1701/1700: Difference between revisions

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{{Infobox Interval

| Name = ~~palingenesis~~ comma, ~~palingenetic comma~~, palingenesma

| Name = palingenetic comma, palingenesis, palingenesma

| Color name = 17uzgg1, suzogugu unison

| Comma = yes

}}

'''1701/1700''', the '''palingenetic comma''', also known as the '''palingenesis''' or '''palingenesma''', is an [[unnoticeable comma|unnoticeable]] [[17-limit]] [[comma]] with a size of roughly 1.02 [[cent]]s. 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 marveltwin and the [[442/441|tannisma]]. See [[#Commatic relations]] below. It also arises as the amount by which a stack consisting of [[27/16]] and [[28/25]] exceeds [[17/9]], and as the difference between [[63/50]] and [[34/27]].

'''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:~~

In [[Sagittal notation]], it is the default comma represented by seven [[tina]]s.

* ([[81/80]])/([[85/84]])

== Commatic relations ==

* ([[126/125]])/([[136/135]])

This comma is the difference between the following superparticular pairs:

* ([[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.~~

* [[81/80]] and [[85/84]] *

* [[126/125]] and [[136/135]] *

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

* [[351/350]] and [[442/441]]

* [[441/440]] and [[595/594]]

* [[729/728]] and [[1275/1274]]

* [[936/935]] and [[2080/2079]]

* [[1001/1000]] and [[2431/2430]]

* [[1089/1088]] and [[3025/3024]]

* [[1225/1224]] and [[4375/4374]] *

It factors into the following superparticular pairs:

* ([[2601/2600]])([[4914/4913]])

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

* ([[2401/2400]])([[5832/5831]])

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

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

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

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

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

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

== Temperaments ==

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 [[essentially tempered chord]]s called [[palingenetic chords]] in the [[21-odd-limit|21-]] and [[27-odd-limit]].

=== Palingenetian ===

[[Subgroup]]: 2.3.5.7.17

{{Mapping|legend=2| 1 0 0 0 -2 | 0 1 0 0 5 | 0 0 1 0 -2 | 0 0 0 1 1 }}

: mapping generators: ~2, ~3, ~5, ~7

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1200.0180{{c}}, ~3/2 = 701.8238{{c}}, ~5/4 = 386.3748{{c}}, ~7/4 = 968.7188{{c}}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.8252{{c}}, ~5/4 = 386.3913{{c}}, ~7/4 = 968.7278{{c}}

~~It also arises as the amount by which a stack consisting of [[27/16]] and [[28/25]] exceeds [[17/9]].~~

{{Optimal ET sequence|legend=1| 27g, 39dg, 41, 46, 53, 72, 99, 171, 472, 525, 571, 643, 742, 913, 1556, 1727, 2351, 2469, 2640, 2994, 3165, 3907, 4078 }}

In [[~~Sagittal notation~~]], ~~it is the default comma represented by seven~~ [[~~tina~~]]s.

[[Badness]] (Sintel): 0.115

=== Palingenetic ===

[[Subgroup]]: 2.3.5.7.11.13.17

[[Mapping]]: <br>

{| class="right-all"

|-

| [⟨ || 1 || 0 || 0 || 0 || 0 || 0 || -2 || ],

|-

| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || 5 || ],

|-

| ⟨ || 0 || 0 || 1 || 0 || 0 || 0 || -2 || ],

|-

| ⟨ || 0 || 0 || 0 || 1 || 0 || 0 || 1 || ],

|-

| ⟨ || 0 || 0 || 0 || 0 || 1 || 0 || 0 || ],

|-

| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ]]

|}

: mapping generators: ~2, ~3, ~5, ~7, ~11, ~13

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1200.0180{{c}}, ~3/2 = 701.8238{{c}}, ~5/4 = 386.3748{{c}}, ~7/4 = 968.7188{{c}}, ~11/8 = 551.2639{{c}}, ~13/8 = 840.4736{{c}}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.8252{{c}}, ~5/4 = 386.3913{{c}}, ~7/4 = 968.7278{{c}}, ~11/8 = 551.2862{{c}}, ~13/8 = 840.4937{{c}}

{{Optimal ET sequence|legend=1| 27eg, 39dfg, 41, 46, 58, 72, 111, 130, 145, 152fg, 159, 171, 183, 217, 224, 270, 354, 400, 441, 460, 571, 597, 624, 643, 684, 742, 814, 1084, 1385, 1609, 1826, 2423, 3211, 3435g, 4249b }} *

<nowiki/>* [[optimal patent val]]: [[4649edo|4649]]

~~== Temperaments ==~~

[[Badness]] (Sintel): 0.855

~~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.

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.

