Music and Acoustics From Instrument to Computer

by Guillaume, Philippe

• ISBN13: 9781905209262
• ISBN10: 1905209266
• Edition: 1st
• Format: Hardcover
• Copyright: 2006-10-24
• Publisher: Wiley-ISTE

Summary

This overview on the nature of musical sounds, from their production by acoustic music instruments to synthesized sounds obtained with computers, includes topics such as sound propagation, Fourier and time-frequency analysis, psychoacoustics, analogue and digital-signal processing theory, computer science, and MP3 sound compression.

Author Biography

Philippe Guillaume is a professor of applied mathematics and musical acoustics at INSA Toulouse, France.

Table of Contents

Foreword	13	(4)
Chapter 1. Sounds	17	(48)
1.1. Sound propagation	17	(10)
1.1.1. A look at the physical models	17	(4)
1.1.1.1. Mass conservation	18	(2)
1.1.1.2. The Euler equation	20	(1)
1.1.1.3. The state equation	21	(1)
1.1.2. The wave equation	21	(2)
1.1.3. The Helmholtz equation	23	(2)
1.1.4. Sound intensity	25	(2)
1.2. Music theory interlude	27	(4)
1.2.1. Intervals, octave	28	(1)
1.2.2. Scientific pitch notation	28	(1)
1.2.3. Dividing the octave into twelve semitones	28	(1)
1.2.4. Diatonic scales	29	(2)
1.2.4.1. Major scale	29	(1)
1.2.4.2. Minor scales	30	(1)
1.3. Different types of sounds	31	(10)
1.3.1. Periodic sounds	32	(3)
1.3.1.1. Fourier series	34	(1)
1.3.2. Sounds with partials	35	(1)
1.3.3. Continuous spectrum sounds	36	(1)
1.3.4. Noise	37	(4)
1.4. Representation of sound	41	(8)
1.4.1. Time or frequency analysis, discrete Fourier transform	42	(2)
1.4.2. Time-frequency analysis, the spectrogram	44	(5)
1.5. Filtering	49	(7)
1.5.1. Discrete spectrum	49	(4)
1.5.1.1. Transfer function	50	(1)
1.5.1.2. Impulse response	51	(2)
1.5.2. Continuous spectrum	53	(1)
1.5.3. Ideal low-pass, band-pass and all-pass filters	53	(3)
1.6. Study problems	56	(2)
1.6.1. Normal reflection on a wall (*)	56	(1)
1.6.2. Comb filtering produced by a microphone located near a wall (**)	56	(1)
1.6.3. Summing intensities (***)	57	(1)
1.6.4. Intensity of a standing wave (**)	58	(1)
1.6.5. Sound of a siren (*)	58	(1)
1.7. Practical computer applications	58	(7)
1.7.1. First sound, vectors	58	(1)
1.7.2. Modifying the parameters: the command file	59	(1)
1.7.3. Creating more complex sounds: using functions	60	(1)
1.7.3.1. Noise and siren interlude	61	(1)
1.7.4. Analysis	61	(2)
1.7.4.1. Time analysis	62	(1)
1.7.4.2. Frequency analysis	62	(1)
1.7.4.3. Time-frequency analysis	63	(1)
1.7.5. Filtering	63	(2)
Chapter 2. Music Instruments	65	(50)
2.1. Strings	66	(6)
2.1.1. Free vibrations of a string	66	(3)
2.1.2. Beats, chords and consonance	69	(3)
2.2. Bars	72	(5)
2.2.1. Bar fixed at both ends	73	(2)
2.2.2. Bar clamped at one end	75	(2)
2.3. Membranes	77	(2)
2.4. Tubes	79	(10)
2.4.1. Pressure control	81	(4)
2.4.1.1. Response to a harmonic excitation	81	(1)
2.4.1.2. The resonance effect	82	(2)
2.4.1.3. Natural modes	84	(1)
2.4.1.4. The resulting sound	84	(1)
2.4.2. Speed control	85	(3)
2.4.2.1. Response to a harmonic excitation	85	(2)
2.4.2.2. Resonance and natural modes	87	(1)
2.4.2.3. Comments on phases	87	(1)
2.4.3. Tuning	88	(1)
2.5. Timbre of instruments	89	(9)
2.5.1. Nature of the spectrum	89	(6)
2.5.1.1. Harmonics or partials, the piano's inharmonicity	90	(1)
2.5.1.2. Richness in higher harmonics	91	(2)
2.5.1.3. Different harmonics distributions	93	(1)
2.5.1.4. The purpose of the resonator	94	(1)
2.5.2. Envelope of the sound	95	(3)
2.5.2.1. Calculation of the envelope	96	(1)
2.5.2.2. Using several envelopes	97	(1)
2.6. Study problems	98	(12)
2.6.1. Vibrations of a string (general case) (**)	98	(2)
2.6.2. Plucked string (*)	100	(1)
2.6.3. Bow drawn across a string (*)	100	(1)
2.6.4. String reduced to one degree of freedom (**)	101	(1)
2.6.5. Coupled string-bridge system and the remanence effect (***)	102	(2)
2.6.6. Calculation of the inharmonicity of a real string (***)	104	(2)
2.6.7. Coincidence frequency of a wave in a board (***)	106	(1)
2.6.8. Resonance of the bourdon (**)	107	(1)
