1701/1700: Difference between revisions

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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]])

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* ([[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:

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* ([[2058/2057]])([[9801/9800]])

* ([[1716/1715]])([[194481/194480]])

~~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.~~

== Temperaments ==

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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]])
@@ Line 14: / Line 19: @@
 * ([[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:
@@ Line 22: / Line 25: @@
 * ([[2058/2057]])([[9801/9800]])
 * ([[1716/1715]])([[194481/194480]])
-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.
 == Temperaments ==