Verfügbarkeit: Rhythm, resonance and harmony

Rhythm, resonance and harmony: the mathematics of music

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Bibliographische Detailangaben
Hauptverfasser:	Arbonés, Javier (VerfasserIn), Milrud, Pablo (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	London RBA 2012
Schriftenreihe:	Everything is mathematical
Schlagworte:	Musik Mathematik
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	159 S. Ill., graph. Darst., Notenbeisp.

Internformat

MARC


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Datensatz im Suchindex

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adam_text	Contents Preface ......................................................................................................................................................... 9 Chapter 1. Tuning Strings ............................................................................................................ 11 The Greek world ................................................................................................................................... 11 The Pythagorean musical system ........................................................................................ 12 Absolute tuning .............................................................................................................................. 14 Intervals and relative tuning ................................................................................................... 16 Tuning a piano ........................................................................................................................................ 20 The Pythagorean scale ............................................................................................................... 20 Doing the sums ............................................................................................................................... 22 The Pythagorean comma ......................................................................................................... 24 Other tunings ........................................................................................................................................... 25 The diatonic scale ......................................................................................................................... 26 There is always a problem ..................................................................................................... 27 Everyone is happy ......................................................................................................................... 28 Cents ...................................................................................................................................................... 31 Commensurability ........................................................................................................................ 32 Chapter 2. The Other Dimension:Time .......................................................................... 37 Rhythmical groupings: rhythm, beat, accents ..................................................................... 37 From Greece to the first proportional notes ............................................................... 38 Perfectum/imperfectum .................................................................................................... 40 Percussion: pure rhythm ............................................................................................................ 44 Covering audible space .................................................................................................... 46 Bars, metres and breakdowns ......................................................................................................... 50 The accent and the bar .............................................................................................................. 50 Types of bar ...................................................................................:........................................... 50 Irregularities ...................................................................................................................................... 52 Layered rhythms ..................................................................................................................... 54 Amalgams .................................................................................................................................... 54 Speed: the metronome ............................................................................................................... 55 Isolated irregularities ........................................................................................................... 57 CONTENTS Modern notation ........................................................................................................................... 59 Without a scale ........................................................................................................................ 60 Chapter З.ТЪе Geometry of Composition ................................................................... 61 Pitch and rhythm: the musical plane ........................................................................................ 62 The elements of musical notation ...................................................................................... 62 The stave ..................................................................................................................................... 62 Notes ............................................................................................................................................. 64 Representing pitches ........................................................................................................... 65 Clefs ................................................................................................................................................ 65 Semitone variations .............................................................................................................. 68 The melodic curve ....................................................................................................................... 68 Geometrical-musical transformations ...................................................................................... 69 Isometric transformations ........................................................................................................ 71 Translations ............................................................................................................................... 71 Horizontal translation: repetition and canon ....................................................... 72 Vertical translation: transposition ................................................................................. 73 Reflections ................................................................................................................................ 76 Reflection on a vertical axis: retrogression ........................................................... 77 Reflection on a horizontal axis: inversion ............................................................ 78 Rotations .................................................................................................................................... 81 Combinations .......................................................................................................................... 83 Horizontal translation and vertical translation ................................................... 83 Vertical translation and reflection on a vertical axis ............................................ 84 Vertical translation and reflection on a horizontal axis ................................. 84 Scalar transformations ................................................................................................................. 88 Horizontal scaling ................................................................................................................. 89 The German Requiem by Johannes Brahms ........................................................... 90 Puttin on the Ritz .......................................................................................................... 90 Vertical scaling ......................................................................................................................... 91 Harmonic symmetries ........................................................................................................................ 92 Symmetric chords ......................................................................................................................... 92 Symmetric scales ............................................................................................................................ 93 The mathematics of musical form ............................................................................................. 95 ABCDE .............................................................................................................................................. 96 Bach s Mass in В minor ..................................................., ............ 97 CONTENTS The golden ratio and music ........................................................................................................... 99 Chapter 4. Waves and Bits .......................................................................................................... 103 The physics of sound .......................................................................................................................... 103 Pure and real tone ......................................................................................................................... 107 Superimposition of waves ........................................................................................................ 109 The harmonic function ............................................................................................................. 110 The synthesis of sounds ..................................................................................................................... Ill Digital audio ............................................................................................................................................. 112 Digitisation ........................................................................................................................................ 113 Returning to analogue ..................!........................................................................................... 114 Compression .................,........................................................................................................................... 116 Raw audio ....................................................................................................................................... 116 Data compression ........................................................................................................................... 116 Methods of compression .......................................................................................................... 117 MIDI ............................................................................................................................................................ 118 The orchestra ................................................................................................................................... 120 Quantisation ..................................................................................................................................... 120 Chapter 5. Mathematics for Composition ...................................................................... 121 Full equality: twelve-tone music ................................................................................................. 121 What is the twelve-tone technique? ................................................................................. 122 Series ...................................................................................................................................................... 123 Numerical and matrix representation .............................................................................. 125 Circular representation ............................................................................................................... 127 Alban Berg ......................................................................................................................................... 130 Serialism, control and chaos ................................................................................................... 131 Stochastic music :............................................................................................................................ 133 Mozart s dice game ............................................................................................................................... 134 How many pieces? ........................................................................................................................ 135 Copying the greats ............................................................................................................................... 136 Markovian birthday ...................................................................................................................... 137 The second birthday .................................................................................................................... 139 EMI ........................................................................................................................................................ 140 Mechanisation ......................................................................................................................................... 140 Inspiration .......................................................................;.................................................................. 141 CONTENTS Algorithmic composition ......................................................................................................... 142 Appendix I. Basic Concepts from Music Theory and Notation ................... 143 Appendix ILA Second Look at the Role of Time in Music .......................... 155 Bibliography ............................................................................................................................................ 157 Index ............................................................................................................................................................. 158
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spelling	Arbonés, Javier Verfasser aut Rhythm, resonance and harmony the mathematics of music Javier Arbonés ; Pablo Milrud London RBA 2012 159 S. Ill., graph. Darst., Notenbeisp. txt rdacontent n rdamedia nc rdacarrier Everything is mathematical Musik (DE-588)4040802-4 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Musik (DE-588)4040802-4 s Mathematik (DE-588)4037944-9 s DE-604 Milrud, Pablo Verfasser aut Digitalisierung BSB Muenchen - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025501939&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Arbonés, Javier Milrud, Pablo Rhythm, resonance and harmony the mathematics of music Musik (DE-588)4040802-4 gnd Mathematik (DE-588)4037944-9 gnd
subject_GND	(DE-588)4040802-4 (DE-588)4037944-9
title	Rhythm, resonance and harmony the mathematics of music
title_auth	Rhythm, resonance and harmony the mathematics of music
title_exact_search	Rhythm, resonance and harmony the mathematics of music
title_full	Rhythm, resonance and harmony the mathematics of music Javier Arbonés ; Pablo Milrud
title_fullStr	Rhythm, resonance and harmony the mathematics of music Javier Arbonés ; Pablo Milrud
title_full_unstemmed	Rhythm, resonance and harmony the mathematics of music Javier Arbonés ; Pablo Milrud
title_short	Rhythm, resonance and harmony
title_sort	rhythm resonance and harmony the mathematics of music
title_sub	the mathematics of music
topic	Musik (DE-588)4040802-4 gnd Mathematik (DE-588)4037944-9 gnd
topic_facet	Musik Mathematik
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