== See also ==

* [[Unnoticeable comma]]

* [[List of superparticular intervals]]

~~== References ==~~

~~<references/>~~

[[Category:Palingenetic]]

[[Category:Commas named by translating something into another language]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Name = palingenesis comma, palingenetic comma, palingenesma
+| Name = palingenetic comma, palingenesis, palingenesma
+| Color name = 17uzgg1, suzogugu unison
 | Comma = yes
 }}
+'''1701/1700''', the '''palingenetic comma''', also known as the '''palingenesis''' or '''palingenesma''', is an [[unnoticeable comma|unnoticeable]] [[17-limit]] [[comma]] with a size of roughly 1.02 [[cent]]s. 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 marveltwin and the [[442/441|tannisma]]. See [[#Commatic relations]] below. It also arises as the amount by which a stack consisting of [[27/16]] and [[28/25]] exceeds [[17/9]], and as the difference between [[63/50]] and [[34/27]].
-'''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:
+In [[Sagittal notation]], it is the default comma represented by seven [[tina]]s.
-* ([[81/80]])/([[85/84]])
+== Commatic relations ==
-* ([[126/125]])/([[136/135]])
+This comma is the difference between the following superparticular pairs:
-* ([[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.
+* [[81/80]] and [[85/84]] *
+* [[126/125]] and [[136/135]] *
+* [[273/272]] and [[325/324]]
+* [[351/350]] and [[442/441]]
+* [[441/440]] and [[595/594]]
+* [[729/728]] and [[1275/1274]]
+* [[936/935]] and [[2080/2079]]
+* [[1001/1000]] and [[2431/2430]]
+* [[1089/1088]] and [[3025/3024]]
+* [[1225/1224]] and [[4375/4374]] *
 It factors into the following superparticular pairs:
-* ([[2601/2600]])([[4914/4913]])
+* [[2601/2600]] and [[4914/4913]]
-* ([[2401/2400]])([[5832/5831]])
+* [[2401/2400]] and [[5832/5831]] *
-* ([[2058/2057]])([[9801/9800]])
+* [[2058/2057]] and [[9801/9800]]
-* ([[1716/1715]])([[194481/194480]])
+* [[1716/1715]] and [[194481/194480]]
+<nowiki/>* both of these commas are also within the 2.3.5.7.17 subgroup.
+== Temperaments ==
+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 [[essentially tempered chord]]s called [[palingenetic chords]] in the [[21-odd-limit|21-]] and [[27-odd-limit]].
+=== Palingenetian ===
+[[Subgroup]]: 2.3.5.7.17
+{{Mapping|legend=2| 1 0 0 0 -2 | 0 1 0 0 5 | 0 0 1 0 -2 | 0 0 0 1 1 }}
+: mapping generators: ~2, ~3, ~5, ~7
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.0180{{c}}, ~3/2 = 701.8238{{c}}, ~5/4 = 386.3748{{c}}, ~7/4 = 968.7188{{c}}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.8252{{c}}, ~5/4 = 386.3913{{c}}, ~7/4 = 968.7278{{c}}
-It also arises as the amount by which a stack consisting of [[27/16]] and [[28/25]] exceeds [[17/9]].
+{{Optimal ET sequence|legend=1| 27g, 39dg, 41, 46, 53, 72, 99, 171, 472, 525, 571, 643, 742, 913, 1556, 1727, 2351, 2469, 2640, 2994, 3165, 3907, 4078 }}
-In [[Sagittal notation]], it is the default comma represented by seven [[tina]]s.
+[[Badness]] (Sintel): 0.115
+=== Palingenetic ===
+[[Subgroup]]: 2.3.5.7.11.13.17
+[[Mapping]]: <br>
+{| class="right-all"
+|-
+| [⟨ || 1 || 0 || 0 || 0 || 0 || 0 || -2 || ],
+|-
+| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || 5 || ],
+|-
+| ⟨ || 0 || 0 || 1 || 0 || 0 || 0 || -2 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 1 || 0 || 0 || 1 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 0 || 1 || 0 || 0 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ]]
+|}
+: mapping generators: ~2, ~3, ~5, ~7, ~11, ~13
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.0180{{c}}, ~3/2 = 701.8238{{c}}, ~5/4 = 386.3748{{c}}, ~7/4 = 968.7188{{c}}, ~11/8 = 551.2639{{c}}, ~13/8 = 840.4736{{c}}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.8252{{c}}, ~5/4 = 386.3913{{c}}, ~7/4 = 968.7278{{c}}, ~11/8 = 551.2862{{c}}, ~13/8 = 840.4937{{c}}
+{{Optimal ET sequence|legend=1| 27eg, 39dfg, 41, 46, 58, 72, 111, 130, 145, 152fg, 159, 171, 183, 217, 224, 270, 354, 400, 441, 460, 571, 597, 624, 643, 684, 742, 814, 1084, 1385, 1609, 1826, 2423, 3211, 3435g, 4249b }} *
+<nowiki/>* [[optimal patent val]]: [[4649edo|4649]]
-== Temperaments ==
+[[Badness]] (Sintel): 0.855
-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.
+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.
 == See also ==
-* [[Unnoticeable comma]]
 * [[List of superparticular intervals]]
-== References ==
-<references/>
 [[Category:Palingenetic]]
+[[Category:Commas named by translating something into another language]]