120/119: Difference between revisions
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'''120/119''', the '''lynchisma''' is | '''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]]. | ||
== Temperaments == | == 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'''. Since 120/119 factors as [[225/224]] | [[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. | ||
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]] temperaments that includes prime 17, though at the cost of accuracy. | |||
=== Lynchismic === | === Lynchismic === | ||
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== See also == | == See also == | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
[[Category:Commas named after composers]] | [[Category:Commas named after composers]] | ||
[[Category:Commas named after music theorists]] | [[Category:Commas named after music theorists]] | ||
Revision as of 10:38, 27 January 2026
| Interval information |
Suruyo comma
reduced
S18⋅S19⋅S20
120/119, the lynchisma, is a small 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.
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 calls this the minor tetrad, and so equating it with the inverse of the major tetrad is quite useful.
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 temperaments that includes prime 17, though at the cost of accuracy.
Lynchismic
Subgroup: 2.3.5.7.11.13.17
| [⟨ | 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
- 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: [⟨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: 10, 12, 19, 22, 26, 31, 41, 53