57/56: Difference between revisions

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{{Infobox Interval

~~| JI glyph =~~

~~| Ratio = 57/56~~

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

~~| Cents = 30.64211~~

| Name = hendrix comma

| Color name =

| Color name = 19or1, noru 1sn,<br>Noru comma

~~| FJS name = P1<sup>19</sup><sub>7~~<~~/sub~~>

| Comma = yes

| ~~Sound~~ =

}}

'''57/56''' is a [[superparticular]] interval of about 30.6¢ which makes the difference between [[4/3]] (about 498¢) and [[19/14]] (about 528.7¢) in [[19-limit]] [[just intonation]]; it is also the difference between [[19/16]] and [[7/6]]. It is also called the '''hendrix comma''', since by tempering it out, one can build an 8:10:12:19 [[hendrix chord]], which has steps of [[5/4]]-[[7/5]]-4/3. [[Patent val]]s which temper out the hendrix comma include those from {{EDOs| 9, 10, 12, 16, 21, 22 and 26 }} edo.

'''57/56''' is a [[superparticular]] interval of about 30.6¢ which makes the difference between [[4/3]] (about 498¢) and [[19/14]] (about 528.7¢) in [[19-limit]] [[just intonation]]; it is also the difference between [[19/16]] and [[7/6]]. It is also called the '''hendrix comma''', since by tempering it out, one can build an 8:10:14:19 [[hendrix chord]], which has steps of [[5/4]]-[[7/5]]-4/3. [[Patent val]]s which temper out the hendrix comma include those from {{EDOs| 9, 10, 12, 16, 21, 22 and 26 }} edo.

57/56 is a comma of the 2.3.7.19 subgroup, and on that subgroup, patent vals tempering it out include those from 9, 12, 14, 17 and 26. The comma defines a rank three temperament on this subgroup.

57/56 is a comma of the 2.3.7.19 subgroup, and on that subgroup, patent vals tempering it out include those from 9, 12, 14, 17 and 26. The comma defines a rank three temperament on this subgroup, called [[hendrix]]. You can also temper it out in a rank-2 temperament in 2.3.19/7, called surprise.

== Temperaments ==

=== Hendrix ===

This is the [[rank-3]] temperament tempering out the hendrix comma, 57/56. This is simply the most sensible name for this temperament.

[[Subgroup]]: 2.3.7.19

[[Comma list]]: 57/56

: mapping generators: ~2, ~3, ~7

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1202.4345{{c}}, ~3/2 = 697.4314{{c}}, ~7/4 = 970.3487{{c}}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 697.3981{{c}}, ~7/4 = 972.1990{{c}}

[[Badness]] (Sintel): 0.155

== See also ==

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* [[List of superparticular intervals]]

~~[[Category:19-limit]]~~

~~[[Category:Small comma]]~~

~~[[Category:Medium comma]]~~

~~[[Category:Superparticular]]~~

[[Category:Hendrix]]

[[Category:Commas named after composers]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| JI glyph =
-| Ratio = 57/56
-| Monzo = -3 1 0 -1 0 0 0 1
-| Cents = 30.64211
 | Name = hendrix comma
-| Color name =
+| Color name = 19or1, noru 1sn,<br>Noru comma
-| FJS name = P1<sup>19</sup><sub>7</sub>
+| Comma = yes
-| Sound =
 }}
-'''57/56''' is a [[superparticular]] interval of about 30.6¢ which makes the difference between [[4/3]] (about 498¢) and [[19/14]] (about 528.7¢) in [[19-limit]] [[just intonation]]; it is also the difference between [[19/16]] and [[7/6]]. It is also called the '''hendrix comma''', since by tempering it out, one can build an 8:10:12:19 [[hendrix chord]], which has steps of [[5/4]]-[[7/5]]-4/3. [[Patent val]]s which temper out the hendrix comma include those from {{EDOs| 9, 10, 12, 16, 21, 22 and 26 }} edo.
+'''57/56''' is a [[superparticular]] interval of about 30.6¢ which makes the difference between [[4/3]] (about 498¢) and [[19/14]] (about 528.7¢) in [[19-limit]] [[just intonation]]; it is also the difference between [[19/16]] and [[7/6]]. It is also called the '''hendrix comma''', since by tempering it out, one can build an 8:10:14:19 [[hendrix chord]], which has steps of [[5/4]]-[[7/5]]-4/3. [[Patent val]]s which temper out the hendrix comma include those from {{EDOs| 9, 10, 12, 16, 21, 22 and 26 }} edo.
-/56 is a comma of the 2.3.7.19 subgroup, and on that subgroup, patent vals tempering it out include those from 9, 12, 14, 17 and 26. The comma defines a rank three temperament on this subgroup.
+/56 is a comma of the 2.3.7.19 subgroup, and on that subgroup, patent vals tempering it out include those from 9, 12, 14, 17 and 26. The comma defines a rank three temperament on this subgroup, called [[hendrix]]. You can also temper it out in a rank-2 temperament in 2.3.19/7, called surprise.
+== Temperaments ==
+=== Hendrix ===
+This is the [[rank-3]] temperament tempering out the hendrix comma, 57/56. This is simply the most sensible name for this temperament.
+[[Subgroup]]: 2.3.7.19
+[[Comma list]]: 57/56
+{{Mapping|legend=2| 1 0 0 3 | 0 1 0 -1 | 0 0 1 1 }}
+: mapping generators: ~2, ~3, ~7
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1202.4345{{c}}, ~3/2 = 697.4314{{c}}, ~7/4 = 970.3487{{c}}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 697.3981{{c}}, ~7/4 = 972.1990{{c}}
+{{Optimal ET sequence|legend=1| 5, 9, 12, 14, 17, 26, 31h }}
+[[Badness]] (Sintel): 0.155
 == See also ==
@@ Line 19: / Line 33: @@
 * [[List of superparticular intervals]]
-[[Category:19-limit]]
-[[Category:Small comma]]
-[[Category:Medium comma]]
-[[Category:Superparticular]]
 [[Category:Hendrix]]
+[[Category:Commas named after composers]]