In musical theory, 34 equal temperament, also referred to as 34-TET, 34-

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or 34-ET, is the tempered tuning derived by dividing the octave into 34 equal-sized steps (equal frequency ratios). Each step represents a frequency ratio of , or 35.29 cents .

History and use

Unlike divisions of the octave into 19, 31 or 53 steps, which can be considered as being derived from ancient Greek intervals (the greater and lesser

diesis In classical music from Western culture, a diesis ( or enharmonic diesis, plural dieses ( , or "difference"; Greek: "leak" or "escape" is either an accidental (see sharp), or a very small musical interval, usually defined as the differe ...

and the

syntonic comma In music theory Music theory is the study of theoretical frameworks for understanding the practices and possibilities of music. ''The Oxford Companion to Music'' describes three interrelated uses of the term "music theory": The first i ...

), division into 34 steps did not arise 'naturally' out of older music theory, although Cyriakus Schneegass proposed a meantone system with 34 divisions based in effect on half a

chromatic Diatonic and chromatic are terms in music theory that are used to characterize scales. The terms are also applied to musical instruments, intervals, chords, notes, musical styles, and kinds of harmony. They are very often used as a pair, es ...

semitone A semitone, also called a minor second, half step, or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically. It is defined as the interval between ...

(the difference between a

major third In music theory, a third is a Interval (music), musical interval encompassing three staff positions (see Interval (music)#Number, Interval number for more details), and the major third () is a third spanning four Semitone, half steps or two ...

and a

minor third In music theory, a minor third is a interval (music), musical interval that encompasses three half steps, or semitones. Staff notation represents the minor third as encompassing three staff positions (see: interval (music)#Number, interval numb ...

, 25:24 or 70.67 cents). Wider interest in the tuning was not seen until modern times, when the computer made possible a systematic search of all possible equal temperaments. While Barbour discusses it,''Tuning and Temperament'', Michigan State College Press, 1951 the first recognition of its potential importance appears to be in an article published in 1979 by the Dutch theorist Dirk de Klerk. The luthier Larry Hanson had an electric guitar refretted from 12 to 34 and persuaded American guitarist Neil Haverstick to take it up. As compared with 31-et, 34-et reduces the combined mistuning from the theoretically ideal just thirds, fifths and sixths from 11.9 to 7.9 cents. Its fifths and sixths are markedly better, and its thirds only slightly further from the theoretical ideal of the 5:4 ratio. Viewed in light of Western diatonic theory, the three extra steps (of 34-et compared to 31-et) in effect widen the intervals between C and D, F and G, and A and B, thus making a distinction between

major tone Major most commonly refers to: * Major (rank), a military rank * Academic major, an academic discipline to which an undergraduate student formally commits * People named Major, including given names, surnames, nicknames * Major and minor in musi ...

s, ratio 9:8 and minor tones, ratio 10:9. This can be regarded either as a resource or as a problem, making

modulation Signal modulation is the process of varying one or more properties of a periodic waveform in electronics and telecommunication for the purpose of transmitting information. The process encodes information in form of the modulation or message ...

in the contemporary Western sense more complex. As the number of divisions of the octave is even, the exact halving of the octave (600 cents) appears, as in 12-et. Unlike 31-et, 34 does not give an approximation to the harmonic seventh, ratio 7:4.

Interval size

The following table outlines some of the intervals of this tuning system and their match to various ratios in the harmonic series.

Scale diagram

The following are 15 of the 34 notes in the scale: The remaining notes can easily be added.

References

J. Murray Barbour James Murray Barbour (1897–1970) is an American acoustician, musicologist, and composer best known for his work ''Tuning and Temperament: A Historical Survey'' (1951, 2d ed. 1953). As the opening of the work describes, it is based upon his unpub ...

, ''Tuning and Temperament'', Michigan State College Press, 1951.

External links

Dirk de Klerk. "Equal Temperament"
''Acta Musicologica'', Vol. 51, Fasc. 1 (Jan. - Jun., 1979), pp. 140-150.
Stickman: Neil Haverstick
- Neil Haverstick is a composer and guitarist who uses microtonal tunings, especially 19, 31 and 34 tone equal temperament. {{Musical tuning Equal temperaments Microtonality