~~Pental~~ family #~~Decal~~|~~Decal~~]]

** [[Quintile family #Decile|Decile]]

** [[Vishnuzmic family #Decavish|Decavish]]

** [[Metric microtemperaments #Decimetra|Decimetra]]

* [[Porwell temperaments #Hendecatonic|Hendecatonic~~]], [[Keemic temperaments #Undeka|undeka~~]] (1\11 period)

* [[Porwell temperaments #Hendecatonic|Hendecatonic]] (1\11 period)

* [[Compton family|Compton]], [[Very high accuracy temperaments #Atomic|atomic]] (1\12 period)

* [[Orwellismic temperaments #Triskaidekic|Triskaidekic]], [[Octagar temperaments #Tridecatonic|tridecatonic]], [[Ragismic microtemperaments #Trideci|trideci]], [[aluminium]] (1\13 period)

Line 128:

Line 195:

* [[Ragismic microtemperaments #Octoid|Hexadecoid]], [[Jubilismic clan #Sedecic|sedecic]] (1\16 period)

* [[Ragismic microtemperaments #Chlorine|Chlorine]] (1\17 period)

* [[~~Ragismic microtemperaments~~ #Ennealimmal|Hemiennealimmal]] (1\18 period)

* [[Septiennealimmal clan #Ennealimmal|Hemiennealimmal]] (1\18 period)

* [[Ragismic microtemperaments #Enneadecal|Enneadecal]], [[Meantone family #Meanmag|meanmag]] (1\19 period)

* [[Hemimage temperaments #Degrees|Degrees]] (1\20 period)

Line 135:

Line 202:

* [[Porwell temperaments #Icositritonic|Icositritonic]] (1\23 period)

* [[Compton family #Hours|Hours]], [[chromium]] (1\24 period)

* [[~~Ragismic microtemperaments~~ #Ennealimmal|Trinealimmal]], [[Tritrizo clan #Cobalt|cobalt]] (1\27 period)

* [[Septiennealimmal clan #Ennealimmal|Trinealimmal]], [[Tritrizo clan #Cobalt|cobalt]] (1\27 period)

* [[Horwell temperaments #Oquatonic|Oquatonic]] (1\28 period)

* [[Hemifamity temperaments #Mystery|Mystery]], [[Copper comma|copper]] (1\29 period)

* [[31st-octave temperaments|Birds]] (1\31 period)

* [[Compton family #~~Decades~~|~~Decades~~]] (1\36 period)

* [[Compton family #Gamelstearn|Gamelstearn]] (1\36 period)

* [[Ragismic microtemperaments #Enneadecal|Hemienneadecal]], [[semihemienneadecal]] (1\38 period)

* [[~~Counterpyth~~ family|~~Counterpyth~~ temperaments]], [[niobium]] (1\41 period)

* [[Countercomp family|Countercomp temperaments]], [[niobium]] (1\41 period)

* [[Mitonismic temperaments #Meridic|Meridic]] (1\43 period)

* [[Ragismic microtemperaments #Palladium|Palladium]] (1\46 period)

* [[Compton family #Omicronbeta|Omicronbeta]] (1\72 period)

* [[The Flashmob#Iridium|Iridium]] (1\77 period)

* [[Parkleiness temperaments #Octogintic|Octogintic]], (1\80 period)

* [[Parkleiness temperaments #Octogintic|Octogintic]] (1\80 period)

* [[Stearnsmic clan #Garistearn|Garistearn]] (1\94 period)

* [[~~Tritrizo~~ clan #Undecentic|Undecentic]] (1\99 period)

* [[Septiennealimmal clan #Undecentic|Undecentic]] (1\99 period)

* [[~~Frameshift clan#Auric|Auric]] (1\159 period)~~

* [[Septiennealimmal clan #Schisennealimmal|Schisennealimmal]] (1\171 period)

* [[Tritrizo clan #Schisennealimmal|Schisennealimmal]] (1\171 period)

* [[Septiennealimmal clan #Lunennealimmal|Lunennealimmal]] (1\441 period)

* [[~~Tritrizo~~ clan #Lunennealimmal|Lunennealimmal]] (1\441 period)

== See also ==

* [[Map of rank-2 temperaments]]: Visual map of many of the temperaments listed here.

