245/243: Difference between revisions

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{{interwiki

| de = 245/243

| en = 245/243

}}

{{Infobox Interval

~~| Ratio = 245/243~~

| Name = sensamagic comma

~~| Monzo = 0 -5 1 2~~

| Color name = zzy2, zozoyo 2nd,<br>Zozoyo comma

~~| Cents = 14.19052~~

| Comma = yes

| Name = ~~Sensamagic~~ comma

| Color name = zzy2, zozoyo 2nd

| ~~Sound~~ =

}}

'''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~~ [[7-limit~~]] ratio of 14.2 cents. It is amount by which two septimal major thirds [[9/7]] fall short of a major sixth [[5/3]], or the difference between [[28/27]] and [[36/35]]. Tempering it out~~ leads to [[sensamagic ~~family~~]], 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.

== 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 [[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 ==

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>

—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 ==

* [[Gallery of just intervals]]

* [[Comma]]

== Notes ==

* [[Gallery of just intervals]]

~~[[Category:7-limit]]~~

~~[[Category:Interval]]~~

~~[[Category:Ratio]]~~

~~[[Category:Comma]]~~

[[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
-| Ratio = 245/243
+| Name = sensamagic comma
-| Monzo = 0 -5 1 2
+| Color name = zzy2, zozoyo 2nd,<br>Zozoyo comma
-| Cents = 14.19052
+| Comma = yes
-| Name = Sensamagic comma
-| Color name = zzy2, zozoyo 2nd
-| Sound =
 }}
+'''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 [[7-limit]] ratio of 14.2 cents. It is amount by which two septimal major thirds [[9/7]] fall short of a major sixth [[5/3]], or the difference between [[28/27]] and [[36/35]]. Tempering it out leads to [[sensamagic family]], 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.
+== 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 [[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 ==
+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
+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 ==
+* [[Gallery of just intervals]]
-* [[Comma]]
+== Notes ==
-* [[Gallery of just intervals]]
+<references />
-[[Category:7-limit]]
-[[Category:Interval]]
-[[Category:Ratio]]
-[[Category:Comma]]
 [[Category:Sensamagic]]
+[[Category:Bohlen–Pierce]]
+[[Category:Commas named by combining multiple temperament names]]