ï~~
TECHNIQUES of
TIMBRAL INTERPOLATION
Ycc-On Lo
Hearing and Speech Sciences
and CCRMA
Stanford University
ABSTRACT
The range of acoustic waveforms in nature is too wide to be described
by any particular set of upecial functions. The ear, which has successfully adapted itself to its environment through the ages of evolution,
is too versatile to limit its capability to short-time Fourier analysis or
judgments based only on some mean-squared criterion. To understand
timbre and to succeed in manipulating it, we propose a model of timbre that emphasizes its kinematic nature and provides a certain unified
perspective for viewing timbre and interpolation of timbres. From this
model, we derive a new analysis/synthesis algorithm that is flexible for
timbral manipulation and computation-efficient. We further propose a
tree data structure to control and refine the process of interpolation.
The hierarchy provides a systematic method for making trade-off decisions on fidelity versus data rate. Finally, we propose a parallelepiped
model of interpolation.
INTRODUCTION
(a) What des itimtbre interpoaltion involve?.A hlackhox view: (1) inpat: feedinig two or inure sound-, called tlihetiti soinils otr aiciors.
itit llackliur called the iiiterptilatcr;
(2) auaalgeise: laving the interpotlater cearnctcoth aliouit the souiuats;
tatd
(3) output: lhaving the Oitterlolator create a scltttiice if tiew t:cits
nerorinug to the ktnowledge (data) olitained iin (2) mat a series 4 ruiles
(algitritltuns) which attttihit to reflect tIe pJtv~itcoutstic cutistraitits
of (i) tin lietwuetitiess criterion (iriirahihity ly sititturitv jnlr;iuwiit),
(ii) the- s tootlitess criterion (iu-categouric~al trtisitiot), idti (iii) the
colt'sivtitess criterion (Idetoleditess;itltiin vaut soundi).
(b) Whyj iterpolate?
(1) For music: Every siuccessfiul set uf iustcrpoilated bob-bes iit tii tinIlly useful collection of tteriatls fir tittisicail eiiutpoisitiini. A c~;itiirailly
successful iiiterinilatioii strategy can tint only fulfil the mtilt:# nt edttc
dream of Scluoi-oherg aboiuit TKlnogfarltuccottijisi ttuInii t also illo~ril
at More aitiitinus uxjtloitntion of tiiuitres that ititeract with tisititl di.
uiinsns usin tile-Curi(( of a sptatii- titttlural tuivirciuuitit tiitil' cirn rgiiig
teclotgy if celular aittittita sit that Lit!s lifiitig o titiniliris iii a ciii piusitim unlie rea:dized tl (iitly inttut'hitt iii Shta:ttittte. Even sitliiu
thme intri'imolest citirreuit coiiittr triuttlogy si +ci ssft1iititirili dilo
teicluns wi tllsodii stittilesiratl totihlel~tlit-jig it ti e thit ii- tinisita;l
manterial intoi the tratlitiiilWe sti-iui ntitisical u-nvirtnttttit. Sitmilairly, it
witidl urictithe etinijuiser's risintircts vlten lie otr shen dsire~s Liiliritig
poetic sjiietclttit a atiusical itttisititi. Sircilitcnlly, thii' uitliiir lhas
beiso iidieeply inspireilby he ii tttral rirtiuss if stinit oititit Cliitise
Poetry that lie thiniks that thie' iuti-try itself is inthi: (wltethtir the is tenier knows ChLtituse orirmutt-after:ill, a sliuken IiL55LIWg iii itty ltiitige~
strippjed oif its sirtautties$ is iitliting lint a cciuiitiuositioii of simtils):t
finely - raftiti tintiliradcuiu sitiuins; that certaii titdiri~ o wtilil it1,igtt
tlut In'antiftil inuigi~ry tiC Liii nit-try (scI. ltat i t ihotithits hinl it w
(Aiism cutt(luf "see" ttieiniagi~ry ); atI cthat i iiitcri~nt.iuiiii na:tltiiue
waindleiPrtivitli.great ecittrid for ttitra stinig anti ltirtiuiiiitgIiittuteti
the liusttry itself andtIe iiiitres that siurriutuil attitl lttiucus it.
(2) Par jusge/ui:ituiutis.: WeWtony learn ime alutt t ittilures ingi t
tmitl flutw iii particnlur they art' riltud (i) Wei tow h1-ait s1 ttitig
alti t Lthe giuuuttry if iuire slat-e liptheuth:illu iatu l hiy ititltia
btit ccitectiuig kttt tittilinis. Fir itititici, bli inlitig the it-tut lit
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241 ICMC 86 Proceedings
