A septimal 1/3-tone (in music) is an interval with the ratio of 28:27, which is the difference between the perfect fourth and the

supermajor third In music, a subminor interval is an interval that is noticeably wider than a diminished interval but noticeably narrower than a minor interval. It is found in between a minor and diminished interval, thus making it below, or subminor to, the min ...

. 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 The comma is a punctuation mark that appears in several variants in different languages. It has the same shape as an apostrophe or single closing quotation mark () in many typefaces, but it differs from them in being placed on the baseline ...

; 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 In classical music from Western culture, a diesis ( , plural dieses ( , "difference"; Greek: δίεσις "leak" or "escape"Benson, Dave (2006). ''Music: A Mathematical Offering'', p.171. . Based on the technique of playing the aulos, where p ...

. The septimal 1/3-tone, along with the

septimal diesis In music, septimal diesis (or slendro diesis) is an interval with the ratio of 49:48 , which is the difference between the septimal whole tone and the septimal minor third. It is about 35.7 cents wide, which is narrower than a quarter-tone but ...

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 Blackwood may refer to: Botany * African blackwood (''Dalbergia melanoxylon''), a timber tree of Africa * African blackwood (''Erythrophleum africanum''), (''Peltophorum africanum'') also Rhodesian blackwood, trees from Africa * Australian black ...

in honor of

Easley Blackwood, Jr. Easley R. Blackwood Jr. (April 21, 1933 – January 22, 2023) was an American professor of music, concert pianist, composer (sometimes using unusual tunings), and the author of books on music theory, including his research into the properties of ...

, 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'').Andrew Barker, ed. (2004). ''Greek Musical Writings: Volume 2, Harmonic and Acoustic Theory'', p.51. .

Septimal sixth tone

The septimal sixth tone, also called the jubilisma, is a 7-limit

musical interval In music theory, an interval is a difference in pitch between two sounds. An interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody, and vertical or ha ...

approximately the size of 1/6 of a whole tone (203.91/6=33.99 cents). An interval with the ratio of 50:49 (), about 34.98 cents, which in

just intonation In music, just intonation or pure intonation is the tuning of musical intervals Interval may refer to: Mathematics and physics * Interval (mathematics), a range of numbers ** Partially ordered set#Intervals, its generalization from numbers to ...

is the difference between the lesser septimal (7:5) tritone, and its inversion, the greater septimal tritone (10:7). This interval is tempered out by

12-TET Twelve-tone equal temperament (12-TET) is the musical system that divides the octave into 12 parts, all of which are equally tempered (equally spaced) on a logarithmic scale, with a ratio equal to the 12th root of 2 ( ≈ 1.05946). That resultin ...

and

22-TET In music, 22 equal temperament, called 22-TET, 22- EDO, or 22-ET, is the tempered scale derived by dividing the octave into 22 equal steps (equal frequency ratios). Each step represents a frequency ratio of , or 54.55 cents (). When composing wi ...

, but not by

19-TET In music, 19 Tone Equal Temperament, called 19 TET, 19 EDO ("Equal Division of the Octave"), or 19 ET, is the tempered scale derived by dividing the octave into 19 equal steps (equal frequency ratios). Each step represent ...

31-TET In music, 31 equal temperament, 31-ET, which can also be abbreviated 31-TET (31 tone ET) or 31- EDO (equal division of the octave), also known as tricesimoprimal, is the tempered scale derived by dividing the octave into 31 equal-sized steps (equ ...

or any other odd division of the octave.

References

{{Intervals, state=expanded 7-limit tuning and intervals Commas (music) 0028:0027