Amity comma: Difference between revisions
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The '''amity comma''' ({{monzo| 9 -13 5 }} = '''1600000/1594323''') is an interval of 6.154 cents, the amount by which five [[10/9|minor whole tones (10/9)]] exceed the [[27/16|Pythagorean major sixth (27/16)]]. It belongs to the [[ | The '''amity comma''' ({{monzo| 9 -13 5 }} = '''1600000/1594323''') is an interval of 6.154 cents, the amount by which five [[10/9|minor whole tones (10/9)]] exceed the [[27/16|Pythagorean major sixth (27/16)]]. It belongs to the [[syntonic–chromatic equivalence continuum]] and is equal to the difference between an [[apotome]] and a stack of five [[syntonic comma]]s ((2187/2048)/(81/80)<sup>5</sup>), or in terms of classic chromatic semitone, between a classic chromatic semitone and a stack of three syntonic commas ((25/24)/(81/80)<sup>3</sup>). | ||
== Temperaments == | == Temperaments == | ||
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== Etymology == | == Etymology == | ||
The corresponding temperament was discovered first | The corresponding temperament was discovered first and named by [[Gene Ward Smith]] as ''acute minor third'' or ''amt'' in 2001–2002<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_2064.html Yahoo! Tuning Group | ''Kleismic & co'']</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_3481.html Yahoo! Tuning Group | ''32 best 5-limit linear temperaments redux'']</ref>. The temperament was renamed to ''amity'', and the comma was at one point dubbed ''amitisma'', both by Gene Ward Smith in late 2002, though it was ''amity comma'' that stuck<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5025.html Yahoo! Tuning Group | ''5-limit comma names'']</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5080.html#5114 Yahoo! Tuning Group | ''Ultimate 5-limit comma list'']</ref>. | ||
== See also == | == See also == | ||
Revision as of 06:23, 17 April 2025
| Interval information |
The amity comma ([9 -13 5⟩ = 1600000/1594323) is an interval of 6.154 cents, the amount by which five minor whole tones (10/9) exceed the Pythagorean major sixth (27/16). It belongs to the syntonic–chromatic equivalence continuum and is equal to the difference between an apotome and a stack of five syntonic commas ((2187/2048)/(81/80)5), or in terms of classic chromatic semitone, between a classic chromatic semitone and a stack of three syntonic commas ((25/24)/(81/80)3).
Temperaments
Tempering it out leads to the amity family of temperaments.
Etymology
The corresponding temperament was discovered first and named by Gene Ward Smith as acute minor third or amt in 2001–2002[1][2]. The temperament was renamed to amity, and the comma was at one point dubbed amitisma, both by Gene Ward Smith in late 2002, though it was amity comma that stuck[3][4].