Shallowtone comma
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Ratio | 295245/262144 |
Factorization | 2^{-18} × 3^{10} × 5 |
Monzo | [-18 10 1⟩ |
Size in cents | 205.86372¢ |
Names | shallowtone comma, ptolemaic doubly-augmented unison |
Color name | LLy1, lalayo unison, Lalayo comma |
FJS name | [math]\text{AA1}^{5}[/math] |
Special properties | reduced, reduced harmonic |
Tenney height (log_{2} nd) | 36.1716 |
Weil height (log_{2} 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.
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