161/160: Difference between revisions

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{{Infobox Interval

| Name = major ~~kirnbergisma~~

| Name = major kirnbergerisma

| Color name = 23ozg2, twethozogu 2nd Twethozogu comma

| Comma = yes

}}

'''161/160''', the '''major ~~kirnbergisma~~''', is a [[small comma|small]] [[23-limit]] [[superparticular]] comma about 10.79 [[cent]]s in size. It forms the difference between [[23/16]] and [[10/7]].

'''161/160''', the '''major kirnbergerisma''', is a [[small comma|small]] [[23-limit]] [[superparticular]] comma about 10.79 [[cent]]s in size. It forms the difference between [[23/16]] and [[10/7]].

== Temperaments ==

Tempering out this comma in the 23-limit leads to the rank-8 '''major kirnbergerismic temperament'''. In the 2.5.7.23 subgroup, tempering it out leads to the rank-3 '''major kirnbergic temperament'''.

=== Major kirnbergerismic ===

[[Subgroup]]: full 23-limit

[[Comma list]]: 161/160

[[Mapping]]: <nowiki>[</nowiki>⟨1 0 0 0 0 0 0 0  5<nowiki>]</nowiki>,  ⟨0 1 0 0 0 0 0 0  0<nowiki>]</nowiki>,  ⟨0 0 1 0 0 0 0 0  1<nowiki>]</nowiki>,  ⟨0 0 0 1 0 0 0 0 -1<nowiki>]</nowiki>,  ⟨0 0 0 0 1 0 0 0  0<nowiki>]</nowiki>,  ⟨0 0 0 0 0 1 0 0  0<nowiki>]</nowiki>,  ⟨0 0 0 0 0 0 1 0  0<nowiki>]</nowiki>,  ⟨0 0 0 0 0 0 0 1  0<nowiki>]]</nowiki>

: Mapping generators: ~2, ~3, ~5, ~7, ~11, ~13, ~17, ~19

[[Optimal tuning]] (POTE): ~2 = 1＼1, ~3/2 = 700.5007, ~5/4 = 385.1726, ~7/4 = 964.8038, ~11/8 = 548.1438, ~13/8 = 837.1324, ~17/16 = 101.2050, ~19/16 = 293.6154

=== Major kirnbergic ===

Subgroup: 2.5.7.23

Comma list: 161/160

Mapping: <nowiki>[</nowiki>⟨1 0 0  5<nowiki>]</nowiki>,  ⟨0 1 0  1<nowiki>]</nowiki>,  ⟨0 0 1 -1<nowiki>]]</nowiki>

: Mapping generators: ~2, ~5, ~7

Optimal tuning (POTE): ~2 = 1＼1, ~5/4 = 385.1726, ~7/4 = 964.8038

== Etymology ==

The name ''major ~~kirnbergisma~~'' is contrast to the ''minor ~~kirnbergisma~~'', [[162/161]], measuring about 10.72¢, which is the difference between [[23/18]] and [[9/7]]. 161/160 is larger than 162/161 by a [[23-limit]] [[unnoticeable comma]], 25921/25920. The word ''~~kirnbergisma~~'' was introduced by [[User:Xenllium|Xenllium]] in 2023, for the following reason - 161/160 or 162/161 may be found in JI-approximated version of [[Kirnberger II]] as the difference between 1/2-comma-flattened fifth and pure fifth.

The name ''major kirnbergerisma'' is contrast to the ''minor kirnbergerisma'', [[162/161]], measuring about 10.72¢, which is the difference between [[23/18]] and [[9/7]]. 161/160 is larger than 162/161 by a [[23-limit]] [[unnoticeable comma]], [[25921/25920]]. The word ''kirnbergerisma'' was introduced by [[User:Xenllium|Xenllium]] in 2023, for the following reason - 161/160 or 162/161 may be found in JI-approximated version of [[Kirnberger II]] as the difference between 1/2-comma-flattened fifth and pure fifth.

