Musical Acoustics & Psychoacoustics

Donald Byrd22 Sept. 2006

Copyright © 2006, Donald Byrd

rev. 8 Sep. 2006 2

Review: Representations of Music

• Three basic forms (representations) of music– Audio: most important for most people (general

public)– MIDI files: often best/essential for some musicians,

especially for pop, rock, film/TV– Notation: often best/ essential for musicians (even

amateurs) & music scholars– Essential difference: how much explicit structure

• Music holdings of Library of Congress: over 10M items– Includes over 6M pieces of sheet music and 100K’s of

scores of operas, symphonies, etc.: all notation!

• Differences are profound

1 Sep. 2006 3

Review: Representations of Music & Audio

Audio (e.g., CD, MP3): like speech

Time-stamped Events (e.g., MIDI file): like unformatted text

Music Notation: like text with complex formatting

Digital Audio

Time-stamped Events

Music Notation

1 Sep. 2006 4

Review: Rudiments of Musical Acoustics

• Need some musical acoustics for almost anything in digital audio

• Acoustics: part of physics– Concepts like frequency & amplitude

• Psychoacoustics: part of psychology– Concepts like pitch & loudness

10 Sept. 2006 5

Review: Materials for Studying Audio

• What are interesting sounds really like?– Sine waves, etc. are boring (cf. addsynenv)– Sounds of acoustic instruments are “rich”– Vary in every way: with pitch, loudness,

time

• Musical instrument samples• Audacity audio editor

– For Windows, Mac OS 9 and X, Linux– Download from

http://audacity.sourceforge.net/

10 Sept. 2006 6

Review: Parameters of Musical Sound

• Four basic parameters of a definite-pitched musical note1. pitch: how high or low the sound is: perceptual

analog of frequency

2. duration: how long the note lasts

3. loudness: perceptual analog of amplitude

4. timbre or tone quality

• Above is decreasing order of importance for most Western music

• …and decreasing order of explicitness in CMN (Conventional Music Notation)!

rev. 11 Sept. 06 7

Musical Acoustics (1)• Acoustics involves physics• Musical (opposed to architectural, etc.) acoustics

– Frequency (=> pitch)– Amplitude (=> loudness)– Spectrum, envelope, & “other” characteristics => timbre– Partials vs. harmonics

• Psychoacoustics involves psychology/perception– Perceptual coding (for “lossy” compression)

• Timbre– Old idea (thru ca. 1960’s?): timbre produced by static

relationships of partials, plus envelope– …but attack often more distinctive than “steady state”!– Rich (interesting) sounds are complex; nothing is static– Time domain (waveform) vs. frequency domain (spectrum,

spectrogram) views

11 Sept. 2006 8

Creating Interesting Sounds (1)

• Periodic, nearly-, & non-periodic signals• Approaches to creating sounds

– Additive synthesis: like painting– Subtractive synthesis: like sculpture– Sampling: like collage– Others: modulation, physical modeling

• Most possible with analog or digital hardware, but analog is limited

rev. 13 Sept. 2006 9

Creating Interesting Sounds (2)

• Cf. “Electronic Music Tutorial” (Ishkur)• Additive Synthesis• Fourier's Theorem

– Any periodic signal => sum of harmonically-related sine waves

• Envelopes: continuous & piecewise linear– Important special case: “ADSR”– Attack, Decay, Sustain, Release

• Phase, interference, & beats– Phase by itself rarely important, but relationships are– Diagrams & demo in CECM Acoustics Primer, Sec. 8– Interference between channels or very close partials

rev. 13 Sept. 06 10

Additive Synthesis & Envelopes• addsynenv does additive synthesis of up to six partials

