1288/1287

Interval information

Ratio	1288/1287
Factorization	23 × 3-2 × 7 × 11-1 × 13-1 × 23
Monzo	[3 -2 0 1 -1 -1 0 0 1⟩
Size in cents	1.344648¢
Names	triaphonisma, santisma
Color name	23o3u1uz2, twethothuluzo 2nd, Twethothuluzo comma
FJS name	[math]\displaystyle{ \text{A1}^{7,23}_{11,13} }[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	20.6607
Weil height (log2 max(n, d))	20.6618
Wilson height (sopfr(nd))	66
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~1.21508 bits
Comma size	unnoticeable
Open this interval in xen-calc

1288/1287, the triaphonisma or santisma is a 23-limit superparticular comma of about 1.34 cents. It is the amount by which a stack consisting of 14/11, 16/13 and 23/18 exceeds an octave. By tempering it out is defined the triaphonismic or santismic temperament (full 23-limit rank-8), or the triaphonic or santic temperament (2.3.7.11.13.23 subgroup rank-5).

Etymology

Santisma was named by Xenllium in 2023. It refers to 1288 Santa, the asteroid. (Why the asteroid itself was initially named Santa is unknown.) However, triaphonisma was attested much earlier.

See also

• Unnoticeable comma
• List of superparticular intervals
• Triaphonismic chords