Fractional-octave temperaments: Difference between revisions

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'''Fractional-octave temperaments'''~~, when viewed from a regular~~ temperament ~~theory perspective, are temperaments~~ which have a period which corresponds to a just interval mapped to a fraction of the octave, that is one step of an [[~~EDO~~]].

'''Fractional-octave temperaments''' are [[temperament]]s which have a [[period]] which corresponds to a [[just]] [[interval]] mapped to a fraction of the [[octave]], that is one step of an [[edo]].

== Theory ==

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=== Terminology ===

The terminology was developed by [[Eliora]]. The equal division containing the mos scale of such a temperament, starting from the tonic, is referred to as a ''wireframe'', and individual notes of that equal division are called ''hinges''. Thus in this context, the wireframe is the tuning consisting of only stacks of the period and no stacks of the generator. Temperament-agnostically, this can be used to refer to any structure embedded in an (x,y)-ET which repeats y times within that period, its "wireframe" is y-ET.

The terminology was developed by [[Eliora]]. The equal division containing the mos scale of such a temperament, starting from the tonic, is referred to as a ''wireframe'', and individual notes of that equal division are called ''hinges''. Thus in this context, the wireframe is the tuning consisting of only stacks of the period and no stacks of the generator. Temperament-agnostically, this can be used to refer to any structure embedded in an (x,y)-ET which repeats y times within that period, its "wireframe" is y-ET. If an equal division is a subset of a temperament, it is said to ''subtend'' the temperament, just how hinges on a ferris wheel subtend the structure to make it rotate and function.

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.

=== Disagreement between ~~regular~~ temperament ~~theory~~ and fractional-octave practice ===

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]].

Traditional regular temperament perspective on periods and generators has a shortcoming when it comes to handling fractional-octave temperaments, as it treats divisions of periods (for example, what [[hemiennealimmal]] is to [[ennealimmal]]) as ~~extensions~~ of a temperament with a subset period. However fractional-octave temperaments and scales are sought for being able to treat an each equal division as an entity in its own right, so a composer might find hemiennealimmal to be a drastically different system to ennealimmal in line with [[18edo]] being very different from [[9edo]].

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

Traditional regular temperament perspective on periods and generators has a shortcoming when it comes to handling fractional-octave temperaments, as it treats divisions of periods (for example, what [[hemiennealimmal]] is to [[ennealimmal]]) as [[extension]]s of a temperament with a subset period. However, fractional-octave temperaments and scales are sought for being able to treat an each equal division as an entity in its own right, so a composer might find hemiennealimmal to be a drastically different system to ennealimmal in line with [[18edo]] being very different from [[9edo]]. This facet is reflected by the distinction of strong and weak extensions.

A particularly strong offender of this is the [[landscape microtemperaments]] list, which features temperaments which are all supersets of 3edo, but from a composer's perspective it contains wildly different temperaments due to the fact that edo multiples of 3 themselves are different. For example, magnesium (12), and zinc (30), are both landscape systems due to being multiples of 3, but 30edo is drastically different from 12edo in terms of composition, and therefore such temperaments are not alike at all.

== Individual pages of temperaments by equal division ==

== 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]]

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

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

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

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

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

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

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

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

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

|-

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

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

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

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

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

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

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

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

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

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

|-

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

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

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

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

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

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

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

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

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

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

|-

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

|-

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

|-

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

| [[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>~~ Mercator family equated with 53rd-octave temperaments until otherwise discovered

C = Countercomp family

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

== Temperaments discussed elsewhere ==

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** [[Varunismic temperaments]]

** [[Lokismic temperaments]]

** [[Nimona|Nimona temperament]]

* 1\3 period temperaments

** [[Augmented family|Augmented temperaments]]

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** [[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]]

** [[~~Qintosec~~ family|~~Qintosec~~ temperaments]]

** [[Quintosec family|Quintosec temperaments]]

** [[Trisedodge family|Trisedodge temperaments]]

** [[Cloudy clan|Cloudy temperaments]]

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** [[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)

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* [[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)

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* [[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)

* Rubidium, dzelic (1\37 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)

* [[Mercator family|Mercator temperaments]] (1\53 period)

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

* [[Compton family #Omicronbeta|Omicronbeta~~]], [[The Flashmob#Hafnium|hafnium~~]] (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)

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

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

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

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

== See also ==

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

[[Category:Temperament collections]]

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

[[Category:Pages with mostly numerical content]]

