music Music is the arrangement of sound to create some combination of Musical form, form, harmony, melody, rhythm, or otherwise Musical expression, expressive content. Music is generally agreed to be a cultural universal that is present in all hum ...

, the major fourth and minor fifth, also known as the paramajor fourth and paraminor fifth, are intervals from the quarter-tone scale, named by

Ivan Wyschnegradsky Ivan Alexandrovich Wyschnegradsky ( ; September 29, 1979), was a Russian composer primarily known for his microtonal compositions. For most of his life, from 1920 onwards, Wyschnegradsky lived in Paris. Life Ivan Wyschnegradsky was born in Sai ...

to describe the tones surrounding the

tritone In music theory, the tritone is defined as a interval (music), musical interval spanning three adjacent Major second, 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 ...

(F/G) found in the more familiar twelve-tone scale,Skinner, Miles Leigh (2007). ''Toward a Quarter-tone Syntax: Analyses of Selected Works by Blackwood, Haba, Ives, and Wyschnegradsky'', p.25. ProQuest. . as shown in the table below:

Major fourth

A major fourth () is the interval that lies midway between the

perfect fourth A fourth is a interval (music), 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 int ...

(500 cents) and the

augmented fourth Augment or augmentation may refer to: Language *Augment (Indo-European), a syllable added to the beginning of the word in certain Indo-European languages * Augment (Bantu languages), a morpheme that is prefixed to the noun class prefix of nouns ...

(600 cents) and is thus 550 cents (F). It inverts to a minor fifth. Wyschnegradsky considered it a good approximation of the

eleventh harmonic In music theory, the tritone is defined as a musical interval spanning 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 adja ...

(11:8 or 551.32 cents). A narrower undecimal major fourth is found at 537 cents (the ratio 15:11).

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

has an interval of 542 cents, which lies in between the two types of undecimal major fourth. The term may also be applied to the "comma-deficient major fourth" (or "chromatic major fourth"), which is the ratio 25:18, or 568.72 cents (F).(1832).
The Edinburgh Encyclopaedia
', Volume 9, p.249. Joseph Parker.

Minor fifth

A minor fifth () is the interval midway between the

diminished fifth Diminished may refer to: *Diminution In Western culture, Western music and music theory, diminution (from Medieval Latin ''diminutio'', alteration of Latin ''deminutio'', decrease) has four distinct meanings. Diminution may be a form of embel ...

(600 cents) and the

perfect fifth In music theory, a perfect fifth is the Interval (music), musical interval corresponding to a pair of pitch (music), pitches with a frequency ratio of 3:2, or very nearly so. In classical music from Western culture, a fifth is the interval f ...

(700 cents) and thus 650 cents (G). It inverts to a major fourth. It approximates the eleventh subharmonic (G), 16:11 (648.68 cents). The term may also be applied to the ratio 64:45 (G-) or 609.77 cents (), formed from the perfect fourth (4/3 = 498.04) and the major semitone (16/15 = 111.73),

Richard Mackenzie Bacon Richard Mackenzie Bacon (1776–1844) was an English Whig journalist, newspaper proprietor, printer, musician, teacher, and writer. Life He was born in the parish of St Peter Mancroft Norwich 1 May 1776 the only son of Richard Bacon (1745-1812) ...

(1821). "Manuscript Work of Francesco Bianchl", ''The Quarterly Musical Magazine and Review'', Volume 3, p.56. which is sharp of the G tritone. The "comma-redundant minor fifth" has the ratio 36:25 (G), or 631.28 cents, and is formed from two minor thirds. The tridecimal minor fifth (13:9), or tridecimal

, is slightly larger at 636.6 cents.

Other

The term major fourth may also be applied to the follow, as minor fifth may be applied to their inversions (in the sense of augmented and diminished): *The "comma-deficient major fourth" (or "chromatic major fourth") is the ratio 25:18, or 568.72 cents (F). *45:32 (F+) or 590.22 cents (), formed from the major third (5/4 = 386.31) and the major tone (9/8 = 203.91) or two major tones (9:8) and one minor tone (10:9) *729:512 (F++) or 611.73 cents (), formed from the perfect fourth and the apotome.

References

Fifths (music) Fourths (music) Major intervals Minor intervals Quarter tones {{music-theory-stub

Major fourth

Minor fifth

Other

See also

References