Shallowtone comma: Difference between revisions

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The '''shallowtone comma''' (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]].
{{Infobox Interval
| Ratio = 295245/262144
| Name = shallowtone comma, ptolemaic doubly-augmented unison
| Color name = LLy1, lalayo unison, Lalayo comma
| 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]].


== Temperaments ==
== Temperaments ==
Tempering out leads to the shallowtone temperament, which implies a fifth slightly smaller than [[7edo]]'s but larger than [[mavila]] fifths. 5/4 is expressed as an A3 in melodic notation or a d3 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.

Revision as of 17:13, 4 April 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, Lalayo 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.

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.