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We see from this, that with these vibration numbers, the mistimed Fifth |1 produces 972 960 = 12 beats per second, between the 2nd and 3rd partials.
Similarly, with the mistuned Minor Thirdtaking r = 824,
24 beats per second would be heard.
It is obvious, therefore, that, although one might fail to perceive that the r of the scale is not in tune with f and 1 as long as we are concerned with melody only; yet as soon as these tones are sounded together, the discordance becomes very conspicuous. For true harmony, therefore, another tone is required in the scale, to form a
Perfect Fifth with 1. Calling this tone rah, we can deduce its vibration number in the scale above from the fact that