245/243: Difference between revisions
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== 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 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 | ||
== Etymology == | |||
The sensamagic comma was named by [[Gene Ward Smith]] in 2010<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_88759.html ''Some unnamed 7-limit temperaments'']</ref>. Before that, it was sometimes known as the ''octarod'' comma. | |||
: ''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 | |||
== See also == | == See also == | ||
* [[Small comma]] | * [[Small comma]] | ||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
== Notes == | |||
[[Category:Sensamagic]] | [[Category:Sensamagic]] | ||
Revision as of 18:07, 13 January 2023
| 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 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
Etymology
The sensamagic comma was named by Gene Ward Smith in 2010[1]. Before that, it was sometimes known as the octarod comma.
- 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