1701/1700

Interval information

Ratio	1701/1700
Factorization	2-2 × 35 × 5-2 × 7 × 17-1
Monzo	[-2 5 -2 1 0 0 -1⟩
Size in cents	1.018074¢
Names	palingenesis comma, palingenesia
FJS name	[math]\displaystyle{ \text{P1}^{7}_{5,5,17} }[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	21.4635
Weil height (log2 max(n, d))	21.4643
Wilson height (sopfr(nd))	53
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1701/1700, the palingenesis comma or palingenesia, is a 17-limit unnoticeable comma with a size of roughly 1.02 cents. It arises as the amount by which a stack consisting of 27/16 and 28/25 exceeds 17/9, and the the amount by which 85/84 falls short of 81/80. When tempered out in a linearly independent fashion, the resulting temperaments are called "palingenesis temperaments", and are characterized by the presence of essentially tempered chords called "palingenic chords".

This comma's names ultimately come from the Ancient Greek word "palingenesía" (meaning "rebith", "regeneration" or "renaissance"), a fitting name since people often hope for a new start after each year. The name is also appropriate in light of how certain essentially tempered chords generated by this comma are evocative of the kinds of chords heard in 24edo, where many microtonalists get their first start, despite 24edo itself not tempering out this comma.

See also

• Unnoticeable comma
• List of superparticular intervals