iPhoneAlle anzeigen
iPhone 11iPhone 11 ProiPhone 11 Pro MaxiPhone 12iPhone 12 ProiPhone 12 Pro MaxiPhone 12 miniiPhone 13iPhone 13 ProiPhone 13 Pro MaxiPhone 13 miniiPhone 14iPhone 14 PlusiPhone 14 ProiPhone 14 Pro MaxiPhone 15iPhone 15 PlusiPhone 15 ProiPhone 15 Pro MaxiPhone 16iPhone 16 PlusiPhone 16 ProiPhone 16 Pro MaxiPhone 16eiPhone 8iPhone 8 PlusiPhone SE 2020iPhone SE 2022iPhone XiPhone XRiPhone XSiPhone XS Max
Galaxy A-SerieAlle anzeigen
Galaxy A12Galaxy A13Galaxy A13 5GGalaxy A14Galaxy A15Galaxy A16Galaxy A17Galaxy A17 5GGalaxy A20eGalaxy A21Galaxy A22Galaxy A23Galaxy A24Galaxy A25Galaxy A26 5GGalaxy A27 5GGalaxy A32Galaxy A33Galaxy A34Galaxy A35Galaxy A36 5GGalaxy A37Galaxy A40Galaxy A41Galaxy A42Galaxy A50Galaxy A51Galaxy A52Galaxy A53Galaxy A54Galaxy A55Galaxy A56 5GGalaxy A57 5GGalaxy A70Galaxy A71Galaxy A72
Redmi SeriesAlle anzeigen
Redmi 10Redmi 13CRedmi 15 5GRedmi Note 10Redmi Note 10 ProRedmi Note 11Redmi Note 11 ProRedmi Note 11 Pro Plus 5GRedmi Note 11sRedmi Note 12Redmi Note 12 5GRedmi Note 12 ProRedmi Note 12 Pro 5GRedmi Note 12 Pro PlusRedmi Note 13Redmi Note 13 5GRedmi Note 13 ProRedmi Note 13 Pro PlusRedmi Note 14Redmi Note 14 Pro PlusRedmi Note 15Redmi Note 15 5GRedmi Note 15 ProRedmi Note 15 Pro 5GRedmi Note 15 Pro Plus 5GRedmi Note 8Redmi Note 8 ProRedmi Note 9Redmi Note 9 Pro
- Startseite
Bücher Englische Bücher Musical Scales and their Mathematics
Derzeit nicht verfügbar
Handgeprüfte Gebrauchtware
Bis zu 50 % günstiger als neu
Der Umwelt zuliebe
Optischer Zustand
Beschreibung
The Musical Scale – A Triviality or a Problem? This book explores a provocative question and soon reveals that combining tones into “harmonious” tonal systems is a surprisingly complex challenge, involving a remarkably rich network of interconnected issues: Why does the familiar scale consist of exactly 12 tones? Could other scales exist? What roles do the famous Pythagorean comma and its various… counterparts play? What do concepts such as consonance, harmony, and purity of intervals mean? What is meant by the temperament characteristic of a musical scale? What is “old tuning”, and is there a new one? These and many other questions are closely interconnected, and mathematics plays a central role in answering them. Beginning with simple ratios and numerical relationships, a rich conceptual network unfolds, allowing for scientific explanations of methods for scale generation, the circles of wolf fifths and Euler lattice selection procedures, as well as models of temperaments. In three parts, the book presents: A modern arithmetic of musical intervals, together with the theory of their division, decomposition, and construction based on prime numbers; The manifold architecture of musical scales, including their models and patterns, step geometries and characteristics, semitones, quarter tones, and commas; A mathematical foundation of tempered systems, accompanied by a novel and consistent classification of historically relevant musical tunings. Numerous examples illustrate the concepts throughout. The mathematical calculations and explanations require only elementary school mathematics, which is developed and applied to musical questions as needed. For readers less interested in the mathematics part, entertaining stories from a fairytale world of mythical musical creatures accompany the text, illustrating it in an amusing way. The English translation was prepared with the assistance of artificial intelligence. The resulting text was subsequently reviewed and revised by the author, with particular attention to technical accuracy and content. Dieses Produkt haben wir gerade leider nicht auf Lager.
Handgeprüfte Gebrauchtware
Bis zu 50 % günstiger als neu
Der Umwelt zuliebe
Technische Daten
Erscheinungsdatum
02.11.2026
Sprache
Englisch
EAN
9783662695401
Herausgeber
Springer Berlin
Serien- oder Bandtitel
Mathematics Study Resources
Sonderedition
Nein
Autor
Karlheinz Schüffler
Seitenanzahl
711
Einbandart
Broschiert
Schlagwörter
Interval arithmetic, Mathematics in music, Music theory, Musical scales, Pythagorean comma, Temperaments, Pythagorean tuning
Thema-Inhalt
PBW - Angewandte Mathematik
AVA - Musikwissenschaft und Musiktheorie
PB - Mathematik
AVM - Musikgeschichte
Höhe
240 mm
Breite
16.8 cm
Transparenz & Sicherheit
Hersteller: Springer Nature Customer Service Center GmbH, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com
-.-
★★★★★
☆☆☆☆☆ Leider noch keine Bewertungen
Leider noch keine Bewertungen
Sicher bei rebuy kaufen
Schreib die erste Bewertung für dieses Produkt!
Wenn du eine Bewertung für dieses Produkt schreibst, hilfst du allen Kund:innen, die noch überlegen, ob sie das Produkt kaufen wollen. Vielen Dank, dass du mitmachst!
Sicher bei rebuy kaufen