Structured Additive Synthesis: Towards a Model of Sound Timbre and Electroacoustic Music Forms M

Home , Additive synthesis

Structured Additive Synthesis: Towards a Model of Sound Timbre and Electroacoustic Music Forms M. Desainte-Catherine, Sylvain Marchand

To cite this version:

M. Desainte-Catherine, Sylvain Marchand. Structured Additive Synthesis: Towards a Model of Sound Timbre and Electroacoustic Music Forms. Proceedings of the International Computer Music Confer- ence (ICMC99), Oct 1999, China. pp.260–263. hal-00308406

HAL Id: hal-00308406 https://hal.archives-ouvertes.fr/hal-00308406 Submitted on 30 Jul 2008

HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés.

Structured Additive Synthesis Towards a Mo del

of Sound Timbre and Electroacoustic Music Forms

Myriam DesainteCatherine myriamlabriubordeauxfr

Sylvain Marchand smlabriubordeauxfr

SCRIME LaBRI Universite Bordeaux I

cours de la Liberation F Talence Cedex France

Abstract

We have develop ed a sound mo del used for exploring sound timbre This mo del is called Structured

Additive Synthesis or SAS for short It has the exibility of additive synthesis while addressing

the fact that basic additive synthesis is extremely dicult to use directly for creating and editing

sounds SAS consists of a complete abstraction of sounds according to only four parameters

amplitude frequency color and warping These parameters are inspired by the vo cabulary of

comp osers of electroacoustic music as well as by the literature and constitute a solid base for

investigating scientic research on the notion of timbre Several analyses of electroacoustic pieces

have b een p erformed in collab oration b etween scientists and musicians We have identied the need

for a certain numb er of manipulations of sound that we have determined to b e straightforward in

our mo del Applications of the SAS mo del are numerous A new language for musical comp osition

has b een implemented and should provide a way to validate and enrich the mo del

tween parameters of dierent parts of the piece Intro duction

When the piece is written the analysis is

The SCRIME is an organization for scientic

based on the musical score which provides the ini

researchers in computer science at the Univer

tial segmentation Electroacoustic musical pieces

sity and music comp osers of the Conservatoire

constitute a very sp ecial case b ecause they are not

to collab orate Pro jects of the SCRIME should

written Their supp ort is magnetic or numeric

not only b e scientically valid but also musically

Among the analyses identied by Francois De

relevant Research pro jects of this structure are

lalande Del we chose to p erform the p oietic

mainly situated in the eld of the assistance for

pro ductionoriented and aesthesic reception

comp osition of electroacoustic music We ob

oriented ones

serve and try to understand actual practices of

electroacoustic comp osers in order to provide our

Poietic analysis is based on pro duction Such

research in sound and music mo deling with new

an analysis can b e carried out in collab oration

elements One motivation is the study of sound

with the comp oser of the piece to analyze Its

timbre from a p erceptual and musical p oint of

ob jective is to study the musical discourse in or

view in collab oration with psychoacousticians

der to nd out information ab out the pro duction

Another motivation is to provide comp osers with

of the piece that is the to ols and the practices

to ols well adapted to their actual needs

that were used in order to build the piece

In this pap er we present three research sub

Aesthesic analysis is based on listening Such

jects that are relevant in order to reach our ob

an analysis can b e p erformed by a comp oser or

jectives The second section presents the analy

by a listener who is very familiar with electro

sis of electroacoustic music which is studied in

acoustic music or by conducting exp eriments in

close collab oration with comp osers The third

volving several listeners This kind of analysis

section presents the SAS sound mo del that has

provides information on the way listeners under

b een implemented and is b een validated in collab

stand electroacoustic music

oration with psychoacousticians and comp osers

As a matter of fact only p oietic and aesthesic

The fourth section shows the applications of this

analyses provide information concerning mo dels

mo del in comp ositional and educational contexts

that are in the comp osers mind when he com

p oses music or when he listens to the music We

Music Analysis

conducted the following two analyses in collab o

ration with comp osers

A musical analysis of a piece consists rst in

segmenting the piece in order to discover a tem We p erformed an aesthesic analysis of the sec

p oral organization b etween several sound ob jects ond movement Balancement of the Variations

