Shallowtone comma: Difference between revisions

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| Ratio = 295245/262144
| Ratio = 295245/262144
| Name = shallowtone comma, ptolemaic doubly-augmented unison
| Name = shallowtone comma, ptolemaic doubly-augmented unison
| Color name = LLy1, lalayo unison, Lalayo comma
| Color name = LLy1, lalayo unison, Lalayobi comma
| Comma = yes
| Comma = yes
}}
}}


The '''shallowtone comma''' or '''ptolemaic doubly-augmented unison''' (ratio:  295245/262144, monzo: {{monzo| -18 -10 1 }}) is an interval of 205.864 cents. It is equal to [[9/8]] raised by a [[schisma]] and is the difference between [[5/4]] and the Pythagorean diminished third [[65536/59049]]. It was named by [[User:CompactStar|CompactStar]] in 2024, referring to shallowtone being an [[2L 5s|antidiatonic]] counterpart of [[deeptone]], as well as it being just below the "surface" ([[5L 2s|diatonic]] fifths).
The '''shallowtone comma''' or '''ptolemaic doubly-augmented unison''' (ratio:  295245/262144, monzo: {{monzo| -18 -10 1 }}) is an interval of 205.864 cents. It is equal to [[9/8]] raised by a [[schisma]] and is the difference between [[5/4]] and the Pythagorean diminished third [[65536/59049]]. It was named by [[User:CompactStar|CompactStar]] in 2024, referring to shallowtone temperament being an [[2L 5s|antidiatonic]] counterpart of [[deeptone]], as well as it being just below the "surface" ([[5L 2s|diatonic]] fifths).


== Temperaments ==
== Temperaments ==
Tempering out leads to the shallowtone temperament, which implies a very flat fifth intermediate between [[mavila]] fifths and [[7edo]]'s fifth. 5/4 is expressed as an augmented third in melodic notation or a diminished third in harmonic notation.
Tempering out leads to the [[shallowtone]] temperament, which implies a very flat fifth intermediate between [[mavila]] fifths and [[7edo]]'s fifth. 5/4 is expressed as an augmented third in melodic notation or a diminished third in harmonic notation.


{{Stub}}
[[Category:Commas named for their regular temperament properties]]

Latest revision as of 06:49, 3 November 2024

Interval information
Ratio 295245/262144
Factorization 2-18 × 310 × 5
Monzo [-18 10 1
Size in cents 205.8637¢
Names shallowtone comma,
ptolemaic doubly-augmented unison
Color name LLy1, lalayo unison, Lalayobi comma
FJS name [math]\displaystyle{ \text{AA1}^{5} }[/math]
Special properties reduced,
reduced harmonic
Tenney norm (log2 nd) 36.1716
Weil norm (log2 max(n, d)) 36.3431
Wilson norm (sopfr(nd)) 71
Comma size large
Open this interval in xen-calc

The shallowtone comma or ptolemaic doubly-augmented unison (ratio: 295245/262144, monzo: [-18 -10 1) is an interval of 205.864 cents. It is equal to 9/8 raised by a schisma and is the difference between 5/4 and the Pythagorean diminished third 65536/59049. It was named by CompactStar in 2024, referring to shallowtone temperament being an antidiatonic counterpart of deeptone, as well as it being just below the "surface" (diatonic fifths).

Temperaments

Tempering out leads to the shallowtone temperament, which implies a very flat fifth intermediate between mavila fifths and 7edo's fifth. 5/4 is expressed as an augmented third in melodic notation or a diminished third in harmonic notation.