88 equal temperament

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In music, 88 equal temperament is the scale derived by dividing the octave into 88 equally large steps.

[edit] Interval size

Here are the sizes of some common intervals and comparison with the ratios arising in the harmonic series; the difference column measures in cents the distance from an exact fit to these ratios.

interval name size (steps) size (cents) just ratio just (cents) difference
perfect fifth (3L+s) 51 695.45 3:2 701.96 6.50
tritone 43 586.36 7:5 582.51 -3.85
perfect fourth (2L+s) 37 504.55 4:3 498.04 -6.50
major third (2L) 28 381.82 5:4 386.31 4.50
minor third (L+s) 23 313.64 6:5 315.64 2.00
septimal minor third 20 272.73 7:6 266.87 -5.86
whole tone, major tone 15 204.55 9:8 203.91 -0.64
Large Interval (L) 14 190.99 - - -
small interval (s) 9 122.54 - - -
diatonic semitone 8 109.09 16:15 111.73 2.64

The matches to small-number ratios in this system are quite poor, especially when compared to other equal temperaments with smaller numbers of divisions of the octave, such as 72-ET or 53-ET. This system has been used and studied not for its close match to ratios but for its other theoretical properties. Using 14 steps as the Large interval (L) and 9 steps as the small interval (s), 88edo gives a close approximation to the diatonic scale LLsLLLs of Lucy tuning, which is derived from pi, and considers integer frequency ratios, as landmarks, which generate beating, rather than musical "harmonics".

[edit] References

  • Tuning Digest, #349, Internet mailing list. [1]

[edit] See also