Synopses & Reviews
This multimedia product (book) lets the reader investigate the mathematical foundations of musical tuning systems as theory and as audible experience. The embedded acoustical examples help to establish immediate connection between the formulas and the acoustical characteristics of different musical scales. The musical temperaments covered in the document are Pure, Pythagorean, Meantone, and Equal, the historically most important tuning systems. For each one of these temperaments the construction principles are explained in detail and with interactive visual aids, and whenever a mathematical formula for an interval is derived, this interval is made audible and can easily be compared with similar intervals in the different tuning systems. The sound examples in the multimedia version cover intervals, scales, and chords in the different tuning systems, and some examples even allow to listen to different scales simultaneously on the two channels of a stereo system. Besides being an introductory text with sound the document also contains a reference part which gives easy access to all the sound examples in a systematic way. The multimedia document can be used on any PC with Microsoft® Windows 95, 3.1 or 3.11 installed. Hardware requirement: 16-bit sound card, correctly installed in Windows.
Table of Contents
Introduction and Fundamental Properties: Pitch and Frequency - Preliminary Remarks, Frequencies and Intervals. - Tuning Systems and Frequencies: Musical Scales in Different Tunings - Pure Tuning, Intervals and Triads in Pure Tuning, Pythagorean Tuning, Intervals and Triads in Pythagorean Tuning, Meantone Tuning, Intervals and Triads in Meantone Tuning, Equal Temperament (Tuning), Intervals and Triads in Equal Temperament (Tuning), Summary. - Appendices: Pictorial Explanations - Tables of Frequencies and Intervals - Operating Instructions - Glossary