guerino mazzola (fall 2015 © ): introduction to music technology iiisymbolic reality iii.2 (we nov...
TRANSCRIPT
![Page 1: Guerino Mazzola (Fall 2015 © ): Introduction to Music Technology IIISymbolic Reality III.2 (We Nov 16) Denotators I—definition of a universal concept space](https://reader035.vdocuments.site/reader035/viewer/2022062423/5697bfab1a28abf838c9b2ba/html5/thumbnails/1.jpg)
Gue
rino
Maz
zola
(F
all 2
015
Gue
rino
Maz
zola
(F
all 2
015©©
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
IIIIII Symbolic RealitySymbolic Reality
III.2 III.2 (We Nov 16) (We Nov 16) Denotators I—definition of a universal concept space Denotators I—definition of a universal concept space and notationsand notations
![Page 2: Guerino Mazzola (Fall 2015 © ): Introduction to Music Technology IIISymbolic Reality III.2 (We Nov 16) Denotators I—definition of a universal concept space](https://reader035.vdocuments.site/reader035/viewer/2022062423/5697bfab1a28abf838c9b2ba/html5/thumbnails/2.jpg)
Gue
rino
Maz
zola
(F
all 2
015
Gue
rino
Maz
zola
(F
all 2
015©©
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
Sylvain Auroux: Sylvain Auroux: La sémiotique des encyclopédistesLa sémiotique des encyclopédistes (1979) (1979)
Three encyclopedic caracteristics of general validity:Three encyclopedic caracteristics of general validity:
• unité (unity)unité (unity) grammar of synthetic discourse grammar of synthetic discourse philosophyphilosophy
• intégralité (completeness)intégralité (completeness) all factsall facts dictionarydictionary
• discours (discourse)discours (discourse) encyclopedic orderingencyclopedic ordering representationrepresentation
Jean le Rond D‘AlembertJean le Rond D‘Alembert Denis DiderotDenis Diderot17511751
![Page 3: Guerino Mazzola (Fall 2015 © ): Introduction to Music Technology IIISymbolic Reality III.2 (We Nov 16) Denotators I—definition of a universal concept space](https://reader035.vdocuments.site/reader035/viewer/2022062423/5697bfab1a28abf838c9b2ba/html5/thumbnails/3.jpg)
Gue
rino
Maz
zola
(F
all 2
015
Gue
rino
Maz
zola
(F
all 2
015©©
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
ramification typeramification type~ completeness~ completeness
reference ~ unityreference ~ unity
linear ordering ~ discourselinear ordering ~ discourse
![Page 4: Guerino Mazzola (Fall 2015 © ): Introduction to Music Technology IIISymbolic Reality III.2 (We Nov 16) Denotators I—definition of a universal concept space](https://reader035.vdocuments.site/reader035/viewer/2022062423/5697bfab1a28abf838c9b2ba/html5/thumbnails/4.jpg)
Gue
rino
Maz
zola
(F
all 2
015
Gue
rino
Maz
zola
(F
all 2
015©©
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
(Kritik der reinen Vernunft, B 324)(Kritik der reinen Vernunft, B 324)
Man kann einen jeden Begriff,Man kann einen jeden Begriff,einen jeden Titel, einen jeden Titel,
darunter viele Erkenntnisse gehören,darunter viele Erkenntnisse gehören,einen logischen Ort nennen.einen logischen Ort nennen.
You may call any concept, You may call any concept, any title (topic) any title (topic)
comprising multiple knowledge,comprising multiple knowledge,a logical site.a logical site.
