Llywelynsma

Interval information

Ratio	4194304/4117715
Factorization	222 × 5-1 × 7-7
Monzo	[22 0 -1 -7⟩
Size in cents	31.90494¢
Names	llywelynsma, llywelyn comma
Color name	sr7g-3, sasepru-agu negative 3rd
FJS name	[math]\text{d}{-3}_{5,7,7,7,7,7,7,7}[/math]
Special properties	reduced, reduced subharmonic
Tenney height (log2 nd)	43.9734
Weil height (log2 max(n, d))	44
Wilson height (sopfr(nd))	98
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~4.48486 bits
Comma size	medium
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The llywelynsma or llywelyn comma (monzo: [22 0 -1 -7⟩, ratio: 4194304/4117715) is a medium 7-limit comma. It is the amount by which seven 8/7's exceed an octave plus a 5/4.

Temperaments

Tempering out this comma in the 7-limit leads to the llywelynsmic temperament, or in the 2.5.7 subgroup, the llywelyn temperament. Edos tempering it out includes 16edo and 37edo.

Etymology

This comma was named by +merlan #flirora in 2021 after Llywelyn Bren.