Landscape comma: Difference between revisions

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The '''landscape comma''' is the [[7-limit]] [[unnoticeable comma]] with a ratio of '''250047/250000''' and a size of 0.33 [[cent]]s. It is the amount by which three [[63/50]] intervals exceed an [[octave]], and is also the amount by which a stack of three [[225/224|septimal kleismas]] falls short of the [[Pythagorean comma]]. Tempering 63/50 interval into one degree of 3edo (exact 400 cents) is highly characteristic of '''landscape temperament'''- any tuning system (41edo, for example) in which the number of divisions of the octave is not a multiple of 3 cannot temper out the landscape comma.
The '''landscape comma''' is the [[7-limit]] [[unnoticeable comma]] with a ratio of '''250047/250000''' and a size of 0.33 [[cent]]s. It is the amount by which three [[63/50]]'s exceed an [[octave]], by which three [[225/224|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. Tempering 63/50 interval into one degree of 3edo (exact 400 cents) is highly characteristic of [[landscape microtemperaments]] – any tuning system (41edo, for example) in which the number of divisions of the octave is not a multiple of 3 cannot temper out the landscape comma.


== See also ==
== See also ==

Revision as of 11:06, 25 December 2020

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
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
Open this interval in xen-calc

The landscape comma is the 7-limit unnoticeable comma with a ratio of 250047/250000 and a size of 0.33 cents. It is the amount by which three 63/50's exceed an octave, 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. Tempering 63/50 interval into one degree of 3edo (exact 400 cents) is highly characteristic of landscape microtemperaments – any tuning system (41edo, for example) in which the number of divisions of the octave is not a multiple of 3 cannot temper out the landscape comma.

See also