2.6.9. Resonance of a cylindrical dual controlled tube (**)	108	(1)
2.6.10. Resonance of a conical tube (1) (**)	109	(1)
2.6.11. Resonance of a conical tube (2) (**)	110	(1)
2.7. Practical computer applications	110	(5)
2.7.1. Create your synthesizer	110	(2)
2.7.1.1. Write your instrument function	111	(1)
2.7.1.2. Add an envelope	111	(1)
2.7.1.3. And play your instrument	112	(1)
2.7.2. Modify the timbre of your instrument	112	(1)
2.7.3. Remanent sound	112	(3)
Chapter 3. Scales and Temperaments	115	(12)
3.1. The Pythagorean scale	116	(1)
3.2. The Zarlino scale	117	(1)
3.3. The tempered scales	118	(3)
3.3.1. Equal temperament	119	(1)
3.3.2. A historical temperament	119	(1)
3.3.3. Equal temperament with perfect fifth	120	(1)
3.3.4. The practice of tuners	120	(1)
3.3.5. The practice of musicians	121	(1)
3.4. A brief history of A4	121	(1)
3.5. Giving names to notes	122	(1)
3.6. Other examples of scales	123	(1)
3.7. Study problems	123	(2)
3.7.1. Frequencies of a few scales (***)	123	(1)
3.7.2. Beats of the fifths and the major thirds (*)	123	(2)
3.8. Practical computer applications	125	(2)
3.8.1. Building a few scales	125	(1)
3.8.2. Listening to beats	125	(2)
Chapter 4. Psychoacoustics	127	(14)
4.1. Sound intensity and loudness	127	(3)
4.1.1. The phon	128	(1)
4.1.2. The sone	129	(1)
4.2. The ear	130	(1)
4.3. Frequency and pitch	131	(5)
4.3.1. The mel scale	132	(1)
4.3.2. Composed sounds	133	(1)
4.3.2.1. Pitch of sounds composed of harmonics	133	(1)
4.3.2.2. Pitch of sounds composed of partials	133	(1)
4.3.3. An acoustic illusion	134	(2)
4.4. Frequency masking	136	(2)
4.5. Study problems	138	(1)
4.5.1. Equal-loudness levels (**)	138	(1)
4.5.2. Frequency masking (**)	138	(1)
4.5.3. Perpetually ascending sound (**)	138	(1)
4.6. Practical computer applications	138	(3)
4.6.1. Frequency masking	138	(1)
4.6.2. Perpetually ascending scale	138	(3)
Chapter 5. Digital Sound	141	(28)
5.1. Sampling	143	(12)
5.1.1. The Nyquist criterion and the Shannon theorem	145	(7)
5.1.1.1. Case of a sinusoidal signal	145	(2)
5.1.1.2. General case	147	(1)
5.1.1.3. Consequences	148	(1)
5.1.1.4. Theoretical impossibility	148	(1)
5.1.1.5. What happens if the Nyquist criterion is not met?	148	(4)
5.1.2. Quantization	152	(2)
5.1.2.1. Error due to quantization	153	(1)
5.1.3. Reconstruction of the sound signal	154	(1)
5.2. Audio compression	155	(5)
5.2.1. Psychoacoustic compression	155	(4)
5.2.2. Entropy compression	159	(1)
5.3. Digital filtering and the Z-transform	160	(4)
5.3.1. Digital filtering	160	(1)
5.3.2. The Z-transform	161	(3)
5.3.2.1. Definition	161	(1)
5.3.2.2. Effect of a delay	162	(1)
5.3.2.3. Filtering and Z-transform	163	(1)
5.4. Study problems	164	(3)
5.4.1. Nyquist criterion (*)	164	(1)
5.4.2. Aliasing of an ascending sound (*)	165	(1)
5.4.3. Another example of reconstruction (***)	165	(1)
5.4.4. Elementary filter bank (**)	166	(1)
5.5. Practical computer applications	167	(2)
5.5.1. Spectrum aliasing	167	(1)
5.5.2. Quantization noise	168	(1)
Chapter 6. Synthesis and Sound Effects	169	(22)
6.1. Synthesis of musical sounds	170	(5)
6.1.1. Subtractive synthesis	170	(1)
6.1.2. Additive synthesis	171	(1)
6.1.3. FM synthesis	171	(3)
6.1.4. Synthesis based on the use of sampled sounds	174	(1)
6.2. Time effects: echo and reverberation	175	(4)
6.2.1. Simple echo	175	(1)
6.2.2. Multiple echo	176	(1)
6.2.3. Reverberation	177	(2)
6.2.3.1. Using the impulse response	177	(1)
6.2.3.2. Using echoes and all-pass filters	178	(1)
6.3. Effects based on spectrum modification	179	(7)
6.3.1. The 'Wah-wah' effect	180	(2)
6.3.1.1. An example of a band-pass filter	180	(2)
6.3.2. AM or FM type sound effects	182	(4)
6.3.2.1. Vibrato	183	(1)
6.3.2.2. Leslie effect	184	(2)
6.4. Study problems	186	(2)
6.4.1. The Doppler effect (**)	186	(1)
6.4.2. FM and Chowning (***)	187	(1)
6.5. Practical computer applications	188	(3)
6.5.1. Sound synthesis	188	(1)
6.5.2. Chowning synthesis	188	(1)
6.5.3. Reverberation	189	(1)
6.5.4. Vibrato	189	(1)
6.5.5. The Leslie effect	189	(2)
Bibliography	191	(2)
Index	193