1701/1700
| Interval information |
palingenesis comma,
palingenesma
reduced
1701/1700, the palingenetic comma, also known as the palingenesis comma, or palingenesma, is a 17-limit unnoticeable comma with a size of roughly 1.02 cents. It identifies the septendecimal submajor third (21/17) by a stack of two 10/9 intervals, therefore making it comparable with the marveltwin (325/324). It is, in fact, the difference between the following superparticular pairs:
- (81/80)/(85/84)
- (126/125)/(136/135)
- (273/272)/(325/324)
- (351/350)/(442/441)
- (441/440)/(595/594)
- (936/935)/(2080/2079)
- (1089/1088)/(3025/3024)
- (1225/1224)/(4375/4374)
where the tannisma (273/272) and the marveltwin (325/324) are particularly notable.
It factors into the following superparticular pairs:
It also arises as the amount by which a stack consisting of 27/16 and 28/25 exceeds 17/9.
In Sagittal notation, it is the default comma represented by seven tinas.
Temperaments
When tempered out in a linearly independent fashion, the resulting temperaments are called palingenetic temperaments, and are characterized by the presence of essentially tempered chords called palingenetic chords in the 27-odd-limit.
Etymology
This comma's names ultimately come from the Ancient Greek word "palingenesía" (meaning "rebirth", "regeneration" or "renaissance"[1]), 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 12edo, which, oddly enough, actually tempers out this comma.