245/243: Difference between revisions

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{{interwiki

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{{Infobox Interval

| Name = sensamagic comma

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== 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 [[4L 5s (3/1-equivalent)|lambda scale]] found in ~~13ed3~~, the [[~~Bohlen~~-~~Pierce scale~~]].

[[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 ==

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—Gene Ward Smith

In 2025, [[Tristan Bay]] proposed ''lambda comma'' to reflect the fact that [[~~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~~).

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]]

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+{{interwiki
+| de = 245/243
+| en = 245/243
+}}
 {{Infobox Interval
 | Name = sensamagic comma
@@ Line 7: / Line 11: @@
 == 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 [[4L 5s (3/1-equivalent)|lambda scale]] found in 13ed3, the [[Bohlen-Pierce scale]].
+[[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 ==
@@ Line 18: / Line 26: @@
 —Gene Ward Smith
-In 2025, [[Tristan Bay]] proposed ''lambda comma'' to reflect the fact that [[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).
+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]]