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Das Buch verfolgt die Entwicklung des Tonsystems seit dem griechischen Altertum in mathematischer Sicht. Themen sind u.a. das Verhältnis der gleichschwebenden Temperatur zur reinen Stimmung und das Tonartencharakteristiken-Problem. Und warum gibt es eigentlich keine 13-Ton-Musik? Die Obertonreihe der Saite, der verschiedenen Pfeifen, und der Pauke wird aus der Wellengleichung und den jeweiligen Randbedingungen hergeleitet. Den Klang bestimmen die Anfangswerte, und damit der Künstler. Für die Pauke sind die Besselfunktionen verantwortlich. Vom Autor berechnete Klangfiguren und Amplituden-Diagramme veranschaulichen den Sachverhalt. Bei aller Mathematik schlägt das Buch eine Brücke zur Musik in kulturgeschichtlichem Zusammenhang.

Musical intervals and scales. --- Music --- Timpani --- Kettledrum --- Timpanum --- Tympani --- Drum --- Musical acoustics --- Physics --- Sound --- Monochord --- Intervals (Music) --- Modes, Musical --- Musical modes --- Musical scales and intervals --- Scales (Music) --- Music theory --- Musical temperament --- Mathematics. --- Acoustics and physics. --- Acoustics. --- Modes

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Maqām --- Music --- Musical intervals and scales. --- 78.34.8 --- 78.33.2 --- 78.16 Sarajevo 2012 --- Intervals (Music) --- Modes, Musical --- Musical modes --- Musical scales and intervals --- Scales (Music) --- Music theory --- Musical temperament --- Makam --- Muğam --- Mugham --- Nagham --- Melody --- Musical intervals and scales --- History and criticism. --- Modes --- Conferences-Meetings --- History and criticism

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The ancient science of harmonics investigates the arrangements of pitched sounds which form the basis of musical melody, and the principles which govern them. It was the most important branch of Greek musical theory, studied by philosophers, mathematicians and astronomers as well as by musical specialists. This 2007 book examines its development during the period when its central ideas and rival schools of thought were established, laying the foundations for the speculations of later antiquity, the Middle Ages and the Renaissance. It concentrates particularly on the theorists' methods and purposes and the controversies that their various approaches to the subject provoked. It also seeks to locate the discipline within the broader cultural environment of the period; and it investigates, sometimes with surprising results, the ways in which the theorists' work draws on and in some cases influences that of philosophers and other intellectuals.

780.901 --- Arts Music Ancient times to 450 A.D. --- Music --- Musical intervals and scales --- Music theory --- Musique --- Théorie musicale --- Acoustics and physics. --- History --- Acoustique et physique --- Intervalles et gammes --- Histoire --- 78.22 --- 78.63 --- Musical theory --- Theory of music --- Intervals (Music) --- Modes, Musical --- Musical modes --- Musical scales and intervals --- Scales (Music) --- Musical temperament --- Musical acoustics --- Physics --- Sound --- Monochord --- Theory --- Modes --- Arts and Humanities

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Tuning, Timbre, Spectrum, Scale focuses on perceptions ofconsonance and dissonance, and how these are dependent on timbre. This alsorelates to musical scale: certain timbres sound more consonant in some scalesthan others. Sensory consonance and the ability to measure it have importantimplications for the design of audio devices and for musical theory andanalysis. Applications include methods of adapting sounds for arbitrary scales,ways to specify scales for nonharmonic sounds, and techniques of soundmanipulation based on maximizing (or minimizing) consonance. Specialconsideration is given here to a new method of adaptive tuning that canautomatically adjust the tuning of a piece based its timbral character so as tominimize dissonance. Audio examples illustrating the ideas presented areprovided for free on the Springer Extras website (http://extras.springer.com). Thisunique analysis of sound and scale will be of interest to physicists andengineers working in acoustics, as well as to musicians and psychologists .

Sound. --- Tuning. --- Tone color (Music) --- Musical intervals and scales. --- Psychoacoustics. --- Music --- Acoustics and physics. --- Psychophysics --- Sound --- Intervals (Music) --- Modes, Musical --- Musical modes --- Musical scales and intervals --- Scales (Music) --- Music theory --- Musical temperament --- Timbre (Music) --- Tone quality --- Musical acoustics --- Physics --- Monochord --- Musical pitch --- Acoustics --- Continuum mechanics --- Mathematical physics --- Pneumatics --- Radiation --- Wave-motion, Theory of --- Modes --- Acoustics and physics --- Electronics. --- Engineering. --- Neurosciences. --- Physiology --- Acoustics. --- Electronics and Microelectronics, Instrumentation. --- Engineering, general. --- Physiological, Cellular and Medical Topics. --- Signal, Image and Speech Processing. --- Mathematics. --- Construction --- Industrial arts --- Technology --- Electrical engineering --- Physical sciences --- Animal physiology --- Animals --- Biology --- Anatomy --- Neural sciences --- Neurological sciences --- Neuroscience --- Medical sciences --- Nervous system --- 78.86.1 --- Microelectronics. --- Biomathematics. --- Signal processing. --- Image processing. --- Speech processing systems. --- Computational linguistics --- Electronic systems --- Information theory --- Modulation theory --- Oral communication --- Speech --- Telecommunication --- Singing voice synthesizers --- Pictorial data processing --- Picture processing --- Processing, Image --- Imaging systems --- Optical data processing --- Processing, Signal --- Information measurement --- Signal theory (Telecommunication) --- Mathematics --- Microminiature electronic equipment --- Microminiaturization (Electronics) --- Electronics --- Microtechnology --- Semiconductors --- Miniature electronic equipment