245/243
| Ratio | 245/243 |
| Factorization | 3-5 × 5 × 72 |
| Monzo | [0 -5 1 2⟩ |
| Size in cents | 14.190522¢ |
| Name | sensamagic comma |
| Color name | zzy2, zozoyo 2nd, Zozoyo comma |
| FJS name | [math]\text{m2}^{5,7,7}[/math] |
| Special properties | reduced |
| Tenney height (log2 nd) | 15.8615 |
| Weil height (log2 max(n, d)) | 15.8733 |
| Wilson height (sopfr(nd)) | 34 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~2.81962 bits |
| Comma size | small |
| S-expression | S7 / S9 |
| open this interval in xen-calc | |
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. Tempering it out in the no-twos 7-limit leads to the non-octave temperament characteristic of 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