== See also ==

Line 19:

Line 44:

[[Category:Kirnbergerismic]]

[[Category:Major kirnbergerismic]]

[[Category:Commas named after music theorists]]

[[Category:Commas named after composers]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Name = major kirnbergisma
+| Name = major kirnbergerisma
 | Color name = 23ozg2, twethozogu 2nd <br>Twethozogu comma
 | Comma = yes
 }}
-'''161/160''', the '''major kirnbergisma''', is a [[small comma|small]] [[23-limit]] [[superparticular]] comma about 10.79 [[cent]]s in size. It forms the difference between [[23/16]] and [[10/7]].
+'''161/160''', the '''major kirnbergerisma''', is a [[small comma|small]] [[23-limit]] [[superparticular]] comma about 10.79 [[cent]]s in size. It forms the difference between [[23/16]] and [[10/7]].
+== Temperaments ==
+Tempering out this comma in the 23-limit leads to the rank-8 '''major kirnbergerismic temperament'''. In the 2.5.7.23 subgroup, tempering it out leads to the rank-3 '''major kirnbergic temperament'''.
+=== Major kirnbergerismic ===
+[[Subgroup]]: full 23-limit
+[[Comma list]]: 161/160
+[[Mapping]]: <br><nowiki>[</nowiki>⟨1 0 0 0 0 0 0 0 &nbsp;5<nowiki>]</nowiki>, <br>&nbsp;⟨0 1 0 0 0 0 0 0 &nbsp;0<nowiki>]</nowiki>, <br>&nbsp;⟨0 0 1 0 0 0 0 0 &nbsp;1<nowiki>]</nowiki>, <br>&nbsp;⟨0 0 0 1 0 0 0 0 -1<nowiki>]</nowiki>, <br>&nbsp;⟨0 0 0 0 1 0 0 0 &nbsp;0<nowiki>]</nowiki>, <br>&nbsp;⟨0 0 0 0 0 1 0 0 &nbsp;0<nowiki>]</nowiki>, <br>&nbsp;⟨0 0 0 0 0 0 1 0 &nbsp;0<nowiki>]</nowiki>, <br>&nbsp;⟨0 0 0 0 0 0 0 1  &nbsp;0<nowiki>]]</nowiki>
+: Mapping generators: ~2, ~3, ~5, ~7, ~11, ~13, ~17, ~19
+[[Optimal tuning]] (POTE): ~2 = 1＼1, ~3/2 = 700.5007, ~5/4 = 385.1726, ~7/4 = 964.8038, ~11/8 = 548.1438, ~13/8 = 837.1324, ~17/16 = 101.2050, ~19/16 = 293.6154
+=== Major kirnbergic ===
+Subgroup: 2.5.7.23
+Comma list: 161/160
+Mapping: <br><nowiki>[</nowiki>⟨1 0 0 &nbsp;5<nowiki>]</nowiki>, <br>&nbsp;⟨0 1 0 &nbsp;1<nowiki>]</nowiki>, <br>&nbsp;⟨0 0 1 -1<nowiki>]]</nowiki>
+: Mapping generators: ~2, ~5, ~7
+Optimal tuning (POTE): ~2 = 1＼1, ~5/4 = 385.1726, ~7/4 = 964.8038
 == Etymology ==
-The name ''major kirnbergisma'' is contrast to the ''minor kirnbergisma'', [[162/161]], measuring about 10.72¢, which is the difference between [[23/18]] and [[9/7]]. 161/160 is larger than 162/161 by a [[23-limit]] [[unnoticeable comma]], 25921/25920. The word ''kirnbergisma'' was introduced by [[User:Xenllium|Xenllium]] in 2023, for the following reason - 161/160 or 162/161 may be found in JI-approximated version of [[Kirnberger II]] as the difference between 1/2-comma-flattened fifth and pure fifth.
+The name ''major kirnbergerisma'' is contrast to the ''minor kirnbergerisma'', [[162/161]], measuring about 10.72¢, which is the difference between [[23/18]] and [[9/7]]. 161/160 is larger than 162/161 by a [[23-limit]] [[unnoticeable comma]], [[25921/25920]]. The word ''kirnbergerisma'' was introduced by [[User:Xenllium|Xenllium]] in 2023, for the following reason - 161/160 or 162/161 may be found in JI-approximated version of [[Kirnberger II]] as the difference between 1/2-comma-flattened fifth and pure fifth.
 == See also ==
@@ Line 19: / Line 44: @@
 [[Category:Kirnbergerismic]]
+[[Category:Major kirnbergerismic]]
+[[Category:Commas named after music theorists]]
+[[Category:Commas named after composers]]