Preface What you are now reading is the written version of an electronic
document that explains the mathematical principles for different musical
temperaments. The electronic version contains many music examples that
you can listen to while you are working with this document at a
computer. The written version obviously cannot offer this possibility.
It serves therefore merely as a parallel study aid and guide and cannot
replace actually working with the electronic text. Musical Temperaments
Contents - V II Contents Introduction and Fundamental Properties 1 Pitch
and Frequency 1 Preliminary Remarks 1 Frequencies and Intervals 2 Tuning
Systems and Frequencies 5 Musical Scales in Different Tunings 5 Pure
Tuning 5 Intervals and Triads in Pure Tuning 12 Pythagorean Tuning 23
Intervals and Triads in Pythagorean Tuning 31 Meantone Tuning 34
Intervals and Triads in Meantone Tuning 39 Equal Temperament (Tuning) 42
Intervals and Triads in Equal Temperament (Tuning) 47 Summary 50
Appendices 53 Pictorial explanations 53 Tables of Frequencies and
Intervals 54 Operating Instructions 62 Glossary 67 Musical Temperaments
Introduction and Fundamental Properties - 1 Introduction and Fundamental
Properties Pitch and Frequency Preliminary Remarks It is well known that
tones consist of periodically recurring phenomena, that is, beats
repeating in a regular pattern. The number of repetitions of beats per
second is measured in Hertz: 440 Hertz mean 440 beats per second. This
number is also called the frequency of a beat.