Justly Intonated Quarter-comma Meantone
A just intonation version of the quarter-comma meantone temperament may be constructed in the same way as Johann Kirnberger's rational version of 12-TET. The value of 51/8 351/3 is very close to 4, that's why a 7-limit interval 6144:6125 (which is the difference between the 5-limit diesis 128:125 and the septimal diesis 49:48), equal to 5.362 cents, appears very close to the quarter-comma of 5.377 cents. So the perfect fifth has the ratio of 6125:4096, which is the difference between three just major thirds and two septimal major seconds; four such fifths exceed the ratio of 5:1 by the tiny interval of 0.058 cents. The wolf fifth there appears to be 49:32, the difference between the septimal minor seventh and the septimal major second.
Read more about this topic: Quarter-comma Meantone
Famous quotes containing the word justly:
“If in this wide world, teeming with abundant supplies for human want, to thousands of wretched creatures no choice is open, save between starvation and sin, may we not justly say that there is something utterly wrong in the system that permits such things to be?”
—Tennessee Claflin (1846–1923)