Musical Temperaments

This multimedia product (book and CD-ROM) 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, making the CD-ROM the first easily and quickly accessible reference for listening to musical examples in different tuning systems. 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.Instructions for Windows XP:On Windows XP just go to the NT4ENG subdirectory of the CDROM and run SETUP.EXE there. This will install the software, and all the necessary files will be installed. The CDROM was designed and implemented before Windows 98, Windows ME, Windows 2000, and Windows XP, therefore START.EXE will not recognize these OS's. Manual install of the Windows NT version will work. Then, all the almost 400 sound files will be accessible.