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17 equal temperament

Musical tuning system with 17 pitches equally-spaced on a logarithmic scale From Wikipedia, the free encyclopedia

17 equal temperament
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In music, 17 equal temperament is the tempered scale derived by dividing the octave into 17 equal steps (equal frequency ratios). Each step represents a frequency ratio of 172, or 70.6 cents.

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Figure 1: 17-ET on the regular diatonic tuning continuum at P5=705.88 cents.[1]
1 step in 17-ET

17-ET is the tuning of the regular diatonic tuning in which the tempered perfect fifth is equal to 705.88 cents, as shown in Figure 1 (look for the label "17-TET").

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History and use

Alexander J. Ellis refers to a tuning of seventeen tones based on perfect fourths and fifths as the Arabic scale.[2] In the thirteenth century, Middle-Eastern musician Safi al-Din Urmawi developed a theoretical system of seventeen tones to describe Arabic and Persian music, although the tones were not equally spaced. This 17-tone system remained the primary theoretical system until the development of the quarter tone scale.[citation needed]

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Notation

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Notation of Easley Blackwood[3] for 17 equal temperament: intervals are notated similarly to those they approximate and enharmonic equivalents are distinct from those of 12 equal temperament (e.g., A/C).

Easley Blackwood Jr. created a notation system where sharps and flats raised/lowered 2 steps. This yields the chromatic scale:

C, D, C, D, E, D, E, F, G, F, G, A, G, A, B, A, B, C

Quarter tone sharps and flats can also be used, yielding the following chromatic scale:

C, Chalf sharp/D, C/Dhalf flat, D, Dhalf sharp/E, D/Ehalf flat, E, F, Fhalf sharp/G, F/Ghalf flat, G, Ghalf sharp/A, G/Ahalf flat, A, Ahalf sharp/B, A/Bhalf flat, B, C
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Interval size

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Perspective

Below are some intervals in 17 EDO compared to just.

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Major chord on C in 17 EDO : All notes are within 37 cents of just intonation (rather than 14 cents for 12 EDO).
17 EDO
just
12 EDO
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I–IV–V–I chord progression in 17 EDO.[4] Whereas in 12 EDO, B is 11 steps, in 17 EDO, B is 16 steps.
More information interval name, size (steps) ...

Relation to 34 EDO

17 EDO is a subset of 34 EDO, equivalent to every other step in the 34 EDO scale.

References

Sources

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