Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book offers an in-depth analysis of musical variation through a systematic approach, heavily influenced by the principles of Grundgestalt and developed variations, both created by the Austrian composer Arnold Schoenberg (1874-1951). The author introduces a new transformational-derivative model and the theory that supports it, specifically crafted for the examination of tonal music. The idea for this book emerged during a sabbatical at Columbia University, while the content is the product of extensive research conducted at the Federal University of Rio de Janeiro, resulting in the development of the Model of Derivative Analysis. This model places emphasis on the connections between musical entities rather than viewing them as separate entities. As a case study, the Intermezzo in A Major Op.118/2 by Brahms is selected for analysis. The author's goal is to provide a formal and structured approach while maintaining the text's readability and appeal for both musicians and mathematicians in the field of music theory. The book concludes with the author's recommendations for further research.

Music—Mathematics. --- Mathematics. --- Mathematics in Music. --- Applications of Mathematics. --- Math --- Science

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Sounds can be harmonic, number sequences too - a coincidence? This book deals with a musical theory of proportions, i.e. the ancient doctrine of proportions as the oldest and most important common anchorage of the two cultural sciences mathematics and music. The musical theory of tones, intervals, tetrachords, sounds and scales is in fact the exact musical image of the laws of arithmetic and its symmetries in the set of rules of playing with numbers, their proportions and their medievals. Alone the miracle of the so-called Harmonia perfecta maxima 6 - 8 - 9 - 12, whose proportions determine the fifth as well as the fourth, form the octave and have the brazen whole tone in their center, shaped the musical edifice of Pythagorean music for thousands of years. This elementary chain of proportions 6 : 8 : 9 : 12 is, moreover, completely symmetrical and built up from the arithmetic as well as from the harmonic medieta of the octave numbers 6 and 12. This book develops the theory of proportions as a mathematical science and always contrasts it with the musical motivation by means of numerous examples. The main idea is the derivation of a theory of symmetry from the Harmonia perfecta maxima to the Harmonia perfecta infinita abstracta, a process of unlimited tone generations by Babylonian mean iterations. From this, both the classical-antique diatonic is simultaneously extracted and the path "from the monochord to the organ" is re-examined. Finally, the work contains a mathematically guided introduction to the ancient tetrachordics as well as to the church tonal scales and concludes with an excursion into the sound worlds of the organ. Here the "foot-number rule of the organ" leads us by means of examples into the world of the tonal dispositions of this instrument and shows the omnipresence of the ancient theory of proportions. This book is suitable for anyone with an interest in mathematics and music. The Author Prof. Dr. Karlheinz Schüffler is a mathematician and musician. As a mathematician he teaches at the University of Krefeld as well as at the University of Düsseldorf. As a musician he practices church music with a focus on organ, Gregorian chant and choir conducting. This book is a translation of an original German edition. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation.

Music --- Mathematics in Music. --- Mathematics. --- Music theory --- Musical intervals and scales. --- Ratio and proportion.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Daniel Hensels Studie bietet einen völlig neuen Blick auf die Entwicklung der Tonalität. Es wurden neben einfachen statistischen Verfahren spezielle Klanganalyse-Visualisierungen erarbeitet, die die Entwicklung der Klangqualität in ihrer zeitlichen Ausprägung über ganze Werkgruppen hinweg darstellen können. Ziel war es herauszufinden, wie sehr die Modi die Harmonik determinieren, ob sie sich statistisch voneinander unterscheiden und sich dadurch in ihrer Existenz beweisen lassen. Hierfür entwickelte der Autor zusammen mit dem Informatiker Ingo Jache den PALESTRiNIZER. Mit ihm untersuchte er die Möglichkeiten der computergestützten automatisierten Musikanalyse anhand des Verhältnisses von Modus und Klang in 253 Motetten von Lassus und Palestrina. Inhalt Musik- und Klanganalyse mit dem Computer Modale Musiktheorie, Stimmungslehre und ihre Bedeutung für die Entwicklung von Harmonik und Kontrapunkt MIDI, JAVA, Statistik Zielgruppen Dozierende und Studierende der Musikwissenschaft, Musiktheorie und Informatik Komponisten und Komponistinnen Der Autor Daniel Hensel ist ein europaweit tätiger Komponist und Musikwissenschaftler. Er wurde als Komponist von Dirigenten wie Manfred Honeck aufgeführt und seit seiner Promotion hat er einen Lehrauftrag an der HfMDK-Frankfurt am Main inne. Seit seiner Habilitation unterrichtet er außerdem als Privatdozent computergestützte Musikanalyse.

Music. --- Mathematics. --- Computer science. --- Mathematics in Music. --- Computer Science, general. --- Lasso, Orlando di, --- Palestrina, Giovanni Pierluigi da,

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The book presents selected papers at the 10th Conference on Sound and Music Technology (CSMT) held in June 2023, China. CSMT is a multidisciplinary conference focusing on audio processing and understanding with bias on music and acoustic signals. The primary aim of the conference is to promote the collaboration between art society and technical society in China. In this book, the paper included covers a wide range topic from speech, signal processing, music understanding, machine learning, and signal processing for advanced medical diagnosis and treatment applications, which demonstrates the target of CSMT merging arts and science research together. Its content caters to scholars, researchers, engineers, artists, and education practitioners not only from academia but also industry, who are interested in audio/acoustics analysis signal processing, music, sound, and artificial intelligence (AI).

Speech processing systems. --- Signal processing. --- Acoustical engineering. --- Music --- Music theory. --- Speech and Audio Processing. --- Engineering Acoustics. --- Mathematics in Music. --- Theory of Music. --- Mathematics.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

In this intriguing book, John Barnes takes us on a journey through aspects of numbers much as he took us on a geometrical journey in Gems of Geometry. Similarly originating from a series of lectures for adult students at Reading and Oxford University, this book touches a variety of amusing and fascinating topics regarding numbers and their uses both ancient and modern. The author intrigues and challenges his audience with both fundamental number topics such as prime numbers and cryptography, and themes of daily needs and pleasures such as counting one's assets, keeping track of time, and enjoying music. Puzzles and exercises at the end of each lecture offer additional inspiration, and numerous illustrations accompany the reader. Furthermore, a number of appendices provides in-depth insights into diverse topics such as Pascal’s triangle, the Rubik cube, Mersenne’s curious keyboards, and many others. A theme running through is the thought of what is our favourite number. Written in an engaging and witty style and requiring only basic school mathematical knowledge, this book will appeal to both young and mature readers fascinated by the curiosities of numbers.

Number theory --- Algebra --- Mathematics --- Applied physical engineering --- Music --- algebra --- toegepaste wiskunde --- economie --- muziek --- wiskunde --- getallenleer --- Number theory. --- Algebra. --- Mathematics. --- Applied mathematics. --- Engineering mathematics. --- Number Theory. --- Mathematics in Music. --- Applications of Mathematics.