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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.
1200
(value in cents) =
---------- -
log
2
log
(frequency ratio) = 10
---------- -
1200
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
Syntonic-Comma (S.C.)
Pythagorean Comma (P.C.)
Schisma
Equal Semi-tone
38
HD-300 Owner's Manual
× log (frequency ratio)
2
× (value in cents)
Frequency Ratio
2
3/2
4/3
5/4
6/5
9/8
10/9
16/15
25/24
5
/2
81/80
–
–
12
2
Cent Value
1200.000
701.955
498.045
386.314
315.641
203.910
182.404
111.731
Difference between the perfect 4th and major 3rd
70.672
Difference between the major 3rd and minor 3rd
193.157
Average between large and small interval whole
tones
21.506
Difference between large and small interval
whole tones
23.460
Difference between the pure 5th ×12 and
7 octaves
1.954
Difference between P.C. and S.C.
100.000
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