1701/1700

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 interval that 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".

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 norm (log2 nd)	21.4635
Weil norm (log2 max(n, d))	21.4643
Wilson norm (sopfr(nd))	53
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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.

See also

• Unnoticeable comma
• List of superparticular intervals