@@ Line 1: / Line 1: @@
-'''Fractional-octave temperaments''', when viewed from a regular temperament theory perspective, are temperaments which have a period which corresponds to a just interval mapped to a fraction of the octave, that is one step of an [[EDO]].
+'''Fractional-octave temperaments''' are [[temperament]]s which have a [[period]] which corresponds to a [[just]] [[interval]] mapped to a fraction of the [[octave]], that is one step of an [[edo]].
 == Theory ==
@@ Line 5: / Line 5: @@
 === Terminology ===
-The terminology was developed by [[Eliora]]. The equal division containing the mos scale of such a temperament, starting from the tonic, is referred to as a ''wireframe'', and individual notes of that equal division are called ''hinges''. Thus in this context, the wireframe is the tuning consisting of only stacks of the period and no stacks of the generator. Temperament-agnostically, this can be used to refer to any structure embedded in an (x,y)-ET which repeats y times within that period, its "wireframe" is y-ET.
+The terminology was developed by [[Eliora]]. The equal division containing the mos scale of such a temperament, starting from the tonic, is referred to as a ''wireframe'', and individual notes of that equal division are called ''hinges''. Thus in this context, the wireframe is the tuning consisting of only stacks of the period and no stacks of the generator. Temperament-agnostically, this can be used to refer to any structure embedded in an (x,y)-ET which repeats y times within that period, its "wireframe" is y-ET. If an equal division is a subset of a temperament, it is said to ''subtend'' the temperament, just how hinges on a ferris wheel subtend the structure to make it rotate and function.
 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.
-=== Disagreement between regular temperament theory and fractional-octave practice ===
+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]].
-Traditional regular temperament perspective on periods and generators has a shortcoming when it comes to handling fractional-octave temperaments, as it treats divisions of periods (for example, what [[hemiennealimmal]] is to [[ennealimmal]]) as extensions of a temperament with a subset period. However fractional-octave temperaments and scales are sought for being able to treat an each equal division as an entity in its own right, so a composer might find hemiennealimmal to be a drastically different system to ennealimmal in line with [[18edo]] being very different from [[9edo]].
+=== Disagreement between temperament catalog strategy and fractional-octave practice ===
+Traditional regular temperament perspective on periods and generators has a shortcoming when it comes to handling fractional-octave temperaments, as it treats divisions of periods (for example, what [[hemiennealimmal]] is to [[ennealimmal]]) as [[extension]]s of a temperament with a subset period. However, fractional-octave temperaments and scales are sought for being able to treat an each equal division as an entity in its own right, so a composer might find hemiennealimmal to be a drastically different system to ennealimmal in line with [[18edo]] being very different from [[9edo]]. This facet is reflected by the distinction of strong and weak extensions.
 A particularly strong offender of this is the [[landscape microtemperaments]] list, which features temperaments which are all supersets of 3edo, but from a composer's perspective it contains wildly different temperaments due to the fact that edo multiples of 3 themselves are different. For example, magnesium (12), and zinc (30), are both landscape systems due to being multiples of 3, but 30edo is drastically different from 12edo in terms of composition, and therefore such temperaments are not alike at all.
-== Individual pages of temperaments by equal division ==
+== 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]]
+| [[12th-octave temperaments|12]]
+| [[13th-octave temperaments|13]]
+| [[14th-octave temperaments|14]]
+| [[15th-octave temperaments|15]]
+| [[16th-octave temperaments|16]]
+| [[17th-octave temperaments|17]]
+| [[18th-octave temperaments|18]]
+| [[19th-octave temperaments|19]]
+| [[20th-octave temperaments|20]]
+|-
+| [[21st-octave temperaments|21]]
+| [[22nd-octave temperaments|22]]
+| [[23rd-octave temperaments|23]]
+| [[24th-octave temperaments|24]]
+| [[25th-octave temperaments|25]]
+| [[26th-octave temperaments|26]]
+| [[27th-octave temperaments|27]]
+| [[28th-octave temperaments|28]]
+| [[29th-octave temperaments|29]]
+| [[30th-octave temperaments|30]]
+|-
