A septimal 1/3-tone (in

music Music is generally defined as the The arts, art of arranging sound to create some combination of Musical form, form, harmony, melody, rhythm or otherwise Musical expression, expressive content. Exact definition of music, definitions of mu ...

) is an interval with the ratio of 28:27, which is the difference between the

perfect fourth A fourth is a musical interval encompassing four staff positions in the music notation of Western culture, and a perfect fourth () is the fourth spanning five semitones (half steps, or half tones). For example, the ascending interval from C to th ...

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 o ...

; 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. 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 b ...

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 An equal temperament is a musical temperament or tuning system, which approximates just intervals by dividing an octave (or other interval) into equal steps. This means the ratio of the frequencies of any adjacent pair of notes is the same, w ...

. 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 7-limit or septimal tunings and intervals are musical instrument tunings that have a limit of seven: the largest prime factor contained in the interval ratios between pitches is seven. Thus, for example, 50:49 is a 7-limit interval, but 14 ...

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 as whole number ratios (such as 3:2 or 4:3) of frequencies. An interval tuned in this way is said to be pure, and is called a just interval. Just intervals (and ...

is the difference between the lesser septimal (7:5)

tritone In music theory, the tritone is defined as a musical interval composed of three adjacent whole tones (six semitones). For instance, the interval from F up to the B above it (in short, F–B) is a tritone as it can be decomposed into the three ad ...

, and its

inversion Inversion or inversions may refer to: Arts * , a French gay magazine (1924/1925) * ''Inversion'' (artwork), a 2005 temporary sculpture in Houston, Texas * Inversion (music), a term with various meanings in music theory and musical set theory * ...

, 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 resulting ...

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 wit ...

, 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 (equa ...

or any other odd division of the octave.

References

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