{"product_id":"die-tonleiter-und-ihre-mathematik","title":"Die Tonleiter Und Ihre Mathematik","description":"\u003cp\u003eAre musical scales just trivial? This book explores this question, revealing the complexity of creating \"harmony\" in tonal systems.\u003c\/p\u003e\u003cp\u003eWhy 12 tones? Are there alternatives? Are 12 fifths equal 7 octaves? What is \"consonance\"? When are intervals \"perfect\" or \"imperfect\"? What is meant by \"tonal characteristics\", \"whole tone\" and \"semitone\"? \"Ancient tuning\" vs potentially new?\u003c\/p\u003e\u003cp\u003eAnswers need thoughtful explanations, revealing interconnectedness. In this context, mathematics is pivotal, explaining scale generation, temperament systems, etc.\u003c\/p\u003e\u003cp\u003eDivided into three parts, this book covers:\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eModern interval arithmetic driven by prime numbers.\u003c\/li\u003e\n\u003cli\u003eArchitectural principles of scales, with examples.\u003c\/li\u003e\n\u003cli\u003eSystematic nature of historical tunings and temperaments.\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eUnderstanding only requires school knowledge, developed into algebraic tools applied musically.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e","brand":"Gardners","offers":[{"title":"Default Title","offer_id":57509994660213,"sku":"9783662695401","price":54.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0612\/7193\/3106\/files\/9783662695401.jpg?v=1787130197","url":"https:\/\/backstory.london\/products\/die-tonleiter-und-ihre-mathematik","provider":"Backstory","version":"1.0","type":"link"}