17_equal_temperament

17 equal temperament

17 equal temperament

Musical tuning system with 17 pitches equally-spaced on a logarithmic scale


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.

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").

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]

Notation

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

Interval size

Below are some intervals in 17-EDO compared to just.

Major chord on C in 17 equal temperament: all notes within 37 cents of just intonation (rather than 14 for 12 equal temperament)
17-et
just
12-et
I–IV–V–I chord progression in 17 equal temperament.[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-ET

17-ET is where every other step in the 34-ET scale is included, and the others are not accessible. Conversely 34-ET is a subdivision of 17-ET.


References

  1. Ellis, Alexander J. (1863). "On the Temperament of Musical Instruments with Fixed Tones", Proceedings of the Royal Society of London, vol. 13. (1863–1864), pp. 404–422.
  2. Blackwood, Easley (Summer 1991). "Modes and Chord Progressions in Equal Tunings". Perspectives of New Music. 29 (2): 166–200 (175). doi:10.2307/833437. JSTOR 833437.

Sources


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