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]].


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 [[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 "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.


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

Revision as of 01:56, 13 May 2022

Interval information
Ratio 1701/1700
Factorization 2-2 × 35 × 5-2 × 7 × 17-1
Monzo [-2 5 -2 1 0 0 -1
Size in cents 1.018074¢
Names palingenesis comma,
palingenetic comma,
palingenesma
FJS name [math]\displaystyle{ \text{P1}^{7}_{5,5,17} }[/math]
Special properties superparticular,
reduced
Tenney norm (log2 nd) 21.4635
Weil norm (log2 max(n, d)) 21.4643
Wilson norm (sopfr(nd)) 53
Open this interval in xen-calc

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.

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.

See also

References