Landscape comma

Interval information

Ratio	250047/250000
Factorization	2-4 × 36 × 5-6 × 73
Monzo	[-4 6 -6 3⟩
Size in cents	0.3254414¢
Name	landscape comma
Color name	z3g63, Trizogugu comma
FJS name	[math]\displaystyle{ \text{ddd3}^{7,7,7}_{5,5,5,5,5,5} }[/math]
Special properties	reduced
Tenney height (log2 nd)	35.8634
Weil height (log2 max(n, d))	35.8637
Wilson height (sopfr(nd))	77
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~1.20009 bits
Comma size	unnoticeable
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The landscape comma (monzo: [-4 6 -6 3⟩, ratio: 250047/250000) is an unnoticeable 7-limit comma with a size of 0.33 cents. It is the amount by which three 63/50's exceed an octave, the amount by which three septimal kleismas fall short of the Pythagorean comma, and also the difference of 2401/2400 and 4375/4374, the two smallest 7-limit superparticular commas.

Temperaments

Tempering out this comma results in the landscape temperament. An octave widened by this comma is [-3 6 -6 3⟩, a monzo with four threeven numbers. Thus landscape temperaments split the octave into three equal parts. It follows that any edo that is not threeven (41, for example) cannot temper out the landscape comma.

See Landscape family for the rank-3 family of temperaments where it is tempered out. See Landscape microtemperaments for a collection of rank-2 temperaments where it is tempered out.

Etymology

This comma was named by Yahya Abdal-Aziz in 2005, referring to landscape painting where there is a three-layer technique, which in turn was a reference to Gene Ward Smith's description of the comma as the three-layer comma.