* [[Map of rank-2 temperaments]]

[[Category:Temperament collections]]

[[Category:~~Lists of temperaments~~]]

[[Category:Pages with mostly numerical content]]

@@ Line 9: / Line 9: @@
 The most common way to produce a fractional-octave temperament is through an excellent approximation of an interval relative to the size of the wireframe edo. For example, [[compton family]] tempers out the Pythagorean comma and maps 7 steps of 12edo to [[3/2]]. Likewise, a lot of 10th-octave temperaments have a [[13/8]] as 7\10, and 26th-octave temperaments often have a [[7/4]] for 21\26.
-However, an equal division does not have to be harmonically decent to be a wireframe for a fractional-octave temperament. If an equal division has multiples which are high in consistency or are zeta equal divisions or otherwise harmonically strong, it can produce a lot of such temperaments - notable examples being [[20edo]] or [[32edo]]. Likewise, proximity of a step of equal division to a comma is often a source of these temperaments - for example [[56edo]]'s step being directly close to [[81/80]], and 44edo's step being extremely close to [[64/63]].
+However, an equal division does not have to be harmonically decent to be a wireframe for a fractional-octave temperament. If an equal division has multiples which are high in consistency or are zeta equal divisions or otherwise harmonically strong, it can produce a lot of such temperaments—notable examples being [[20edo]] or [[32edo]]. Likewise, proximity of a step of equal division to a comma is often a source of these temperaments—for example [[56edo]]'s step being directly close to [[81/80]], and 44edo's step being extremely close to [[64/63]].
 === Disagreement between temperament catalog strategy and fractional-octave practice ===
@@ Line 18: / Line 18: @@
 == Individual pages of temperaments by subtending equal division ==
-=== 2 to 40 ===
+=== 2 to 100 ===
 Many pages are yet to be created.
 {| class="wikitable"
 |+
 |
-|[[2nd-octave temperaments|2]]
+| [[2nd-octave temperaments|2]]
-|[[3rd-octave temperaments|3]]
+| [[3rd-octave temperaments|3]]
-|[[4th-octave temperaments|4]]
+| [[4th-octave temperaments|4]]
-|[[5th-octave temperaments|5]]
+| [[5th-octave temperaments|5]]
-|[[6th-octave temperaments|6]]
+| [[6th-octave temperaments|6]]
-|[[7th-octave temperaments|7]]
+| [[7th-octave temperaments|7]]
-|[[8th-octave temperaments|8]]
+| [[8th-octave temperaments|8]]
-|[[9th-octave temperaments|9]]
+| [[9th-octave temperaments|9]]
-|[[10th-octave temperaments|10]]
+| [[10th-octave temperaments|10]]
 |-
-|[[11th-octave temperaments|11]]
+| [[11th-octave temperaments|11]]
-|[[12th-octave temperaments|12]]
+| [[12th-octave temperaments|12]]
-|[[13th-octave temperaments|13]]
+| [[13th-octave temperaments|13]]
-|[[14th-octave temperaments|14]]
+| [[14th-octave temperaments|14]]
-|[[15th-octave temperaments|15]]
+| [[15th-octave temperaments|15]]
-|[[16th-octave temperaments|16]]
+| [[16th-octave temperaments|16]]
-|[[17th-octave temperaments|17]]
+| [[17th-octave temperaments|17]]
-|[[18th-octave temperaments|18]]
+| [[18th-octave temperaments|18]]
-|[[19th-octave temperaments|19]]
+| [[19th-octave temperaments|19]]
-|[[20th-octave temperaments|20]]
+| [[20th-octave temperaments|20]]
 |-
-|[[21st-octave temperaments|21]]
