A septimal 1/3-tone (in

music Music is generally defined as the art of arranging sound to create some combination of form, harmony, melody, rhythm or otherwise expressive content. Exact definitions of music vary considerably around the world, though it is an aspect ...

) 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 ...

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 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. 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 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 In Western music theory, a major second (sometimes also called whole tone or a whole step) is a second spanning two semitones (). A second is a musical interval encompassing two adjacent staff positions (see Interval number for more deta ...

) 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 approximately the size of 1/6 of a

whole tone In Western music theory, a major second (sometimes also called whole tone or a whole step) is a second spanning two semitones (). A second is a musical interval encompassing two adjacent staff positions (see Interval number for more det ...

(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 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 a ...

, 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 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, 31-TET or any other odd division of the octave.

References

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