245/243: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = sensamagic comma | | Name = sensamagic comma,<br>lambda comma | ||
| Color name = zzy2, zozoyo 2nd,<br>Zozoyo comma | | Color name = zzy2, zozoyo 2nd,<br>Zozoyo comma | ||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
'''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''' or '''lambda 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 it out 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]]. 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. Tempering it out in the no-twos 7-limit leads to the non-octave | Tempering it out 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]]. 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. Tempering it out in the no-twos 7-limit leads to the non-octave [[4L 5s (3/1-equivalent)|lambda scale]] found in 13ed3, the [[Bohlen-Pierce scale]]. | ||
== Etymology == | == Etymology == | ||
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—Gene Ward Smith | —Gene Ward Smith | ||
The other name, ''lambda comma'', was given by [[Tristan Bay]] to reflect the fact that [[EDO|edo]]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 edo). | |||
== See also == | == See also == | ||
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== Notes == | == Notes == | ||
< | <references /> | ||
[[Category:Sensamagic]] | [[Category:Sensamagic]] | ||
[[Category:Bohlen–Pierce]] | [[Category:Bohlen–Pierce]] | ||
[[Category:Commas named by combining multiple temperament names]] | [[Category:Commas named by combining multiple temperament names]] | ||
Revision as of 18:59, 25 May 2025
| Interval information |
lambda comma
Zozoyo comma
245/243, the sensamagic comma or lambda 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 it out 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. 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. Tempering it out in the no-twos 7-limit leads to the non-octave lambda scale found in 13ed3, the Bohlen-Pierce scale.
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
The other name, lambda comma, was given by Tristan Bay to reflect the fact that edos which temper this comma out contain the aforementioned lambda scale (and is accurately tuned in the corresponding temperament, relative to the size of the edo).