1701/1700: Difference between revisions
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'''1701/1700''', the '''palingenesis comma''' or '''palingenesia''', is a [[17-limit]] [[unnoticeable comma]] with a size of roughly 1.02 cents. | '''1701/1700''', the '''palingenesis comma''' or '''palingenesia''', 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]]'s, therefore 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 "'''palingenesis temperaments'''", and are characterized by the presence of [[Dyadic chord|essentially tempered chord]]s called "[[palingenic chords]]" in the [[21-odd-limit]]. | ||
This comma's names ultimately come from the Ancient Greek word "palingenesía" (meaning "rebith", "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 [[24edo]], where many microtonalists get their first start, despite 24edo itself not tempering out this comma. | This comma's names ultimately come from the Ancient Greek word "palingenesía" (meaning "rebith", "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 [[24edo]], where many microtonalists get their first start, despite 24edo itself not tempering out this comma. | ||
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[[Category:Palingenesis]] | [[Category:Palingenesis]] | ||
Revision as of 07:14, 15 February 2021
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palingenesia
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1701/1700, the palingenesis comma or palingenesia, 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's, therefore 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 "palingenesis temperaments", and are characterized by the presence of essentially tempered chords called "palingenic chords" in the 21-odd-limit.
This comma's names ultimately come from the Ancient Greek word "palingenesía" (meaning "rebith", "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 24edo, where many microtonalists get their first start, despite 24edo itself not tempering out this comma.