Musical discourse can b e analyzed on the basis of p our une p orte et un soupir by Pierre Henry

those sound ob jects by p ointing out relations b e this work has b een carried out in collab oration

orem which states that any p erio dic function can with the comp oser Edgar Nicouleau DCN In

b e mo deled as a sum of sinusoids at various am that movement inexions of the grating do or are

plitudes and harmonic frequencies For pseudo very close to voice mo dulation so that they re

p erio dic sounds these amplitudes and frequen mind listeners of melo dic rhythmic and dynamic

cies evolve slowly with time controlling a set structures that are usually analyzed in that case

of pseudosinusoidal oscillators commonly called Sound ob jects of the piece have b een itemized

partials The audio signal a can b e calculated and then group ed in several families A com

from these additive parameters using the follow mon formalism p ermits the description of the evo

ing equations lutions of frequencies durations and amplitudes

for all the sound ob jects This analysis leads to

quite classical results since it involves wellknown

at a t cos t

structures like melo dy dynamic and rhythm Of

p p

p=1

course the case of the analyzed piece is very par

ticular and such results cannot b e obtained with

any electroacoustic piece Anyway this research

t f u du

p p p

may continue with the study of the timbre struc

tures

where P is the numb er of partials and f a and

p p

We also p erformed a p oietic analysis of the

are resp ectively the instantaneous frequency

second movement of La chute dIcare by Jean

amplitude and phase of the pieth partial The

Michel Rivet this work has b een carried out in

P pairs f a are the parameters of the addi

p p

collab oration with him DCR A rst seg

tive mo del and represent p oints in the frequency

mentation is prop osed as well as a classication

amplitude space as shown in gure

of the sounds according to the pro duction of the

Any sound can b e faithfully synthesized in real

piece Then several segmentations based on this

time from the mo del equations containing these

classication are studied and a temp oral struc

parameters The realtime synthesis has b een im

ture is discovered This analysis has p ointed out

plemented in the ReSp ect software to ol MS

structures that were p ertinent for the comp oser

The diculty is then to obtain these parame

For example a classication of sounds was obtain

ters from real existing sounds For that reason

according to the comp osers criteria for cho osing

we have develop ed an analysis metho d capable

one sound rather than another Those criteria

of converting sampled sounds into the SAS pa

may vary from one comp oser to another and ac

rameters implemented in the InSp ect program

cording to his ob jectives so that it is necessary to

MS It is of course p ossible to eliminate anal

make the same kind of collab oration with several

ysis entirely and create new sounds directly us

comp osers The ob jective is on the one hand

ing the parameters of our mo del This is indeed

to nd out some musical elements which could

p ossible b ecause there is a close corresp ondence

b e useful to several comp osers and to help us in

b etween these parameters and real music p ercep

sound mo deling on the other hand

tion

All these analyses of electroacoustic pieces

have b een p erformed in collab oration b etween sci

entists and musicians of the SCRIME We have

amplitude

identied the need for a certain numb er of manip

ulations of sounds Among these are mo dulation

mixing ltering time stretching crosssynthesis

morphing as well as new ways to create hybrid

f a

p p

sounds The problem was yet to nd a sound

mo del allowing the comp osers to p erform these

manipulations in an intuitive and musical way

The SAS Mo del

The Structured Additive Synthesis SAS

mo del is a sp ectral sound mo del based on additive

frequency

synthesis The SAS parameters are inspired by

time

the vo cabulary of comp osers of electroacoustic

music as well as by the literature We prop ose to

fo cus on the p erception of the sound rather than

Figure the sp ectrum of an harmonic sound

its physical cause in order to unify sound mi

croscopic and music macroscopic We prop ose

as well to consider the musical intention of the

Structured Additive Synthesis

instrumentalist instead of his physical action on

The additive synthesis mo del is extremely dif

the instrument

cult to use directly for creating and editing

Additive Synthesis

sounds The reason for this diculty is the huge

Additive synthesis is the original sp ectrum numb er of mo del parameters which are only re