Immanuel KantImmanuel Kantconcepts are points in concept spaces
concepts are points in concept spaces
![Page 5: Guerino Mazzola (Fall 2015 © ): Introduction to Music Technology IIISymbolic Reality III.2 (We Nov 16) Denotators I—definition of a universal concept space](https://reader035.vdocuments.site/reader035/viewer/2022062423/5697bfab1a28abf838c9b2ba/html5/thumbnails/5.jpg)
Gue
rino
Maz
zola
(F
all 2
015
Gue
rino
Maz
zola
(F
all 2
015©©
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
<denotator_name<denotator_name><form_name>(><form_name>(coordinates) coordinates)
<form_name><type>(coordinator)<form_name><type>(coordinator)
FF11
FFnn
DD11
DDs-1s-1
DDss
formform
denotatordenotator
![Page 6: Guerino Mazzola (Fall 2015 © ): Introduction to Music Technology IIISymbolic Reality III.2 (We Nov 16) Denotators I—definition of a universal concept space](https://reader035.vdocuments.site/reader035/viewer/2022062423/5697bfab1a28abf838c9b2ba/html5/thumbnails/6.jpg)
Gue
rino
Maz
zola
(F
all 2
015
Gue
rino
Maz
zola
(F
all 2
015©©
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
Simple Forms = Elementary Spaces Simple Forms = Elementary Spaces
![Page 7: Guerino Mazzola (Fall 2015 © ): Introduction to Music Technology IIISymbolic Reality III.2 (We Nov 16) Denotators I—definition of a universal concept space](https://reader035.vdocuments.site/reader035/viewer/2022062423/5697bfab1a28abf838c9b2ba/html5/thumbnails/7.jpg)
Gue
rino
Maz
zola
(F
all 2
015
Gue
rino
Maz
zola
(F
all 2
015©©
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
<form_name><type>(coordinator)<form_name><type>(coordinator)
example:example:‘‘Loudness’Loudness’
<denotator_name><denotator_name><form_name><form_name>(coordinates) (coordinates)
example:example:‘‘mezzoforte’mezzoforte’
A = A = STRGSTRG = = set of strings (words) set of strings (words) from a given alphabetfrom a given alphabet
a string of lettersa string of letters
example:example:mfmf
SimpleSimple
Simple 1Simple 1
![Page 8: Guerino Mazzola (Fall 2015 © ): Introduction to Music Technology IIISymbolic Reality III.2 (We Nov 16) Denotators I—definition of a universal concept space](https://reader035.vdocuments.site/reader035/viewer/2022062423/5697bfab1a28abf838c9b2ba/html5/thumbnails/8.jpg)
Gue
rino
Maz
zola
(F
all 2
015
Gue
rino
Maz
zola
(F
all 2
015©©
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
<form_name><type>(coordinator)<form_name><type>(coordinator)
example:example:‘‘HiHat-State’HiHat-State’
<denotator_name><denotator_name><form_name><form_name>(coordinates) (coordinates)
example:example:‘‘openHiHat’openHiHat’
A = Boole = {NO, YES} (boolean)A = Boole = {NO, YES} (boolean)
boolean valueboolean value
example:example:YESYES
SimpleSimple
Simple 2Simple 2
![Page 9: Guerino Mazzola (Fall 2015 © ): Introduction to Music Technology IIISymbolic Reality III.2 (We Nov 16) Denotators I—definition of a universal concept space](https://reader035.vdocuments.site/reader035/viewer/2022062423/5697bfab1a28abf838c9b2ba/html5/thumbnails/9.jpg)
Gue
rino
Maz
zola
(F
all 2
015
Gue
rino
Maz
zola
(F
all 2
015©©
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
<form_name><type>(coordinator)<form_name><type>(coordinator)
example:example:‘‘Pitch’Pitch’
<denotator_name><denotator_name><form_name><form_name>(coordinates) (coordinates)
example:example:‘‘thisPitch’thisPitch’
A = integers A = integers Ÿ Ÿ == {...-2,-1,0,1,2,3,...}{...-2,-1,0,1,2,3,...}
integer numberinteger numberfromfrom Ÿ Ÿ
example:example:b-flat ~ 58b-flat ~ 58
SimpleSimple
Simple 3Simple 3
![Page 10: Guerino Mazzola (Fall 2015 © ): Introduction to Music Technology IIISymbolic Reality III.2 (We Nov 16) Denotators I—definition of a universal concept space](https://reader035.vdocuments.site/reader035/viewer/2022062423/5697bfab1a28abf838c9b2ba/html5/thumbnails/10.jpg)
Gue
rino
Maz
zola
(F
all 2
015
Gue
rino
Maz
zola
(F
all 2
015©©
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
<form_name><type>(coordinator)<form_name><type>(coordinator)
example:example:‘‘Onset’Onset’
<denotator_name><denotator_name><form_name><form_name>(coordinates) (coordinates)
example:example:‘‘myOnset’myOnset’
A = A = real (= decimal) numbersreal (= decimal) numbers — —
real numberreal numberfromfrom — —
example:example:11.2511.25
SimpleSimple
Simple 4Simple 4
![Page 11: Guerino Mazzola (Fall 2015 © ): Introduction to Music Technology IIISymbolic Reality III.2 (We Nov 16) Denotators I—definition of a universal concept space](https://reader035.vdocuments.site/reader035/viewer/2022062423/5697bfab1a28abf838c9b2ba/html5/thumbnails/11.jpg)
Gue
rino
Maz
zola
(F
all 2
015
Gue
rino
Maz
zola
(F
all 2
015©©
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
example:example:‘‘Eulerspace’Eulerspace’
example:example:‘‘myEulerpoint’myEulerpoint’
Extend to more general Extend to more general mathematical spaces mathematical spaces MM!!
point inpoint inMM
e.g. Euler pitch e.g. Euler pitch spaces....spaces....
