# 34 equal temperament

In musical theory,

**34 equal temperament**, also referred to as 34-tet, 34-edo or 34-et, is the tempered tuning derived by dividing the octave into 34 equal-sized steps. Each step represents a frequency ratio of 2^{1/34}, or 35.29 cents.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 and thesyntonic comma ), division into 34 steps did not arise 'naturally' out of older music theory, although Cyriac Schneegass proposed ameantone system with 34 divisions based in effect on half achromatic semitone (the difference between amajor third and aminor third , 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. 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 well-known 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 tones , ratio 9/8 andminor tones , ratio 10/9. This can be regarded either as a resource or as a problem, making modulation 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.**cale diagram**The following are 15 of the 34 notes in the scale:

The remaining notes can easily be added.

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

Although the 34-et is an improvement over 31-et with respect to fifths and the major and minor thirds, it offers a markedly poor fit to the

septimal whole tone ,septimal minor third , andseptimal major third , intervals which are handled very naturally by 31-et, and even somewhat better by 22-et.The 11th harmonic is handled much better. 34-et closely matches and distinguishes between a variety of ratios involving this harmonic that are either not matched closely, or not distinguished between in other systems. These include 11:9, 12:11, 14:11 and 15:11, and of course their inversions. It even more accurately matches many 13-limit intervals,such as 15:13, 13:11, and 13:9. 34-et tempers out the interval 144:143, which separates the 11:9 and 16:13 neutral thirds.

**References**J. Murray Barbour, "Tuning and Temperament", Michigan State College Press, 1951.

**External links*** [

*http://links.jstor.org/sici?sici=0001-6241(197901%2F06)1%3A51%3A1%3C140%3AET%3E2.0.CO%3B2-3 Dirk de Klerk "Equal Temperament"*]

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### Look at other dictionaries:

**Equal temperament**— is a musical temperament, or a system of tuning in which every pair of adjacent notes has an identical frequency ratio. In equal temperament tunings an interval mdash; usually the octave mdash; is divided into a series of equal steps (equal… … Wikipedia**Equal temperament**— Equal E qual, a. [L. aequalis, fr. aequus even, equal; akin to Skr. ?ka, and perh. to L. unus for older oinos one, E. one.] 1. Agreeing in quantity, size, quality, degree, value, etc.; having the same magnitude, the same value, the same degree,… … The Collaborative International Dictionary of English**Equal temperament**— Temperament Tem per*a*ment, n. [L. temperamentum a mixing in due proportion, proper measure, temperament: cf. F. temp[ e]rament. See {Temper}, v. t.] 1. Internal constitution; state with respect to the relative proportion of different qualities,… … The Collaborative International Dictionary of English**equal temperament**— Music. the division of an octave into 12 equal semitones, as in the tuning of a piano. * * * ▪ music in music, a tuning system in which the octave is divided into 12 semitones of equal size. Because it enables keyboard instruments (keyboard … Universalium**equal temperament**— noun the division of the scale based on an octave that is divided into twelve exactly equal semitones equal temperament is the system commonly used in keyboard instruments • Hypernyms: ↑temperament … Useful english dictionary**53 equal temperament**— In music, 53 equal temperament, called 53 TET, 53 EDO, or 53 ET, is the tempered scale derived by dividing the octave into fifty three equally large steps. Each step represents a frequency ratio of 21/53, or 22.6415 cents, an interval sometimes… … Wikipedia**19 equal temperament**— In music, 19 equal temperament, called 19 TET, 19 EDO, or 19 ET, is the tempered scale derived by dividing the octave into 19 equally large steps. Each step represents a frequency ratio of 21/19, or 63.16 cents. Because 19 is a prime number, one… … Wikipedia**31 equal temperament**— In music, 31 equal temperament, which can be abbreviated 31 tET, 31 EDO, 31 ET, is the tempered scale derived by dividing the octave into 31 equal sized steps. Each step represents a frequency ratio of 21/31, or 38.71 cents.Division of the octave … Wikipedia**72 equal temperament**— In music, 72 equal temperament, called twelfth tone, 72 tet, 72 edo, or 72 et, is the tempered scale derived by dividing the octave into twelfth tones, or in other words 72 equally large steps. Each step represents a frequency ratio of 21/72, or… … Wikipedia**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 equally large steps. Each step represents a frequency ratio of 21/22, or 54.55 cents.The idea of dividing the octave… … Wikipedia