245/243: Difference between revisions

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{{Infobox Interval

| 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]].

== 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 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 ==

~~The sensamagic~~ comma was named by [[Gene Ward Smith]] in ~~2010. It is the concatenation~~ of [[~~sensi~~]] and [[~~magic~~]]. ~~Before that~~, it was ~~sometimes known as the~~ ''~~octarod~~'' ~~comma~~<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_88759.html ''Some unnamed 7-limit temperaments'']</ref>.

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>.

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>

: ''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 [[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 ==

* [[Small comma]]

* [[Gallery of just intervals]]

== Notes ==

[[Category:Sensamagic]]

[[Category:Bohlen–Pierce]]

[[Category:Commas named by combining multiple temperament names]]

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+{{interwiki
+| de = 245/243
+| en = 245/243
+}}
 {{Infobox Interval
 | Name = sensamagic comma
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 | 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]].
 == 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 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 ==
-The sensamagic comma was named by [[Gene Ward Smith]] in 2010. It is the concatenation of [[sensi]] and [[magic]]. Before that, it was sometimes known as the ''octarod'' comma<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_88759.html ''Some unnamed 7-limit temperaments'']</ref>.
+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>
-: ''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 [[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 ==
-* [[Small comma]]
 * [[Gallery of just intervals]]
 == Notes ==
+<references />
 [[Category:Sensamagic]]
+[[Category:Bohlen–Pierce]]
+[[Category:Commas named by combining multiple temperament names]]