In classical music from

Western culture image:Da Vinci Vitruve Luc Viatour.jpg, Leonardo da Vinci's ''Vitruvian Man''. Based on the correlations of ideal Body proportions, human proportions with geometry described by the ancient Roman architect Vitruvius in Book III of his treatise '' ...

, a diminished third () is the

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 ...

produced by narrowing a

minor third In music theory, a minor third is a musical interval that encompasses three half steps, or semitones. Staff notation represents the minor third as encompassing three staff positions (see: interval number). The minor third is one of two com ...

by a

chromatic semitone In modern Western tonal music theory an augmented unison or augmented prime is the interval between two notes on the same staff position, or denoted by the same note letter, whose alterations cause them, in ordinary equal temperament, to be o ...

.Benward & Saker (2003). ''Music: In Theory and Practice, Vol. I'', p.54. . For instance, the interval from A to C is a minor third, three semitones wide, and both the intervals from A to C, and from A to C are diminished thirds, two semitones wide. Being diminished, it is considered a dissonant interval. In

equal temperament 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, ...

a diminished third is

enharmonic In modern musical notation and tuning, an enharmonic equivalent is a note, interval, or key signature that is equivalent to some other note, interval, or key signature but "spelled", or named differently. The enharmonic spelling of a written ...

with the

major second 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 ...

, both having a value of 200 cents. However, in meantone tunings with fifths flatter than the 700 cents of equal temperament, the diminished third is wider than the major second. In 19 equal temperament it is in fact enharmonically equivalent to an

augmented second In classical music from Western culture, an augmented second is an interval that, in equal temperament, is sonically equivalent to a minor third, spanning three semitones, and is created by widening a major second by a chromatic semitone.Benw ...

, both having a value of 252.6 cents. In 31 equal temperament it has a more typical value of 232.3 cents. In a twelve-note keyboard tuned in a meantone tuning from E to G, the dimininished third appears between C and E, and again between G and B. In superpythagorean tunings, the diminished third is narrower than the major second. In the special case of 17 equal temperament, the chromatic semitone and diminished third are in fact represented by the same interval of 141.18 cents, which allows the minor third to be evenly divided in half. In

22 equal temperament 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 ...

, the diminished third is ~ 109 cents while the chromatic semitone is ~ 163 cents and the diatonic semitone is ~ 55 cents. Thus, 22-ET is a system in which both "semitones" are not in fact semitones, but the diminished third ''is'' a semitone! In

septimal meantone temperament In music, septimal meantone temperament, also called ''standard septimal meantone'' or simply ''septimal meantone'', refers to the tempering of 7-limit musical intervals by a meantone temperament tuning in the range from fifths flattened by the ...

the diminished third is considered to approximate the interval of a

septimal major second In music, the septimal whole tone, septimal major second, or supermajor second is the interval (music), musical interval exactly or approximately equal to an 8/7 ratio of frequencies.Andrew Horner, Lydia Ayres (2002). ''Cooking with Csound: Wo ...

(), with ratio 8/7, and in any meantone tuning in the vicinity of quarter-comma meantone, such as 31-equal temperament, it will come close to that value; for instance in 31-equal temperament the diminished third is a cent sharp of 8/7. The complementary interval to the diminished third is the

augmented sixth In classical music from Western culture, an augmented sixth () is an interval produced by widening a major sixth by a chromatic semitone.Benward & Saker (2003). ''Music: In Theory and Practice, Vol. I'', p.54. . Specific example of an A6 not ...

, and the numerous chords of common practice music described as augmented sixth chords thereby contain the diminished third as well. For example, a German sixth chord E-G-B-C-E' exhibits a diminished third between C and E' which complements the augmented sixth between E and C. The just diminished third arises in the extended C major scale between F and A,Paul, Oscar (1885).
A manual of harmony for use in music-schools and seminaries and for self-instruction
', p.165. Theodore Baker, trans. G. Schirmer. and between B and D.

References

{{DEFAULTSORT:Diminished Third Diminished intervals Thirds (music)

See also

References