120/119: Difference between revisions

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{{Infobox Interval

~~| Ratio = 120/119~~

~~| Monzo = 3 1 1 -1 0 0 -1~~

~~| Cents = 14.48740~~

| Name = lynchisma

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

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

~~| FJS name = d-257,17~~<~~/sub~~>

| Comma = yes

| ~~Sound~~ =

}}

'''120/119''', the '''lynchisma''', is a [[small comma|small]] [[17-limit]] [[superparticular]] [[comma]] of about 14.49 [[cent]]s. It is the difference between [[20/17]] and [[7/6]], [[17/10]] and [[12/7]], or [[30/17]] and [[7/4]].

'''~~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.

== 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. In either case, it allows you to assign [[10:12:15:17]] as the inverse of [[4:5:6:7]], an otonal chord that 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~~]].

Since 120/119 factors as ([[225/224]])⋅([[256/255]]), it would make sense to temper them both out, so lynchic can be further tempered to a simple extension of [[marvel]] that adds prime 17 known as [[char]], though it loses accuracy when compared to marvel.

[[~~Category~~:17-~~limit~~]]

=== Lynchic ===

[[Category:~~Small commas~~]]

[[Subgroup]]: 2.3.5.7.17

[[Category:~~Superparticular~~]]

{{Mapping|legend=2| 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]]s:

* [[WE]]: ~2 = 1198.9483{{c}}, ~3/2 = 702.1229{{c}}, ~5/4 = 386.5249{{c}}, ~7/4 = 973.6693{{c}}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.8985{{c}}, ~5/4 = 385.5601{{c}}, ~7/4 = 973.5597{{c}}

{{Optimal ET sequence|legend=1| 10, 12, 19, 22, 27g, 31, 41, 53, 198ddggg }}

[[Badness]] (Sintel): 0.220

=== 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]]s:

* [[WE]]: ~2 = 1198.9483{{c}}, ~3/2 = 702.1229{{c}}, ~5/4 = 386.5249{{c}}, ~7/4 = 973.6693{{c}}, ~11/8 = 554.4584{{c}}, ~13/8 = 843.6671{{c}}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.8985{{c}}, ~5/4 = 385.5601{{c}}, ~7/4 = 973.5597{{c}}, ~11/8 = 553.3440{{c}}, ~13/8 = 842.6949{{c}}

{{Optimal ET sequence|legend=1| 19, 22, 26, 27eg, 31, 41, 49fg, 53, 65d, 84g, 92defg, 106g, 123dfgg, 128dg, 137gg, 145dgg, 171dgg }}

[[Badness]] (Sintel): 0.603

== See also ==

* [[List of superparticular intervals]]

[[Category:Lynchismic]]

[[Category:Commas named after composers]]

[[Category:Commas named after music theorists]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Ratio = 120/119
-| Monzo = 3 1 1 -1 0 0 -1
-| Cents = 14.48740
 | Name = lynchisma
-| Color name = suruyo negative 2nd, 17ury-2
+| Color name = 17ury-2, suruyo negative 2nd, <br>Suruyo comma
-| FJS name = d-2<sup>5</sup><sub>7,17</sub>
+| Comma = yes
-| Sound =
 }}
+'''120/119''', the '''lynchisma''', is a [[small comma|small]] [[17-limit]] [[superparticular]] [[comma]] of about 14.49 [[cent]]s. It is the difference between [[20/17]] and [[7/6]], [[17/10]] and [[12/7]], or [[30/17]] and [[7/4]].
-'''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.
+== 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. In either case, it allows you to assign [[10:12:15:17]] as the inverse of [[4:5:6:7]], an otonal chord that 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]].
+Since 120/119 factors as ([[225/224]])⋅([[256/255]]), it would make sense to temper them both out, so lynchic can be further tempered to a simple extension of [[marvel]] that adds prime 17 known as [[char]], though it loses accuracy when compared to marvel.
-[[Category:17-limit]]
+=== Lynchic ===
-[[Category:Small commas]]
+[[Subgroup]]: 2.3.5.7.17
-[[Category:Superparticular]]
+{{Mapping|legend=2| 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]]s:
+* [[WE]]: ~2 = 1198.9483{{c}}, ~3/2 = 702.1229{{c}}, ~5/4 = 386.5249{{c}}, ~7/4 = 973.6693{{c}}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.8985{{c}}, ~5/4 = 385.5601{{c}}, ~7/4 = 973.5597{{c}}
+{{Optimal ET sequence|legend=1| 10, 12, 19, 22, 27g, 31, 41, 53, 198ddggg }}
+[[Badness]] (Sintel): 0.220
+=== 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]]s:
+* [[WE]]: ~2 = 1198.9483{{c}}, ~3/2 = 702.1229{{c}}, ~5/4 = 386.5249{{c}}, ~7/4 = 973.6693{{c}}, ~11/8 = 554.4584{{c}}, ~13/8 = 843.6671{{c}}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.8985{{c}}, ~5/4 = 385.5601{{c}}, ~7/4 = 973.5597{{c}}, ~11/8 = 553.3440{{c}}, ~13/8 = 842.6949{{c}}
+{{Optimal ET sequence|legend=1| 19, 22, 26, 27eg, 31, 41, 49fg, 53, 65d, 84g, 92defg, 106g, 123dfgg, 128dg, 137gg, 145dgg, 171dgg }}
+[[Badness]] (Sintel): 0.603
+== See also ==
+* [[List of superparticular intervals]]
+[[Category:Lynchismic]]
+[[Category:Commas named after composers]]
+[[Category:Commas named after music theorists]]