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- catalog contributor b13160764.
- catalog created "2003.".
- catalog date "2003".
- catalog date "2003.".
- catalog dateCopyrighted "2003.".
- catalog description "3.2.2 Computation of Wigner-Ville transforms 45 -- 3.3 Decomposition problem 49 -- 3.3.1 A pseudodifferential calculus 49 -- 3.3.2 Instantaneous frequency 51 -- 3.3.3 Wigner-Ville transform of asymptotic tones 53 -- 3.3.4 Return to the problem of optimal decomposition of tones into time-frequency atoms 54 -- 4 Pitch granulation and ambiguity 57 -- 4.1 Garbuzov zones: strife 57 -- 4.1.1 An classical experiment 57 -- 4.1.2 Psychological model 61 -- 4.2 Geometric nets 64 -- 4.2.1 Z-chain condition 64 -- 4.2.2 Discrete geometric nets 68 -- 4.2.3 Various net representations of a tone system 71 -- 4.2.4 The harmony-melody uncertainty 72 -- II Special Systems 73 -- 5 Equal temperaments 75 -- 5.1 Algebraic language and harmony 75 -- 5.1.1 Formal language for the theory of harmony 75 -- 5.1.2 Tone systems and chords 77 -- 5.1.3 Structure of chords and pointed chords".
- catalog description "341 -- A.5 Dodekatonics 350 -- A.6 More than 12 tones per octave 358 -- B Historical organs with subsemitones, 1468-1721 369.".
- catalog description "7.2.1 Possibility of free transpositions 197 -- 7.2.2 Basic musical intervals sound as pure 198 -- 7.2.3 We cannot avoid uncertainty 198 -- 7.3 Well tempered tone systems 199 -- 7.3.1 Symmetry and octave equivalence 199 -- 7.3.2 The tempered fifth approximations 200 -- 7.3.4 A formalization of well tempered tone systems 202 -- 7.4 The Petzval's tone systems 202 -- 7.5 Bimeasures and the last square method 213 -- 7.5.1 Optimal temperatures 214 -- 8 12 and 10 granulations 219 -- 8.1 The major scale extensions 219 -- 8.1.1 Unimodular matrices and diatonic scales 219 -- 8.1.2 TDS geometric nets 224 -- 8.1.3 Construction of generated tone systems 229 -- 8.1.4 Comment to superparticular ratios 231 -- 8.1.5 Classification of diatonic scales 232 -- 8.1.6 Application to partial monounary algebras 237 -- 8.2 10 granulation 245 -- 8.2.1 Gamelan 245 -- 8.2.2".
- catalog description "79 -- 5.1.4 Representations of harmonic structures 81 -- 5.2 Chord and tone rows enumerations 87 -- 5.2.1 Chords 88 -- 5.2.2 Tone rows 90 -- 5.2.3 Computation of numbers of fixed elements 91 -- 5.3 Measuring equal temperaments 92 -- 5.3.1 Continued fraction method 92 -- 5.3.2 Increasing number of keys per octave 94 -- 5.3.3 Fifths of equal temperaments 97 -- 5.4 Equal temperaments in practice 98 -- 5.4.1 Music of nations 98 -- 5.4.2 Present equal temperament inspired systems 108 -- 6 Mean tone systems 117 -- 6.1 Pythagorean System 117 -- 6.1.1 Pythagorean minor and major semitones 117 -- 6.1.2 Images in the plane 120 -- 6.1.3 Fuzziness and beats 123 -- 6.2 Pythagorean System worldwide 126 -- 6.2.1 Indian systems 126 -- 6.2.2 Europe 129 -- 6.2.3 Tone systems of China 131 -- 6.3 On two algorithms in music acoustics 133 -- 6.3.1".
- catalog description "Description of the algorithms 134 -- 6.3.2 Isomorphism of the fifth and third tunings 136 -- 6.3.3 Pipe organs with subsemitones, 1468-1721 141 -- 6.3.4 The Petzval's keyboard 146 -- 6.4 Overview of meantones 148 -- 6.4.1 Era of meantones 148 -- 6.4.2 Meantone zones 150 -- 6.4.3 Further examples of mean-tone systems 156 -- 6.5 Anatomy of the Pythagorean whole tone 159 -- 6.5.1 The second level: algebraic numbers 161 -- 6.5.2 Semitone metric space 168 -- 6.5.3 Searching in transcendental numbers 169 -- 6.5.4 Adaptive Pythagorean system 171 -- 7 Well tempered systems 175 -- 7.1 Well temperament periods 175 -- 7.1.1 Historical well temperaments 175 -- 7.1.2 More than 12 183 -- 7.1.3 A revival of interest in the 20th century 192 -- 7.1.4 Temperature and mistuning 192 -- 7.1.5 Three types of temperaments -- examples 194 -- 7.2 Harmonic mean based measures 195 --".