– Each has arbitrary partial no., starting phase, "ADSR" envelope

– Partial no. can be non-integer => not harmonic– ADSR = Attack/Decay/Sustain/Release (3 breakpoints)– …but addsynenv allows much more complex envelopes– Plays one note with waveform specified by partial nos. &

their envelopes (maybe also phases)– Simultaneously displays “spectrogram” or “sonogram”– …but not waveform– Phase in real world normally has little effect, but can be

critical in recording & digital worlds (e.g., cancellation)• Additive synthesis can’t create aperiodic (non-definite

pitch) sounds• ...or many realistic attacks

11 Sept. 2006 11

Creating Interesting Sounds (3)

• Early CCRMA (Stanford) studies of acoustic instrument sounds– Envelope for each partial with a few segments– Similar to addsynenv

• Subtractive Synthesis• Early (analog: Moog, etc.) synthesizer model• Signal source: sine/square/sawtooth (for

additive)• …or noise & filters (for subtractive)• LFO to add vibrato, tremolo, glissando, etc.• ADSR envelope for entire sound

rev. 20 Sep. 2006 12

Scholars (and others) Beware!• Plausible (at the time) assumptions

– Stomach ulcers can’t be caused by organisms (20th century)

– Men have more teeth than women (ancient)

• What you expect & what you see– Sponges, dinosaurs, etc.: discuss later

• What you expect & what you hear– Don & the Kurzweil 250 flute sound– Don, a famous musician, & K250 handclaps– Huron on what he “knew” & learned

• R. Moog at Kurzweil & piano touch

22 Sep. 2006 13

Uncompressed Audio Files are Big

• 1 byte = 8 bits (nearly always)• How much data on a CD?

– CD audio is 44,100 samples/channel/sec. * 2 bytes/sample * 2 channels = 176,400 bytes/sec., or 10.5 MByte/min.

– CD can store up to 74 min. (or 80) of music– 10.5 MByte/min. * 74 min. = 777 MBytes– Actually more: also index, error correction

data, etc.

16 Feb. 06 14

Compressed Audio: Lossless & Lossy

• Don’t confuse data compression and dynamic-range compression (a.k.a. audio level compression, limiting)

• Codec = COmpressor/DECompressor• Lossless compression

– Standard methods (LZW: .zip, etc.) don’t do much for audio

– Audio specific methods

• MLP used for DVD-Audio• Apple & Microsoft Lossless

• Lossy compression– Depends on psychoacoustics (“perceptual coding”)

13 Feb. 06 15

Specs for Some Common Audio Formats

22 Sep. 2006 16

Psychoacoustics & Perceptual Coding

• Pohlmann, Ken (2005). Principles of Digital Audio, 5th ed., Chapter 10: Perceptual Coding

• Rationale: much better data compression• Physiology of ear and critical bands

– Not fixed frequency: any sound creates one or more critical bands

• Masking– Depends on relative loudness & frequency– Noise is much better than pitched sounds

• Threshhold of hearing– Depends greatly on frequency

22 Feb. 06 17

Compressed Audio: Lossy Compression

• General method1. Divide signal into sub-bands by frequency2. Take advantage of:

• Masking (“shadows”), via amplitude within critical bands

• Threshhold of audibility (varies w/ frequency)• Redundancy among channels

• MPEG-1 layers I thru III (MP-1, 2, 3), AAC get better & better compression via more & more complex techniques– “There is probably no limit to the complexity of

psychoacoustics.” --Pohlmann, 5th ed.– However, there probably is an “asymptotic” limit to

compression!• Implemented in hardware or software codecs

rev. 20 Sep. 2006 18

Another “Analog vs. Digital” Battle

• Merton, Orren (2006, February). The Sum of All Tracks. Electronic Musician 22,2, pp. 57-63

• Discusses summing (mixing) with analog vs. digital hardware

• Tested with excellent hardware, panel of experts

• Cf. methodology to– ISO’s validation of MP3, AAC, etc.– …or ff123 et al’s of Ogg Vorbis

• But is this fair? Does it really matter?– Electronic Musician isn’t a scholarly journal– True, but in this case...