septimal third tone

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A septimal 1/3-tone (in music) is an interval with the ratio of 28:27,Haluska, Jan (2003). The Mathematical Theory of Tone Systems, p.xxiv. {{ISBN|0-8247-4714-3}}. 1/3-tone, Archytas inferior 1/4-tone. which is the difference between the perfect fourth and the supermajor third. It is about 62.96 cents wide. The septimal 1/3-tone can be viewed either as a musical interval in its own right, or as a comma; if it is tempered out in a given tuning system, the distinction between these two intervals is lost. The septimal 1/3-tone may be derived from the harmonic series as the interval between the twenty-seventh and twenty-eighth harmonics. It may be considered a diesis.Thomas Christensen, ed. (2002). The Cambridge History of Western Music Theory, p.186. {{ISBN|9780521623711}}.

The septimal 1/3-tone, along with the septimal diesis is tempered out by five-tone equal temperament, and equal temperaments which divide the octave into a small multiple of 5 steps, such as 15-TET and 25-TET. This family of scales is known as Blackwood temperament in honor of Easley Blackwood, Jr., who first analyzed 10-note subsets of 15-TET that take advantage of the temperament.

When added to the 15:14 semitone, the 21:20 semitone and 28:27 semitone produce the 9:8 tone (major tone) and 10:9 tone (minor tone), respectively.

It is the difference between 7/6 and 9/8 (tritē and paramesē).Huffman, Carl (2005). Archytas of Tarentum: Pythagorean, Philosopher and Mathematician King, p.420. {{ISBN|9781139444071}}.Andrew Barker, ed. (2004). Greek Musical Writings: Volume 2, Harmonic and Acoustic Theory, p.51. {{ISBN|9780521616973}}.