1701/1700: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = palingenetic comma, palingenesis, palingenesma | |||
| Color name = 17uzgg1, suzogugu unison | |||
| Comma = yes | |||
| Name = palingenesis | |||
| Color name = | |||
| | |||
}} | }} | ||
'''1701/1700''', the '''palingenesis | '''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]]. | ||
This comma's names ultimately come from the Ancient Greek word | 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]] 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]] 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. | |||
== 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 [[Dyadic chord|essentially tempered chord]]s called [[palingenetic chords]] in the [[21-odd-limit|21-]] and [[27-odd-limit]]. | |||
== Etymology == | |||
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 == | == See also == | ||
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* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
[[Category:Palingenetic]] | |||
[[Category:Commas named by translating something into another language]] | |||
[[Category: | |||
[[Category: | |||
Latest revision as of 01:57, 16 November 2024
| Interval information |
palingenesis,
palingenesma
reduced
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 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 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 and 4914/4913
- 2401/2400 and 5832/5831 *
- 2058/2057 and 9801/9800
- 1716/1715 and 194481/194480
* 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 chords called palingenetic chords in the 21- and 27-odd-limit.
Etymology
This comma was named by Aura in 2020. Its names ultimately come from the Ancient Greek word 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.