1701/1700: Difference between revisions

| Name = palingenetic comma, palingenesis, palingenesma

'''1701/1700''', the '''palingenetic comma''', also known as the '''palingenesis''', 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.

This comma is the difference between the following superparticular pairs:

 

* [[273/272]] and [[325/324]]

* [[2601/2600]] and [[4914/4913]]

* [[2401/2400]] and [[5832/5831]] *

* [[2058/2057]] and [[9801/9800]]

* [[1716/1715]] and [[194481/194480]]

<nowiki>*</nowiki> both of these commas are also within the 2.3.5.7.17 subgroup.

When tempered out in the full 17-limit, the resulting temperament is called the '''palingenetic temperament''', or in the 2.3.5.7.17 subgroup, the '''palingenetian temperament'''. Both are characterized by the presence of [[Dyadic chord|essentially tempered chord]]s called [[palingenetic chords]] in the [[21-odd-limit|21-]] and [[27-odd-limit]].

This comma was named by [[Aura]] in 2020. Its names ultimately come from the Ancient Greek word [[Wiktionary: palingenesis #English|''palingenesía'']] ("rebirth", "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 [[12edo]], which, oddly enough, actually tempers out this comma.