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'''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 [[21/17|septendecimal submajor third (21/17)]] by a stack of two [[10/9]] intervals, therefore making it comparable with the [[325/324|marveltwin (325/324)]]. It is, in fact, the difference between the following superparticular pairs: | '''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 [[21/17|septendecimal submajor third (21/17)]] by a stack of two [[10/9]] intervals, therefore making it comparable with the [[325/324|marveltwin (325/324)]]. It is, in fact, the difference between the tannisma and the marveltwin. See [[#Commatic relations]] below. 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 [[tina]]s. | |||
== Commatic relations == | |||
This comma is the difference between the following superparticular pairs: | |||
* ([[81/80]])/([[85/84]]) | * ([[81/80]])/([[85/84]]) | ||
| Line 14: | Line 19: | ||
* ([[1089/1088]])/([[3025/3024]]) | * ([[1089/1088]])/([[3025/3024]]) | ||
* ([[1225/1224]])/([[4375/4374]]) | * ([[1225/1224]])/([[4375/4374]]) | ||
It factors into the following superparticular pairs: | It factors into the following superparticular pairs: | ||
| Line 22: | Line 25: | ||
* ([[2058/2057]])([[9801/9800]]) | * ([[2058/2057]])([[9801/9800]]) | ||
* ([[1716/1715]])([[194481/194480]]) | * ([[1716/1715]])([[194481/194480]]) | ||
== Temperaments == | == Temperaments == | ||
Revision as of 03:22, 13 November 2022
| 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 tannisma and the marveltwin. See #Commatic relations below. 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.
Commatic relations
This comma is 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)
It factors into the following superparticular pairs:
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.