+| [[31st-octave temperaments|31]]
+| [[32nd-octave temperaments|32]]
+| [[33rd-octave temperaments|33]]
+| [[34th-octave temperaments|34]]
+| [[35th-octave temperaments|35]]
+| [[36th-octave temperaments|36]]
+| [[37th-octave temperaments|37]]
+| [[38th-octave temperaments|38]]
+| [[39th-octave temperaments|39]]
+| [[40th-octave temperaments|40]]
 |-
-|[[11th-octave temperaments|11]]
+| [[41st-octave temperaments|41]] / [[Countercomp family|C]]
-|[[12th-octave temperaments|12]]
+| [[42nd-octave temperaments|42]]
-|[[13th-octave temperaments|13]]
+| [[43rd-octave temperaments|43]]
-|[[14th-octave temperaments|14]]
+| [[44th-octave temperaments|44]]
-|[[15th-octave temperaments|15]]
+| [[45th-octave temperaments|45]]
-|[[16th-octave temperaments|16]]
+| [[46th-octave temperaments|46]]
-|[[17th-octave temperaments|17]]
+| [[47th-octave temperaments|47]]
-|[[18th-octave temperaments|18]]
+| [[48th-octave temperaments|48]]
-|[[19th-octave temperaments|19]]
+| [[49th-octave temperaments|49]]
-|[[20th-octave temperaments|20]]
+| [[50th-octave temperaments|50]]
 |-
-|[[21st-octave temperaments|21]]
+| [[51st-octave temperaments|51]]
-|[[22nd-octave temperaments|22]]
+| [[52nd-octave temperaments|52]]
-|[[23rd-octave temperaments|23]]
+| [[53rd-octave temperaments|53]] / [[Mercator family|M]]
-|[[24th-octave temperaments|24]]
+| [[54th-octave temperaments|54]]
-|[[25th-octave temperaments|25]]
+| [[55th-octave temperaments|55]]
-|[[26th-octave temperaments|26]]
+| [[56th-octave temperaments|56]]
-|[[27th-octave temperaments|27]]
+| [[57th-octave temperaments|57]]
-|[[28th-octave temperaments|28]]
+| [[58th-octave temperaments|58]]
-|[[29th-octave temperaments|29]]
+| [[59th-octave temperaments|59]]
-|[[30th-octave temperaments|30]]
+| [[60th-octave temperaments|60]]
 |-
-|[[31st-octave temperaments|31]]
+| [[61st-octave temperaments|61]]
-|[[32nd-octave temperaments|32]]
+| [[62nd-octave temperaments|62]]
-|[[33rd-octave temperaments|33]]
+| [[63rd-octave temperaments|63]]
-|[[34th-octave temperaments|34]]
+| [[64th-octave temperaments|64]]
-|[[35th-octave temperaments|35]]
+| [[65th-octave temperaments|65]]
-|[[36th-octave temperaments|36]]
+| [[66th-octave temperaments|66]]
-|[[37th-octave temperaments|37]]
+| [[67th-octave temperaments|67]]
-|[[38th-octave temperaments|38]]
+| [[68th-octave temperaments|68]]
-|[[39th-octave temperaments|39]]
+| [[69th-octave temperaments|69]]
-|[[40th-octave temperaments|40]]
+| [[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]], [[44th-octave temperaments|44]], [[Mercator family|53*]], [[56th-octave temperaments|56]], [[60th-octave temperaments|60]], [[61st-octave temperaments|61]], [[65th-octave temperaments|65]], [[80th-octave temperaments|80]], [[91st-octave temperaments|91]], [[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]]
-&lt;nowiki&gt;*&lt;/nowiki&gt; Mercator family equated with 53rd-octave temperaments until otherwise discovered
+C = Countercomp family
+M = Mercator family equated with 53rd-octave temperaments until otherwise discovered, also contains 106th-octave temperaments
 == Temperaments discussed elsewhere ==
@@ Line 79: / Line 150: @@
 ** [[Varunismic temperaments]]
 ** [[Lokismic temperaments]]
+** [[Nimona|Nimona temperament]]
 * 1\3 period temperaments
 ** [[Augmented family|Augmented temperaments]]
@@ Line 84: / 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]]
-** [[Qintosec family|Qintosec temperaments]]
+** [[Quintosec family|Quintosec temperaments]]
 ** [[Trisedodge family|Trisedodge temperaments]]
 ** [[Cloudy clan|Cloudy temperaments]]
@@ Line 97: / 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 123: / 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 130: / 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)
-* Rubidium, dzelic (1\37 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)
-* [[Mercator family|Mercator temperaments]] (1\53 period)
+* [[Compton family #Omicronbeta|Omicronbeta]] (1\72 period)
-* [[Compton family #Omicronbeta|Omicronbeta]], [[The Flashmob#Hafnium|hafnium]] (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)
-* [[Tritrizo clan #Schisennealimmal|Schisennealimmal]] (1\171 period)
+* [[Septiennealimmal clan #Schisennealimmal|Schisennealimmal]] (1\171 period)
-* [[Tritrizo clan #Lunennealimmal|Lunennealimmal]] (1\441 period)
+* [[Septiennealimmal clan #Lunennealimmal|Lunennealimmal]] (1\441 period)
+== See also ==
+* [[Map of rank-2 temperaments]]: Visual map of many of the temperaments listed here.
 [[Category:Temperament collections]]
-[[Category:Lists of temperaments]]
+[[Category:Pages with mostly numerical content]]