120/119: Difference between revisions

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{{Infobox Interval

| Name = lynchisma

| Color name = suruyo negative 2nd, ~~17ury-2~~

| Color name = 17ury-2, suruyo negative 2nd, Suruyo comma

| Comma = yes

}}

'''120/119''', the '''lynchisma''' is the [[17-limit]] [[superparticular]] comma of about 14.49 cents. It is the difference between [[20/17]] and [[7/6]], [[17/10]] and [[12/7]], or [[30/17]] and [[7/4]]. Tempering this comma allows you to assign 10:12:15:17 as the inverse of 4:5:6:7, a much simpler version of what would otherwise be 70:84:105:120. [[William Lynch's ~~Thoughts~~ on ~~Septimal Harmony~~ and ~~22 EDO~~|William Lynch]] calls this the minor tetrad, and so equating it with the inverse of the major tetrad is quite useful.

'''120/119''', the '''lynchisma''' is the [[17-limit]] [[superparticular]] comma of about 14.49 cents. It is the difference between [[20/17]] and [[7/6]], [[17/10]] and [[12/7]], or [[30/17]] and [[7/4]]. Tempering this comma allows you to assign 10:12:15:17 as the inverse of 4:5:6:7, a much simpler version of what would otherwise be 70:84:105:120. [[William Lynch's thoughts on septimal harmony and 22edo|William Lynch]] calls this the minor tetrad, and so equating it with the inverse of the major tetrad is quite useful.

By tempering it out ~~is defined~~ the '''~~lynchismic~~ temperament''', ~~which enables the~~ [[~~lynchismic chords~~]]. ~~EDOs supporting this temperament includes~~ {{~~EDOs~~|10, 12, 19, 22, 26, 31, 41}} ~~and~~ [[~~53edo|53~~]].

== Temperaments ==

Tempering out this comma in the 17-limit leads to the rank-6 '''lynchismic temperament'''. In the 2.3.5.7.17 subgroup, tempering it out results in the rank-4 '''lynchic temperament'''.

=== Lynchismic ===

[[Subgroup]]: 2.3.5.7.11.13.17

[[Mapping]]:

{| class="right-all"

|-

| [⟨ || 1 || 0 || 0 || 0 || 0 || 0 || 3 || ],

|-

| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || 1 || ],

|-

| ⟨ || 0 || 0 || 1 || 0 || 0 || 0 || 1 || ],

|-

| ⟨ || 0 || 0 || 0 || 1 || 0 || 0 || -1 || ],

|-

| ⟨ || 0 || 0 || 0 || 0 || 1 || 0 || 0 || ],

|-

| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ]]

|}

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

[[Optimal tuning]]:

* [[TE]]: ~2 = 1198.953, ~3 = 1901.078, ~5 = 2784.431, ~7 = 3371.578

* [[CTE]]: ~2 = 1200.000 (1\1), ~3/2 = 700.835, ~5/4 = 383.910, ~7/4 = 972.340

=== Lynchic ===

Subgroup: 2.3.5.7.17

Mapping: {{mapping| 1 0 0 0 3 | 0 1 0 0 1 | 0 0 1 0 1 | 0 0 0 1 -1 }}

: Mapping generators: ~2, ~3, ~5, ~7

Optimal tuning (CTE): ~2 = 1200.000 (1\1), ~3/2 = 700.835, ~5/4 = 383.910, ~7/4 = 972.340

{{Optimal ET sequence|legend=0| 10, 12, 19, 22, 26, 31, 41, 53 }}

== See also ==

* [[Small comma]]

* [[List of superparticular intervals]]

[[Category:Commas named after composers]]

[[Category:Commas named after music theorists]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
 | Name = lynchisma
-| Color name = suruyo negative 2nd, 17ury-2
+| Color name = 17ury-2, suruyo negative 2nd, <br>Suruyo comma
 | Comma = yes
 }}
-'''120/119''', the '''lynchisma''' is the [[17-limit]] [[superparticular]] comma of about 14.49 cents. It is the difference between [[20/17]] and [[7/6]], [[17/10]] and [[12/7]], or [[30/17]] and [[7/4]]. Tempering this comma allows you to assign 10:12:15:17 as the inverse of 4:5:6:7, a much simpler version of what would otherwise be 70:84:105:120. [[William Lynch's Thoughts on Septimal Harmony and 22 EDO|William Lynch]] calls this the minor tetrad, and so equating it with the inverse of the major tetrad is quite useful.
+'''120/119''', the '''lynchisma''' is the [[17-limit]] [[superparticular]] comma of about 14.49 cents. It is the difference between [[20/17]] and [[7/6]], [[17/10]] and [[12/7]], or [[30/17]] and [[7/4]]. Tempering this comma allows you to assign 10:12:15:17 as the inverse of 4:5:6:7, a much simpler version of what would otherwise be 70:84:105:120. [[William Lynch's thoughts on septimal harmony and 22edo|William Lynch]] calls this the minor tetrad, and so equating it with the inverse of the major tetrad is quite useful.
-By tempering it out is defined the '''lynchismic temperament''', which enables the [[lynchismic chords]]. EDOs supporting this temperament includes {{EDOs|10, 12, 19, 22, 26, 31, 41}} and [[53edo|53]].
+== Temperaments ==
+Tempering out this comma in the 17-limit leads to the rank-6 '''lynchismic temperament'''. In the 2.3.5.7.17 subgroup, tempering it out results in the rank-4 '''lynchic temperament'''.
+=== Lynchismic ===
+[[Subgroup]]: 2.3.5.7.11.13.17
+[[Mapping]]: <br>
+{| class="right-all"
+|-
+| [⟨ || 1 || 0 || 0 || 0 || 0 || 0 || 3 || ],
+|-
+| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || 1 || ],
+|-
+| ⟨ || 0 || 0 || 1 || 0 || 0 || 0 || 1 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 1 || 0 || 0 || -1 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 0 || 1 || 0 || 0 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ]]
+|}
+: Mapping generators: ~2, ~3, ~5, ~7, ~11, ~13
+[[Optimal tuning]]:
+* [[TE]]: ~2 = 1198.953, ~3 = 1901.078, ~5 = 2784.431, ~7 = 3371.578
+* [[CTE]]: ~2 = 1200.000 (1<span style="font-family:'Arial', sans-serif">\</span>1), ~3/2 = 700.835, ~5/4 = 383.910, ~7/4 = 972.340
+=== Lynchic ===
+Subgroup: 2.3.5.7.17
+Mapping: {{mapping| 1 0 0 0 3 | 0 1 0 0 1 | 0 0 1 0 1 | 0 0 0 1 -1 }}
+: Mapping generators: ~2, ~3, ~5, ~7
+Optimal tuning (CTE): ~2 = 1200.000 (1<span style="font-family:'Arial', sans-serif">\</span>1), ~3/2 = 700.835, ~5/4 = 383.910, ~7/4 = 972.340
+{{Optimal ET sequence|legend=0| 10, 12, 19, 22, 26, 31, 41, 53 }}
+== See also ==
+* [[Small comma]]
+* [[List of superparticular intervals]]
+[[Category:Commas named after composers]]
+[[Category:Commas named after music theorists]]