57/56: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = hendrix comma | | Name = hendrix comma | ||
| Color name = | | Color name = 19or1, noru 1sn,<br>Noru comma | ||
| Comma = yes | |||
| | |||
}} | }} | ||
'''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: | '''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|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 == | == See also == | ||
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* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
[[Category:Hendrix]] | [[Category:Hendrix]] | ||
[[Category:Commas named after composers]] | |||
Latest revision as of 13:06, 31 March 2026
| Interval information |
Noru comma
reduced
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 vals which temper out the hendrix comma include those from 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, 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
Subgroup-val mapping: [⟨1 0 0 3], ⟨0 1 0 -1], ⟨0 0 1 1]]
- mapping generators: ~2, ~3, ~7
- WE: ~2 = 1202.4345 ¢, ~3/2 = 697.4314 ¢, ~7/4 = 970.3487 ¢
- CWE: ~2 = 1200.0000 ¢, ~3/2 = 697.3981 ¢, ~7/4 = 972.1990 ¢
Optimal ET sequence: 5, 9, 12, 14, 17, 26, 31h
Badness (Sintel): 0.155