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 [[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]]. | ||
It factors into the following superparticular pairs: | |||
* ([[2601/2600]])([[4914/4913]]) | |||
* ([[2401/2400]])([[5832/5831]]) | |||
* ([[2058/2057]])([[9801/9800]]) | |||
* ([[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. | 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. | ||
Revision as of 06:16, 8 November 2022
| Interval information |
palingenetic comma,
palingenesma
reduced
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 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. 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 essentially tempered chords called "palingenetic chords" in the 27-odd-limit.
It factors into the following superparticular pairs:
This comma's names ultimately come from the Ancient Greek word "palingenesía" (meaning "rebirth", "regeneration" or "renaissance"[1]), 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.
In Sagittal notation, it is the default comma represented by seven tinas.