Yamaha HD-300 HD-300 Owners Manual - Page 38

Appendix About the Temperaments Used in This Instrument Interval  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) = -1l-o-2---g0---20-- × log (frequency ratio) (frequency ratio) = 10 1-l-o-2--g-0---20-- × (value in cents)  Frequency Ratio and Cent Values for the Main Intervals Interval Octave Pure Perfect 5th Pure Perfect 4th Pure Major 3rd Pure Minor 3rd Pure Large Interval Whole Tone Pure Small Interval Whole Tone Pure Diatonic Scale Semi-tone Pure Chromatic Scale Semi-tone Meantone Frequency Ratio 2 3/2 4/3 5/4 6/5 9/8 10/9 16/15 25/24 5 /2 Syntonic-Comma (S.C.) 81/80 Pythagorean Comma (P.C.) - Schisma - Equal Semi-tone 12 2 Cent Value 1200.000 701.955 498.045 386.314 315.641 203.910 182.404 111.731 70.672 193.157 21.506 23.460 1.954 100.000 Comments Difference between the perfect 4th and major 3rd Difference between the major 3rd and minor 3rd Average between large and small interval whole tones Difference between large and small interval whole tones Difference between the pure 5th ×12 and 7 octaves Difference between P.C. and S.C. 38 HD-300 Owner's Manual