+| [[21st-octave temperaments|21]]
-|[[22nd-octave temperaments|22]]
+| [[22nd-octave temperaments|22]]
-|[[23rd-octave temperaments|23]]
+| [[23rd-octave temperaments|23]]
-|[[24th-octave temperaments|24]]
+| [[24th-octave temperaments|24]]
-|[[25th-octave temperaments|25]]
+| [[25th-octave temperaments|25]]
-|[[26th-octave temperaments|26]]
+| [[26th-octave temperaments|26]]
-|[[27th-octave temperaments|27]]
+| [[27th-octave temperaments|27]]
-|[[28th-octave temperaments|28]]
+| [[28th-octave temperaments|28]]
-|[[29th-octave temperaments|29]]
+| [[29th-octave temperaments|29]]
-|[[30th-octave temperaments|30]]
+| [[30th-octave temperaments|30]]
 |-
-|[[31st-octave temperaments|31]]
+| [[31st-octave temperaments|31]]
-|[[32nd-octave temperaments|32]]
+| [[32nd-octave temperaments|32]]
-|[[33rd-octave temperaments|33]]
+| [[33rd-octave temperaments|33]]
-|[[34th-octave temperaments|34]]
+| [[34th-octave temperaments|34]]
-|[[35th-octave temperaments|35]]
+| [[35th-octave temperaments|35]]
-|[[36th-octave temperaments|36]]
+| [[36th-octave temperaments|36]]
-|[[37th-octave temperaments|37]]
+| [[37th-octave temperaments|37]]
-|[[38th-octave temperaments|38]]
+| [[38th-octave temperaments|38]]
-|[[39th-octave temperaments|39]]
+| [[39th-octave temperaments|39]]
-|[[40th-octave temperaments|40]]
+| [[40th-octave temperaments|40]]
+|-
+| [[41st-octave temperaments|41]] / [[Countercomp family|C]]
+| [[42nd-octave temperaments|42]]
+| [[43rd-octave temperaments|43]]
+| [[44th-octave temperaments|44]]
+| [[45th-octave temperaments|45]]
+| [[46th-octave temperaments|46]]
+| [[47th-octave temperaments|47]]
+| [[48th-octave temperaments|48]]
+| [[49th-octave temperaments|49]]
+| [[50th-octave temperaments|50]]
+|-
+| [[51st-octave temperaments|51]]
+| [[52nd-octave temperaments|52]]
+| [[53rd-octave temperaments|53]] / [[Mercator family|M]]
+| [[54th-octave temperaments|54]]
+| [[55th-octave temperaments|55]]
+| [[56th-octave temperaments|56]]
+| [[57th-octave temperaments|57]]
+| [[58th-octave temperaments|58]]
+| [[59th-octave temperaments|59]]
+| [[60th-octave temperaments|60]]
+|-
+| [[61st-octave temperaments|61]]
+| [[62nd-octave temperaments|62]]
+| [[63rd-octave temperaments|63]]
+| [[64th-octave temperaments|64]]
+| [[65th-octave temperaments|65]]
+| [[66th-octave temperaments|66]]
+| [[67th-octave temperaments|67]]
+| [[68th-octave temperaments|68]]
+| [[69th-octave temperaments|69]]
+| [[70th-octave temperaments|70]]
+|-
+| [[71st-octave temperaments|71]]
+| [[72nd-octave temperaments|72]]
+| [[73rd-octave temperaments|73]]
+| [[74th-octave temperaments|74]]
+| [[75th-octave temperaments|75]]
+| [[76th-octave temperaments|76]]
+| [[77th-octave temperaments|77]]
+| [[78th-octave temperaments|78]]
+| [[79th-octave temperaments|79]]
+| [[80th-octave temperaments|80]]
+|-
+| [[81st-octave temperaments|81]]
+| [[82nd-octave temperaments|82]]
+| [[83rd-octave temperaments|83]]
+| [[84th-octave temperaments|84]]
+| [[85th-octave temperaments|85]]
+| [[86th-octave temperaments|86]]
+| [[87th-octave temperaments|87]]
+| [[88th-octave temperaments|88]]
+| [[89th-octave temperaments|89]]
+| [[90th-octave temperaments|90]]
+|-
+| [[91st-octave temperaments|91]]
+| [[92nd-octave temperaments|92]]
+| [[93rd-octave temperaments|93]]
+| [[94th-octave temperaments|94]]
