Shallowtone comma

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]\text{AA1}^{5}[/math]
Special properties	reduced, reduced harmonic
Tenney height (log2 nd)	36.1716
Weil height (log2 max(n, d))	36.3431
Wilson height (sopfr(nd))	71
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~4.19865 bits
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.