Aseptimal 1/3-tone (inmusic) is aninterval with the ratio of 28:27,[1] which is the difference between theperfect fourth and thesupermajor third. It is about 62.96cents wide. Theseptimal 1/3-tone can be viewed either as a musical interval in its own right, or as acomma; 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 theharmonic series as the interval between the twenty-seventh and twenty-eighth harmonics. It may be considered adiesis.[2]
The septimal 1/3-tone, along with theseptimal diesis is tempered out byfive-tone equal temperament, and equal temperaments which divide the octave into a small multiple of 5 steps, such as15-TET and25-TET. This family of scales is known asBlackwood temperament in honor ofEasley Blackwood, Jr., who first analyzed 10-note subsets of15-TET that take advantage of the temperament.
When added to the15:14 semitone, the21:20 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 andparamesē).[3][4]
Theseptimal sixth tone, also called thejubilisma, is a7-limitmusical interval approximately the size of 1/6 of awhole tone (203.91/6=33.99 cents). An interval with the ratio of 50:49 (playⓘ), about 34.98 cents, which injust intonation is the difference between the lesser septimal (7:5)tritone, and itsinversion, the greater septimal tritone (10:7). This interval is tempered out by12-TET and22-TET, but not by19-TET,31-TET or any other odd division of the octave.
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