<form_name><type>(coordinator)<form_name><type>(coordinator)
<denotator_name><form_name>(coordinates) <denotator_name><form_name>(coordinates)
SimpleSimple
octave
fifth
third
Simple +Simple +
![Page 12: Guerino Mazzola (Fall 2015 © ): Introduction to Music Technology IIISymbolic Reality III.2 (We Nov 16) Denotators I—definition of a universal concept space](https://reader035.vdocuments.site/reader035/viewer/2022062423/5697bfab1a28abf838c9b2ba/html5/thumbnails/12.jpg)
Gue
rino
Maz
zola
(F
all 2
015
Gue
rino
Maz
zola
(F
all 2
015©©
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
<form_name><type>(coordinator)<form_name><type>(coordinator)
A module A module MM over a ring over a ring RR (e.g., a (e.g., a real vector space)real vector space)
SimpleSimple
Examples:Examples:
• M = M = ——33 space for space music description space for space music description• M = M = ––3 3 pitch space o.log(2) + f.log(3) + t.log(5)pitch space o.log(2) + f.log(3) + t.log(5)• M = M = ŸŸ1212,, ŸŸ33,, ŸŸ4 4 for pitch classesfor pitch classes
• M =M = ŸŸ ŸŸ365 365 ŸŸ24 24 ŸŸ60 60 ŸŸ60 60 ŸŸ28 28 (y:d:h:m:s:fr) for time(y:d:h:m:s:fr) for time
• M = M = ¬¬,, Polynomials R[X] etc. for sound, analysis, etc.Polynomials R[X] etc. for sound, analysis, etc.
<PitchClass><Simple>(<PitchClass><Simple>(ŸŸ1212))
![Page 13: Guerino Mazzola (Fall 2015 © ): Introduction to Music Technology IIISymbolic Reality III.2 (We Nov 16) Denotators I—definition of a universal concept space](https://reader035.vdocuments.site/reader035/viewer/2022062423/5697bfab1a28abf838c9b2ba/html5/thumbnails/13.jpg)
Gue
rino
Maz
zola
(F
all 2
015
Gue
rino
Maz
zola
(F
all 2
015©©
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
![Page 14: Guerino Mazzola (Fall 2015 © ): Introduction to Music Technology IIISymbolic Reality III.2 (We Nov 16) Denotators I—definition of a universal concept space](https://reader035.vdocuments.site/reader035/viewer/2022062423/5697bfab1a28abf838c9b2ba/html5/thumbnails/14.jpg)
Gue
rino
Maz
zola
(F
all 2
015
Gue
rino
Maz
zola
(F
all 2
015©©
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
Compound Forms = Recursive SpacesCompound Forms = Recursive Spaces
![Page 15: Guerino Mazzola (Fall 2015 © ): Introduction to Music Technology IIISymbolic Reality III.2 (We Nov 16) Denotators I—definition of a universal concept space](https://reader035.vdocuments.site/reader035/viewer/2022062423/5697bfab1a28abf838c9b2ba/html5/thumbnails/15.jpg)
Gue
rino
Maz
zola
(F
all 2
015
Gue
rino
Maz
zola
(F
all 2
015©©
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
spaces/formsspaces/formsspaces/formsspaces/forms
product/limitproduct/limitproduct/limitproduct/limit union/colimitunion/colimitunion/colimitunion/colimit collections/collections/powersetspowersets
collections/collections/powersetspowersets
exist three compound space types:exist three compound space types:exist three compound space types:exist three compound space types:
![Page 16: Guerino Mazzola (Fall 2015 © ): Introduction to Music Technology IIISymbolic Reality III.2 (We Nov 16) Denotators I—definition of a universal concept space](https://reader035.vdocuments.site/reader035/viewer/2022062423/5697bfab1a28abf838c9b2ba/html5/thumbnails/16.jpg)
Gue
rino
Maz
zola
(F
all 2
015
Gue
rino
Maz
zola
(F
all 2
015©©
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
<form_name><type>(coordinator)<form_name><type>(coordinator)
example:example:‘‘Note’Note’
<denotator_name><denotator_name><form_name><form_name>(coordinates) (coordinates)
example:example:‘‘myNote’myNote’
n denotators fromn denotators fromFF11, , FF11,... ,... FFnn
example (n=2):example (n=2): ((‘myOnset’‘myOnset’,,’thisPitch’’thisPitch’))
LimitLimit
sequence sequence FF11, , FF22,... ,... FFnn
of n formsof n forms
![Page 17: Guerino Mazzola (Fall 2015 © ): Introduction to Music Technology IIISymbolic Reality III.2 (We Nov 16) Denotators I—definition of a universal concept space](https://reader035.vdocuments.site/reader035/viewer/2022062423/5697bfab1a28abf838c9b2ba/html5/thumbnails/17.jpg)
Gue
rino
Maz
zola
(F
all 2
015
Gue
rino
Maz
zola
(F
all 2
015©©
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
example:example:‘‘Interval’Interval’
example:example:‘‘myInterval’myInterval’
n denotators, plus arrow n denotators, plus arrow conditions conditions example: example: (‘note(‘note11’,’on’,’note’,’on’,’note22’)’)
Note Onset NoteNote Onset Note
<form_name><type>(coordinator)<form_name><type>(coordinator)
<denotator_name><form_name>(coordinates) <denotator_name><form_name>(coordinates)
LimitLimit
extend to diagram ofextend to diagram ofn forms + functionsn forms + functions
FF11
FFnnFFii
K-nets (networks!)K-nets (networks!)
