57/56: Difference between revisions
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'''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 [[9edo|9]], [[10edo|10]], [[12edo|12]], [[16edo|16]], [[21edo|21]], [[22edo|22]] and [[26edo|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 8:10:12:19 [[hendrix chord]], which has steps of [[5/4]]-[[7/5]]-4/3. [[Patent val]]s which temper out the hendrix comma include those from [[9edo|9]], [[10edo|10]], [[12edo|12]], [[16edo|16]], [[21edo|21]], [[22edo|22]] and [[26edo|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. | ||
Revision as of 17:37, 9 January 2021
| Interval information |
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 8:10:12:19 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.