- catalog description "I Fundamentals 1 -- 1 Tone systems and uncertainty theory 3 -- 1.1.1 A piece of metaphysics 3 -- 1.1.2 Practical manners of the tone system description 4 -- 1.2 Current trends 6 -- 1.2.1 America 7 -- 1.2.2 Europe 9 -- 1.2.3 Africa 13 -- 1.3 Uncertainty-based information theory 16 -- 1.3.1 Classical harmonic analysis theory 16 -- 1.3.2 Significance of uncertainty 20 -- 1.3.3 Uncertainty forms and principles 24 -- 2 Fuzziness and sonance 27 -- 2.1 Dissonance functions 28 -- 2.2 Relatedness tone system [left and right arrow] timbre 33 -- 2.2.1 Direction: timbre to tone system 33 -- 2.2.2 Direction: tone system to timbre 34 -- 3 Wavelets and nonspecificity 39 -- 3.1 Time-frequency plane 39 -- 3.1.1 Gabor's time-frequency atoms 41 -- 3.1.2 Lienard's time-frequency atoms 43 -- 3.2 Wigner-Ville transform 44 -- 3.2.1 Definition of the transform 44 --".
- catalog description "Includes bibliographical references (p. 307-318) and index.".
- catalog description "Superparticular pentatonics 249 -- 8.2.3 Pacific Ocean region, the fuzzy tone systems 257 -- 9 Ptolemy System 261 -- 9.1 Tetrachords 261 -- 9.1.1 The set of all tetrachords 262 -- 9.1.2 Tetrachord lattice 265 -- 9.1.3 Superparticular tetrachords 266 -- 9.1.4 Symmetry: Slendro versus 12 granulation 269 -- 9.1.5 Ancient Greece 277 -- 9.2 Ptolemy System in the 20th century 283 -- 9.2.1 Ptolemy System 284 -- 9.2.2 Set of all superparticular ratios 286 -- 9.3 Commas 291 -- 9.3.1 Aestetics of ratios of small natural numbers 291 -- 9.3.2 Mean tone aesthetics 293 -- 9.3.3 Approximations of temperaments 294 -- 9.3.4 Pythagorean approximation of Just Intonation 297 -- 9.3.5 Comma 32 805/32 768 (Schizma) 302 -- A Extended lists of tone systems 319 -- A.1 Tetrachords (2 periods) 319 -- A.2 Pentatonics 325 -- A.3 Heptatonics 328 -- A.4 6, 8, 9, 10, 11 tones per octave".
- catalog extent "xxix, 380 p. :".
- catalog identifier "0824747143 (M. Dekker)".
- catalog identifier "8088683289 (Ister)".
- catalog isPartOf "Pure and applied mathematics series ; 262".
- catalog issued "2003".
- catalog issued "2003.".
- catalog language "eng".
- catalog publisher "New York : Marcel Dekker ; Bratislava : Ister Science,".
- catalog subject "414.6 21".
- catalog subject "ML3809 .H36 2004".
- catalog subject "Mathematical analysis.".
- catalog subject "Music Acoustics and physics.".
- catalog tableOfContents "3.2.2 Computation of Wigner-Ville transforms 45 -- 3.3 Decomposition problem 49 -- 3.3.1 A pseudodifferential calculus 49 -- 3.3.2 Instantaneous frequency 51 -- 3.3.3 Wigner-Ville transform of asymptotic tones 53 -- 3.3.4 Return to the problem of optimal decomposition of tones into time-frequency atoms 54 -- 4 Pitch granulation and ambiguity 57 -- 4.1 Garbuzov zones: strife 57 -- 4.1.1 An classical experiment 57 -- 4.1.2 Psychological model 61 -- 4.2 Geometric nets 64 -- 4.2.1 Z-chain condition 64 -- 4.2.2 Discrete geometric nets 68 -- 4.2.3 Various net representations of a tone system 71 -- 4.2.4 The harmony-melody uncertainty 72 -- II Special Systems 73 -- 5 Equal temperaments 75 -- 5.1 Algebraic language and harmony 75 -- 5.1.1 Formal language for the theory of harmony 75 -- 5.1.2 Tone systems and chords 77 -- 5.1.3 Structure of chords and pointed chords".
- catalog tableOfContents "341 -- A.5 Dodekatonics 350 -- A.6 More than 12 tones per octave 358 -- B Historical organs with subsemitones, 1468-1721 369.".
- catalog tableOfContents "7.2.1 Possibility of free transpositions 197 -- 7.2.2 Basic musical intervals sound as pure 198 -- 7.2.3 We cannot avoid uncertainty 198 -- 7.3 Well tempered tone systems 199 -- 7.3.1 Symmetry and octave equivalence 199 -- 7.3.2 The tempered fifth approximations 200 -- 7.3.4 A formalization of well tempered tone systems 202 -- 7.4 The Petzval's tone systems 202 -- 7.5 Bimeasures and the last square method 213 -- 7.5.1 Optimal temperatures 214 -- 8 12 and 10 granulations 219 -- 8.1 The major scale extensions 219 -- 8.1.1 Unimodular matrices and diatonic scales 219 -- 8.1.2 TDS geometric nets 224 -- 8.1.3 Construction of generated tone systems 229 -- 8.1.4 Comment to superparticular ratios 231 -- 8.1.5 Classification of diatonic scales 232 -- 8.1.6 Application to partial monounary algebras 237 -- 8.2 10 granulation 245 -- 8.2.1 Gamelan 245 -- 8.2.2".