mo deling technique It is ro oted in Fouriers the motely related to musical parameters as p erceived

can not pro duce noises or transients Recent by a listener The Structured Additive Synthesis

mo deling techniques like SMS Ser Sp ectral SAS mo del has the exibility of additive syn

Mo deling Synthesis and STN VM Si thesis while addressing these problems It im

nusoidsNoiseTransients were prop osed to ex p oses constraints on the additive parameters giv

tend the additive mo del The SAS mo del can b e ing birth to structured parameters as close to

extended to include noises since every noise can p erception and musical terminology as p ossible

b e mo deled as a ltered or colored white noise thus reintro ducing a p erceptive and musical con

at a certain amplitude The amplitude and color sistency back into the mo del The remaining of

parameters exist also for noises and are sucient this section quickly presents the SAS mo del An

to dene any of them White noise has a white extended presentation can b e found in DCM

color C and every noise named after an

Structured Parameters

analogy with a light sp ectrum matches this cor

SAS consists of a complete abstraction of

resp ondence of terminology On the other hand

sounds according to only four physical parame

very short sounds like transients can not b e rep

ters functions closely related to p erception

resented in this sp ectral mo del

Amplitude A time amplitude

Human b eings p erceive amplitude on a logarith

Applications of the Mo del

mic scale Amplitude can b e calculated from the

SAS constitutes a solid base for investigat

a t additive parameters like this At

p=1

ing scientic and musical research on the no

Calculating the volume in dB from the amplitude

tion of timbre Applications of the mo del are

is easy l og

0dB

numerous A new sound synthesis language for

Frequency F time frequency

musical comp osition has b een implemented and

The way of calculating the frequency from the ad

should provide a way to validate and enrich the

ditive parameters is trickier and can b e found in

mo del A p edagogical to ol for earlylearning

DCM Anyway for harmonic sounds F coin

electroacoustic music is based on this mo del It

cides with the fundamental p ossibly missing or

provides sound controls that are wellsuited for

virtual The frequency is also p erceived on a

young children b ecause they are based on sound

logarithmic scale For example the MIDI pitch

listening rather than signal synthesis

is a function of frequency l og

440

Creation

Color C frequency time amplitude

The SAS parameters are closely related to the

Color coincides with an interp olated version of

musical ones Figure shows the french a vowel

the sp ectral envelop e Ris We call it color by

sung on three notes We can clearly see the dy

analogy b etween audible and visible sp ectra This

namic and the melo dy of the song resp ectively in

analogy is already wellknown for noises white

the A and F sound parameters The arbitrary

blue etc

distinction b etween music and sound parameters

Warping W frequency time frequency

simply disapp ears

Generally the partial frequencies are not exactly

multiples of the fundamental frequency F Warp

ing gives the real frequency of a partial from the

theoretical one it should have had if the sound

had b een harmonic Of course for all harmonic

sounds W t Id that is t W f t f

Structured Equations

From the four structured parameters we can

calculate the the audio signal a

C W pF t t tcos t

p=1

at At

C W pF t t t

p=1

max

cg where P max fb

F (t)