+| [[95th-octave temperaments|95]]
+| [[96th-octave temperaments|96]]
+| [[97th-octave temperaments|97]]
+| [[98th-octave temperaments|98]]
+| [[99th-octave temperaments|99]]
+| [[100th-octave temperaments|100]]
 |}
-=== 40 and up ===
+=== 101 and up ===
-[[41st-octave temperaments|41]] ([[Countercomp family|c*]]), [[44th-octave temperaments|44]], [[45th-octave temperaments|45]], [[46th-octave temperaments|46]], [[Mercator family|53**]], [[56th-octave temperaments|56]], [[60th-octave temperaments|60]], [[61st-octave temperaments|61]], [[65th-octave temperaments|65]], [[69th-octave temperaments|69]], [[72nd-octave temperaments|72]], [[79th-octave temperaments|79]], [[80th-octave temperaments|80]], [[87th-octave temperaments|87]], [[91st-octave temperaments|91]], [[97th-octave temperaments|97]], [[111th-octave temperaments|111]], [[118th-octave temperaments|118]]
+[[111th-octave temperaments|111]], [[118th-octave temperaments|118]], [[159th-octave temperaments|159]], [[400th-octave temperaments|400]], [[665th-octave temperaments|665]]
-<nowiki>*</nowiki> Countercomp family
+C = Countercomp family
-<nowiki>**</nowiki> Mercator family equated with 53rd-octave temperaments until otherwise discovered, also contains 106th-octave temperaments
+M = Mercator family equated with 53rd-octave temperaments until otherwise discovered, also contains 106th-octave temperaments
 == Temperaments discussed elsewhere ==
@@ Line 78: / Line 145: @@
 * 1\2 period temperaments
-**[[Diaschismic family|Diaschismic temperaments]]
+** [[Diaschismic family|Diaschismic temperaments]]
 ** [[Vishnuzmic family|Vishnuzmic temperaments]]
 ** [[Jubilismic clan|Jubilismic temperaments]]
@@ Line 89: / Line 156: @@
 ** [[Landscape microtemperaments|Landscape temperaments]]
 * 1\4 period temperaments
-** [[Dimipent family|Diminished temperaments]]
+** [[Diminished family|Diminished temperaments]]
 ** [[Undim family|Undim temperaments]]
 * 1\5 period temperaments
-** [[Pental family|Pental temperaments]]
+** [[Quintile family|Quintile temperaments]]
 ** [[Quintosec family|Quintosec temperaments]]
 ** [[Trisedodge family|Trisedodge temperaments]]
@@ Line 102: / Line 169: @@
 ** [[Stearnsmic clan #Stearnscape|Stearnscape]]
 * [[Akjaysma|Akjaysmic temperaments]] (1\7 period)
-**[[Ragismic microtemperaments #Brahmagupta|Brahmagupta]]
+** [[Ragismic microtemperaments #Brahmagupta|Brahmagupta]]
 ** [[Schismatic family #Septant|Septant]]
-** [[Apotome family #Whitewood|Whitewood]]
+** [[Whitewood family #Whitewood|Whitewood temperaments]]
 ** [[Keemic temperaments #Sevond|Sevond]]
 ** [[Mistismic temperaments #Neutron|Neutron]]
 * [[Ragismic microtemperaments #Octoid|Octoid]], [[Schismatic family #Octant|octant]] (1\8 period)
-* [[Tritrizo clan|Tritrizo temperaments]] (1\9 period)
+* [[Septiennealimmal clan|Septiennealimmal temperaments]] (1\9 period)
 ** [[Ragismic microtemperaments #Ennealimmal|Ennealimmal]]
 ** [[Augmented family #Niner|Niner]]
 ** [[Marvel temperaments #Enneaportent|Enneaportent]]
 ** [[Kleismic family #Novemkleismic|Novemkleismic]]
-* [[15/14 equal-step tuning|Linus temperaments]] (1\10 period)
+* [[Linus]] temperaments (1\10 period)
 ** [[Breedsmic temperaments #Decoid|Decoid]]
 ** [[Ragismic microtemperaments #Deca|Deca]]
 ** [[Cloudy clan #Decic|Decic]]
 ** [[Stearnsmic clan #Decistearn|Decistearn]]
-** [[Pental family #Decal|Decal]]
