245/243: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = sensamagic comma | | Name = sensamagic comma | ||
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'''245/243''', the '''sensamagic comma''', is a [[small comma|small]] [[7-limit]] [[comma]] measuring 14.2 [[cent]]s. It is the amount by which two septimal major thirds ([[9/7]]) fall short of a classic major sixth ([[5/3]]), or the difference between [[28/27]] and [[36/35]]. | '''245/243''', the '''sensamagic comma''', is a [[small comma|small]] [[7-limit]] [[comma]] measuring 14.2 [[cent]]s. It is the amount by which two septimal major thirds ([[9/7]]) fall short of a classic major sixth ([[5/3]]), or the difference between [[28/27]] and [[36/35]]. | ||
== Temperaments == | == Temperaments == | ||
Tempering | [[Tempering out]] this comma alone in the 7-limit leads to the [[sensamagic]] temperament, where 5/3 is split into two equal parts, each representing 9/7~[[35/27]], and may be extended to represent higher-limit ratios like [[13/10]], [[22/17]], etc. It enables [[sensamagic chords]]. | ||
Tempering it out in the [[3.5.7 subgroup]] leads to the non-octave [[BPS]] temperament, which features a [[4L 5s (3/1-equivalent)|lambda scale]] as is found in [[13edt]], the [[Bohlen–Pierce scale]]. | |||
See [[Sensamagic family]] for the rank-3 temperament family where it is tempered out. See [[Sensamagic clan]] for the rank-2 clan where it is tempered out. | |||
== Etymology == | == Etymology == | ||
This comma was first named as ''octarod'' by [[Gene Ward Smith]] in 2005 as a contraction of ''[[octacot]]'' and ''[[rodan]]''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_12900.html Yahoo! Tuning Group | ''Seven limit comma names from pairs of temperament names'']</ref>, and was renamed to ''sensamagic'' in 2010 as a concatenation of [[sensi]] and [[magic]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_88759.html Yahoo! Tuning Group | ''Some unnamed 7-limit temperaments'']</ref>. | |||
<blockquote> | |||
Here's a thought: 245/243 tells us that two 9/7['s] make up a 5/3. Hence, the temperaments which most exploit this and for which the comma is most characteristic are the ones where 9/7 has a low complexity. And this means sensi (complexity 1) and magic (complexity 2). So my proposal "sensamagic" is the way to go by this reasoning, which strikes me as pretty strong. | |||
</blockquote> | |||
—Gene Ward Smith | —Gene Ward Smith | ||
In 2025, [[Tristan Bay]] proposed ''lambda comma'' to reflect the fact that [[edt]]s which temper this comma out contain the aforementioned lambda scale (and is accurately tuned in the corresponding temperament, relative to the size of the edt). | |||
== See also == | == See also == | ||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
== Notes == | == Notes == | ||
<references /> | |||
[[Category:Sensamagic]] | [[Category:Sensamagic]] | ||
[[Category:Bohlen–Pierce]] | |||
[[Category:Commas named by combining multiple temperament names]] | |||
Latest revision as of 11:48, 16 November 2025
| Interval information |
Zozoyo comma
245/243, the sensamagic comma, is a small 7-limit comma measuring 14.2 cents. It is the amount by which two septimal major thirds (9/7) fall short of a classic major sixth (5/3), or the difference between 28/27 and 36/35.
Temperaments
Tempering out this comma alone in the 7-limit leads to the sensamagic temperament, where 5/3 is split into two equal parts, each representing 9/7~35/27, and may be extended to represent higher-limit ratios like 13/10, 22/17, etc. It enables sensamagic chords.
Tempering it out in the 3.5.7 subgroup leads to the non-octave BPS temperament, which features a lambda scale as is found in 13edt, the Bohlen–Pierce scale.
See Sensamagic family for the rank-3 temperament family where it is tempered out. See Sensamagic clan for the rank-2 clan where it is tempered out.
Etymology
This comma was first named as octarod by Gene Ward Smith in 2005 as a contraction of octacot and rodan[1], and was renamed to sensamagic in 2010 as a concatenation of sensi and magic[2].
Here's a thought: 245/243 tells us that two 9/7['s] make up a 5/3. Hence, the temperaments which most exploit this and for which the comma is most characteristic are the ones where 9/7 has a low complexity. And this means sensi (complexity 1) and magic (complexity 2). So my proposal "sensamagic" is the way to go by this reasoning, which strikes me as pretty strong.
—Gene Ward Smith
In 2025, Tristan Bay proposed lambda comma to reflect the fact that edts which temper this comma out contain the aforementioned lambda scale (and is accurately tuned in the corresponding temperament, relative to the size of the edt).