Yamaha Harmony Director HD-300, Руководство пользователя

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Appendix
HD-300 Owner’s Manual 38
About the Temperaments Used in This Instrument

Unit of interval
A cent is a unit used to measure musical intervals. The logarithm of the frequency ratio of two sounds is taken, and a
semitone of equal temperament is defined as 100 cents. Using cents to measure intervals, we can calculate the interval
using simple addition/subtraction rather than multiplication/division. For this reason, the cent is commonly and
internationally used in fields such as music and acoustics as a standard for measuring intervals.
(value in cents) = × log (frequency ratio)
(frequency ratio) = 10 × (value in cents)

Frequency Ratio and Cent Values for the Main Intervals
Interval
Interval Frequency Ratio Cent Value Comments
Octave 2 1200.000
Pure Perfect 5th 3/2 701.955
Pure Perfect 4th 4/3 498.045
Pure Major 3rd 5/4 386.314
Pure Minor 3rd 6/5 315.641
Pure Large Interval Whole Tone 9/8 203.910
Pure Small Interval Whole Tone 10/9 182.404
Pure Diatonic Scale Semi-tone 16/15 111.731 Difference between the perfect 4th and major 3rd
Pure Chromatic Scale Semi-tone 25/24 70.672 Difference between the major 3rd and minor 3rd
Meantone /2 193.157 Average between large and small interval whole
tones
Syntonic-Comma (S.C.) 81/80 21.506 Difference between large and small interval
whole tones
Pythagorean Comma (P.C.) – 23.460 Difference between the pure 5th ×12 and
7 octaves
Schisma – 1.954 Difference between P.C. and S.C.
Equal Semi-tone 100.000
1200
2 log
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2 log
1200
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5
2
12