+** [[Quintile family #Decile|Decile]]
 ** [[Vishnuzmic family #Decavish|Decavish]]
 ** [[Metric microtemperaments #Decimetra|Decimetra]]
-* [[Porwell temperaments #Hendecatonic|Hendecatonic]], [[Keemic temperaments #Undeka|undeka]] (1\11 period)
+* [[Porwell temperaments #Hendecatonic|Hendecatonic]] (1\11 period)
 * [[Compton family|Compton]], [[Very high accuracy temperaments #Atomic|atomic]] (1\12 period)
 * [[Orwellismic temperaments #Triskaidekic|Triskaidekic]], [[Octagar temperaments #Tridecatonic|tridecatonic]], [[Ragismic microtemperaments #Trideci|trideci]], [[aluminium]] (1\13 period)
@@ Line 128: / Line 195: @@
 * [[Ragismic microtemperaments #Octoid|Hexadecoid]], [[Jubilismic clan #Sedecic|sedecic]] (1\16 period)
 * [[Ragismic microtemperaments #Chlorine|Chlorine]] (1\17 period)
-* [[Ragismic microtemperaments #Ennealimmal|Hemiennealimmal]] (1\18 period)
+* [[Septiennealimmal clan #Ennealimmal|Hemiennealimmal]] (1\18 period)
 * [[Ragismic microtemperaments #Enneadecal|Enneadecal]], [[Meantone family #Meanmag|meanmag]] (1\19 period)
 * [[Hemimage temperaments #Degrees|Degrees]] (1\20 period)
@@ Line 135: / Line 202: @@
 * [[Porwell temperaments #Icositritonic|Icositritonic]] (1\23 period)
 * [[Compton family #Hours|Hours]], [[chromium]] (1\24 period)
-* [[Ragismic microtemperaments #Ennealimmal|Trinealimmal]], [[Tritrizo clan #Cobalt|cobalt]] (1\27 period)
+* [[Septiennealimmal clan #Ennealimmal|Trinealimmal]], [[Tritrizo clan #Cobalt|cobalt]] (1\27 period)
 * [[Horwell temperaments #Oquatonic|Oquatonic]] (1\28 period)
 * [[Hemifamity temperaments #Mystery|Mystery]], [[Copper comma|copper]] (1\29 period)
 * [[31st-octave temperaments|Birds]] (1\31 period)
-* [[Compton family #Decades|Decades]] (1\36 period)
+* [[Compton family #Gamelstearn|Gamelstearn]] (1\36 period)
 * [[Ragismic microtemperaments #Enneadecal|Hemienneadecal]], [[semihemienneadecal]] (1\38 period)
-* [[Counterpyth family|Counterpyth temperaments]], [[niobium]] (1\41 period)
+* [[Countercomp family|Countercomp temperaments]], [[niobium]] (1\41 period)
 * [[Mitonismic temperaments #Meridic|Meridic]] (1\43 period)
 * [[Ragismic microtemperaments #Palladium|Palladium]] (1\46 period)
 * [[Compton family #Omicronbeta|Omicronbeta]] (1\72 period)
 * [[The Flashmob#Iridium|Iridium]] (1\77 period)
-* [[Parkleiness temperaments #Octogintic|Octogintic]], (1\80 period)
+* [[Parkleiness temperaments #Octogintic|Octogintic]] (1\80 period)
 * [[Stearnsmic clan #Garistearn|Garistearn]] (1\94 period)
-* [[Tritrizo clan #Undecentic|Undecentic]] (1\99 period)
+* [[Septiennealimmal clan #Undecentic|Undecentic]] (1\99 period)
-* [[Frameshift clan#Auric|Auric]] (1\159 period)
+* [[Septiennealimmal clan #Schisennealimmal|Schisennealimmal]] (1\171 period)
-* [[Tritrizo clan #Schisennealimmal|Schisennealimmal]] (1\171 period)
+* [[Septiennealimmal clan #Lunennealimmal|Lunennealimmal]] (1\441 period)
-* [[Tritrizo clan #Lunennealimmal|Lunennealimmal]] (1\441 period)
 == See also ==
+* [[Map of rank-2 temperaments]]: Visual map of many of the temperaments listed here.
-* [[Map of rank-2 temperaments]]
 [[Category:Temperament collections]]
-[[Category:Lists of temperaments]]
+[[Category:Pages with mostly numerical content]]