1701/1700: Difference between revisions

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'''1701/1700''', the '''palingenesis comma''', also known as the '''palingenetic 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 [[273/272~~|tannisma~~]] ~~and the marveltwin. It also arises as the amount by which a stack consisting of~~ [[27/16]] ~~and~~ [[28/25]] ~~exceeds~~ [[17/9]]~~, and the the amount by which~~ [[85/84]] ~~falls short of~~ [[81/80]]~~. When tempered out in a linearly independent fashion, the resulting temperaments are called "'''palingenetic temperaments'''", and are characterized by the presence of~~ [[~~Dyadic chord|essentially tempered chord~~]]~~s called "~~[[~~palingenetic chords~~]]~~" in the~~ [[~~27-odd-limit~~]].

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

* ([[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:

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

~~This comma's names ultimately come from~~ the ~~Ancient Greek word "palingenesía" (meaning "rebirth", "regeneration" or "renaissance"<ref>~~[[~~Wiktionary: palingenesis #English~~]]</ref>), 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~~.

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 ==

When tempered out in a linearly independent fashion, the resulting temperaments are called '''palingenetic temperaments''', and are characterized by the presence of [[Dyadic chord|essentially tempered chord]]s 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"<ref>[[Wiktionary: palingenesis #English]]</ref>), 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.

== See also ==

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 }}
-'''1701/1700''', the '''palingenesis comma''', also known as the '''palingenetic 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 [[273/272|tannisma]] and the marveltwin.  It also arises as the amount by which a stack consisting of [[27/16]] and [[28/25]] exceeds [[17/9]], and the the amount by which [[85/84]] falls short of [[81/80]].  When tempered out in a linearly independent fashion, the resulting temperaments are called "'''palingenetic temperaments'''", and are characterized by the presence of [[Dyadic chord|essentially tempered chord]]s called "[[palingenetic chords]]" in the [[27-odd-limit]].
+'''1701/1700''', the '''palingenesis comma''', also known as the '''palingenetic 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:
+* ([[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:
@@ Line 12: / Line 23: @@
 * ([[1716/1715]])([[194481/194480]])
-This comma's names ultimately come from the Ancient Greek word "palingenesía" (meaning "rebirth", "regeneration" or "renaissance"<ref>[[Wiktionary: palingenesis #English]]</ref>), 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.
+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 ==
+When tempered out in a linearly independent fashion, the resulting temperaments are called '''palingenetic temperaments''', and are characterized by the presence of [[Dyadic chord|essentially tempered chord]]s 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"<ref>[[Wiktionary: palingenesis #English]]</ref>), 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.
 == See also ==