4wtn

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4WTN, if the attempt is made to use it as an actual scale, would optimally alternate dividing the just perfect fifth into two equal parts, each of size 350.9775 cents, which is to say sqrt(3/2) as a frequency ratio, alternating these with two equal steps of another interval between 300 and 400 cents. This will create an interval exactly halfway between an interval between 600 and 800 cents and the just perfect fifth. If we want to consider it to be a temperament, it tempers out 6/5, 9/7, 32/27, and 81/80 in the patent val.

Factoids about 4WTN

60/49 and 49/40 are good rational representations of the square root of 3/2.

The best tunings of 4WTN are closely related to the hemififths temperament, which tempers out 2401/2400 and 5120/5103 in the 7-limit.

Intervals

“fifth” 2 = 600¢ “nonet” = 1351.429¢ step 2 = 11/9 “nonet” = 1460¢ “fifth” 2 = 800¢
1 350.9775
2 701.955
3 1001.955 1026.692 1049.363 1080.9775 1101.955
4 1301.955 1351.429 1396.771 1460 1501.955
Todo: clarify, unify precision