- catalog tableOfContents "79 -- 5.1.4 Representations of harmonic structures 81 -- 5.2 Chord and tone rows enumerations 87 -- 5.2.1 Chords 88 -- 5.2.2 Tone rows 90 -- 5.2.3 Computation of numbers of fixed elements 91 -- 5.3 Measuring equal temperaments 92 -- 5.3.1 Continued fraction method 92 -- 5.3.2 Increasing number of keys per octave 94 -- 5.3.3 Fifths of equal temperaments 97 -- 5.4 Equal temperaments in practice 98 -- 5.4.1 Music of nations 98 -- 5.4.2 Present equal temperament inspired systems 108 -- 6 Mean tone systems 117 -- 6.1 Pythagorean System 117 -- 6.1.1 Pythagorean minor and major semitones 117 -- 6.1.2 Images in the plane 120 -- 6.1.3 Fuzziness and beats 123 -- 6.2 Pythagorean System worldwide 126 -- 6.2.1 Indian systems 126 -- 6.2.2 Europe 129 -- 6.2.3 Tone systems of China 131 -- 6.3 On two algorithms in music acoustics 133 -- 6.3.1".
- catalog tableOfContents "Description of the algorithms 134 -- 6.3.2 Isomorphism of the fifth and third tunings 136 -- 6.3.3 Pipe organs with subsemitones, 1468-1721 141 -- 6.3.4 The Petzval's keyboard 146 -- 6.4 Overview of meantones 148 -- 6.4.1 Era of meantones 148 -- 6.4.2 Meantone zones 150 -- 6.4.3 Further examples of mean-tone systems 156 -- 6.5 Anatomy of the Pythagorean whole tone 159 -- 6.5.1 The second level: algebraic numbers 161 -- 6.5.2 Semitone metric space 168 -- 6.5.3 Searching in transcendental numbers 169 -- 6.5.4 Adaptive Pythagorean system 171 -- 7 Well tempered systems 175 -- 7.1 Well temperament periods 175 -- 7.1.1 Historical well temperaments 175 -- 7.1.2 More than 12 183 -- 7.1.3 A revival of interest in the 20th century 192 -- 7.1.4 Temperature and mistuning 192 -- 7.1.5 Three types of temperaments -- examples 194 -- 7.2 Harmonic mean based measures 195 --".
- catalog tableOfContents "I Fundamentals 1 -- 1 Tone systems and uncertainty theory 3 -- 1.1.1 A piece of metaphysics 3 -- 1.1.2 Practical manners of the tone system description 4 -- 1.2 Current trends 6 -- 1.2.1 America 7 -- 1.2.2 Europe 9 -- 1.2.3 Africa 13 -- 1.3 Uncertainty-based information theory 16 -- 1.3.1 Classical harmonic analysis theory 16 -- 1.3.2 Significance of uncertainty 20 -- 1.3.3 Uncertainty forms and principles 24 -- 2 Fuzziness and sonance 27 -- 2.1 Dissonance functions 28 -- 2.2 Relatedness tone system [left and right arrow] timbre 33 -- 2.2.1 Direction: timbre to tone system 33 -- 2.2.2 Direction: tone system to timbre 34 -- 3 Wavelets and nonspecificity 39 -- 3.1 Time-frequency plane 39 -- 3.1.1 Gabor's time-frequency atoms 41 -- 3.1.2 Lienard's time-frequency atoms 43 -- 3.2 Wigner-Ville transform 44 -- 3.2.1 Definition of the transform 44 --".
- catalog tableOfContents "Superparticular pentatonics 249 -- 8.2.3 Pacific Ocean region, the fuzzy tone systems 257 -- 9 Ptolemy System 261 -- 9.1 Tetrachords 261 -- 9.1.1 The set of all tetrachords 262 -- 9.1.2 Tetrachord lattice 265 -- 9.1.3 Superparticular tetrachords 266 -- 9.1.4 Symmetry: Slendro versus 12 granulation 269 -- 9.1.5 Ancient Greece 277 -- 9.2 Ptolemy System in the 20th century 283 -- 9.2.1 Ptolemy System 284 -- 9.2.2 Set of all superparticular ratios 286 -- 9.3 Commas 291 -- 9.3.1 Aestetics of ratios of small natural numbers 291 -- 9.3.2 Mean tone aesthetics 293 -- 9.3.3 Approximations of temperaments 294 -- 9.3.4 Pythagorean approximation of Just Intonation 297 -- 9.3.5 Comma 32 805/32 768 (Schizma) 302 -- A Extended lists of tone systems 319 -- A.1 Tetrachords (2 periods) 319 -- A.2 Pentatonics 325 -- A.3 Heptatonics 328 -- A.4 6, 8, 9, 10, 11 tones per octave".
- catalog title "The mathematical theory of tone systems / Ján Halus̆ka.".
- catalog type "text".