F is the highest audible frequency and

max

t W pF u u du

p p

W Id

These equations are the structured version of

equations and All these equations require

Figure singing voice in the SAS mo del

approximately the same computation time

Noise and Transients Most of musical transformations can b e sim

SAS can faithfully repro duce a wide vari ply expressed as SAS parameter variations De

ety of sounds as additive synthesis do es p ending on the rate of these variations com

provided they are monophonic However it p osers can mo dify b oth the microstructure and

his In order to use SAS for the whole comp o the macrostructure of musical pieces in a multi

sitional pro cess a hierarchic mo del must b e de scale comp osition Vag DCM When the

signed on the top of SAS and incorp orated in the variations are slow enough they can b e written

language on a score This is the domain of writing When

Again the SCRIME allows scientists and mu they are to o fast to b e written we enter the con

sicians to help each other Comp osers lead re trol or interpretation domain Figure gives

searchers to understand their musical practices a brief summary of the relations b etween musi

while researchers try to provide comp osers with cal terminology and SAS for these two domains

real to ols for assistance for comp osition in har Multiscale comp osition using SAS can b e found

mony with their musical needs in DCM

References

Writing Control

BS M Balaban and C Samoun Hierarchy

Hz Hz

Time and Inheritance in Music Mo del

Amplitude Dynamic Tremolo

ing Languages of design

Crescendo Roughness

DCM Myriam DesainteCatherine and Syl

Frequency Melo dy Vibrato

vain Marchand Vers un mo dele p our

Trill Scintillating

unier musique et son dans une com

Color Orchestral Sp ectral

p osition multiechelle In Proceedings of

Sonority Envelop e

the Journees dInformatique Musicale

Warping Chords Sp ectral

JIM pages

Aggregates Harmonicity

DCN M DesainteCatherine and Edgard

Nicouleau Segmentation et formali

Figure some relations b etween musical

sation dune o euvre electroacoustique

terminology and the four SAS parameters

Submitted to Musurgia

for two ranges of variation rates

DCR M DesainteCatherine and JM Rivet

A la recherche de mo deles p oetiques To ease the comp osition with SAS symb olic

Submitted to Musurgia structures must b e added on the top of the sub

symb olic sound mo del like the hierarchic temp o

Del Francois Delalande En labsence de

ral organization of musical structures prop osed by

partition Analyse Musicale pages

Balaban BS

Education

MS S Marchand and R Strandh In

Since SAS is based on p erceptive and musical

Sp ect and ReSp ect sp ectral mo del

criteria we think it is wellsuited for computer

ing analysis and realtime synthesis

assisted earlylearning music Dolabip is a multi

software to ols for researchers and com

eld pro ject whose ob jective is the creation of

p osers In Proceedings of the Inter

a metainstrument to b e used for earlylearning

national Computer Music Conference

electroacoustic music Practical exp erience in

ICMC Beijing

nursery scho ol is lead by a musician a teacher

a psychologist and a music teaching sp ecialist

Ris JC Risset Timbre et synthese de

This pro ject is comp osed mainly of two parts

sons Analyse musicale pages

The rst one is an hardware device consisting of

p otentiometers and buttons wellsuited for ma

Ser Xavier Serra Musical Signal Process

nipulation by children The second one is a soft

ing chapter Musical Sound Mo deling

ware to ol pro ducing sounds according to the data

with Sinusoids plus Noise pages

sent by the device The software to ol allows the

Studies on New Music Research

user to change the way the data get interpreted

Swets Zeitlinger Lisse the Nether

The development teams of the software and hard

lands

ware parts build to ols that are necessary for ex

p erimenting the p edagogical program

Vag H Vaggione Transformations mor

phologiques In Proceedings of

Conclusion

the Journees dInformatique Musicale

In this pap er we have presented the Struc

JIM page G

tured Additive Synthesis SAS mo del This

mo del represents sounds as temp oral evolutions

VM Tony S Verma and Teresa HY

of parameters close to p erception and musical ter

Meng Time Scale Mo dication Us

minology thus favoring the unication of sound

ing a SinesTransientsNoise Signal

and music at a subsymb olic level

Mo del In Proceedings of the Digi

We are developing a sound synthesis language

tal Audio Eects Workshop DAFX

based on SAS that has b een used by JeanMichel

Barcelona pages

Rivet to pro duce interesting sounds in a piece of