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Many people intuitively sense that there is a connection between mathematics and music. If nothing else, both involve counting. There is, of course, much more to the association. David Wright's book is an investigation of the interrelationships between mathematics and music, reviewing the needed background concepts in each subject as they are encountered. Along the way, readers will augment their understanding of both mathematics and music. The text explores the common foundations of the two subjects, which are developed side by side. Musical and mathematical notions are brought together, such as scales and modular arithmetic, intervals and logarithms, tone and trigonometry, and timbre and harmonic analysis. When possible, discussions of musical and mathematical notions are directly interwoven. Occasionally the discourse dwells for a while on one subject and not the other, but eventually the connection is established, making this an integrative treatment of the two subjects. The book is a text for a freshman level college course suitable for musically inclined or mathematically inclined students, with the intent of breaking down any apprehension that either group might have for the other subject. Exercises are given at the end of each chapter. The mathematical prerequisites are a high-school level familiarity with algebra, trigonometry, functions, and graphs. Musically, the student should have had some exposure to musical staffs, standard clefs, and key signatures, though all of these are explained in the text [Publisher description].

Musical intervals and scales. --- Music theory --- Intervals (Music) --- Modes, Musical --- Music --- Musical modes --- Musical scales and intervals --- Scales (Music) --- Musical temperament --- Mathematics. --- Modes --- Musical intervals and scales --- Mathematics

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Musical intervals and scales --- Music theory --- Music --- Musical theory --- Theory of music --- Intervals (Music) --- Modes, Musical --- Musical modes --- Musical scales and intervals --- Scales (Music) --- Musical temperament --- Theory --- Modes --- Music theory. --- Musical intervals and scales.

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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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Musical intervals and scales --- Music --- Intervals (Music) --- Modes, Musical --- Musical modes --- Musical scales and intervals --- Scales (Music) --- Music theory --- Musical temperament --- Art music --- Art music, Western --- Classical music --- Musical compositions --- Musical works --- Serious music --- Western art music --- Western music (Western countries) --- History and criticism --- Modes --- modaliteit (muziek) --- muziektheorie --- Arab states --- Iran

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John of Garland --- Musical intervals and scales --- Music theory --- Gregorian chants --- -Chant (Plain, Gregorian, etc.) --- Chants (Plain, Gregorian, etc.) --- Franco-Roman chants --- Gregorian chant --- Old Roman chants --- Plainchant --- Plainchants --- Plainsong --- Roman chants --- Chants --- Music --- Musical theory --- Theory of music --- Intervals (Music) --- Modes, Musical --- Musical modes --- Musical scales and intervals --- Scales (Music) --- Musical temperament --- Instruction and study --- Theory --- Modes --- Johannes de Garlandia --- -Instruction and study --- -Music --- Chant (Plain, Gregorian, etc.) --- Johannes, --- Garlandia, Johannes de