![Page 18: Guerino Mazzola (Fall 2015 © ): Introduction to Music Technology IIISymbolic Reality III.2 (We Nov 16) Denotators I—definition of a universal concept space](https://reader035.vdocuments.site/reader035/viewer/2022062423/5697bfab1a28abf838c9b2ba/html5/thumbnails/18.jpg)
Gue
rino
Maz
zola
(F
all 2
015
Gue
rino
Maz
zola
(F
all 2
015©©
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
Db}
JJ11 JJ22 JJ33 JJ44
Klumpenhouwer (hyper)networksKlumpenhouwer (hyper)networks
![Page 19: Guerino Mazzola (Fall 2015 © ): Introduction to Music Technology IIISymbolic Reality III.2 (We Nov 16) Denotators I—definition of a universal concept space](https://reader035.vdocuments.site/reader035/viewer/2022062423/5697bfab1a28abf838c9b2ba/html5/thumbnails/19.jpg)
Gue
rino
Maz
zola
(F
all 2
015
Gue
rino
Maz
zola
(F
all 2
015©©
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy ŸŸ1212
ŸŸ1212
ŸŸ1212
ŸŸ1212
TT44
TT22
TT55.-1.-1 TT1111.-1.-1
33 77
22 44
ŸŸ1212
ŸŸ1212
ŸŸ1212
ŸŸ1212
TT44
TT22
TT55.-1.-1 TT1111.-1.-1limit
![Page 20: Guerino Mazzola (Fall 2015 © ): Introduction to Music Technology IIISymbolic Reality III.2 (We Nov 16) Denotators I—definition of a universal concept space](https://reader035.vdocuments.site/reader035/viewer/2022062423/5697bfab1a28abf838c9b2ba/html5/thumbnails/20.jpg)
Gue
rino
Maz
zola
(F
all 2
015
Gue
rino
Maz
zola
(F
all 2
015©©
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
<form_name><type>(coordinator)<form_name><type>(coordinator)
example:example:‘‘Orchestra’Orchestra’
<denotator_name><denotator_name><form_name><form_name>(coordinates) (coordinates)
example:example:‘‘mySelection’mySelection’
one denotator for one denotator for i-th form i-th form FFii
example:example:Select a note from Select a note from celestacelesta
ColimitColimit
sequence sequence FF11, , FF22,... ,... FFnn
of n formsof n forms
![Page 21: Guerino Mazzola (Fall 2015 © ): Introduction to Music Technology IIISymbolic Reality III.2 (We Nov 16) Denotators I—definition of a universal concept space](https://reader035.vdocuments.site/reader035/viewer/2022062423/5697bfab1a28abf838c9b2ba/html5/thumbnails/21.jpg)
Gue
rino
Maz
zola
(F
all 2
015
Gue
rino
Maz
zola
(F
all 2
015©©
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
<form_name><type>(coordinator)<form_name><type>(coordinator)
Example:Example:‘‘Motif’Motif’
<denotator_name><denotator_name><form_name><form_name>(coordinates) (coordinates)
example:example:‘‘thisMotif’thisMotif’
one form one form FF
A set of A set of denotators denotators of form of form FF
example:example:{n{n11,n,n22,n,n33,n,n44,n,n55}} F = NoteF = Note
PowersetPowersetPowersetPowerset
Power 1Power 1
![Page 22: Guerino Mazzola (Fall 2015 © ): Introduction to Music Technology IIISymbolic Reality III.2 (We Nov 16) Denotators I—definition of a universal concept space](https://reader035.vdocuments.site/reader035/viewer/2022062423/5697bfab1a28abf838c9b2ba/html5/thumbnails/22.jpg)
Gue
rino
Maz
zola
(F
all 2
015
Gue
rino
Maz
zola
(F
all 2
015©©
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
<form_name><type>(coordinator)<form_name><type>(coordinator)
Example:Example:‘‘Chord’Chord’
<denotator_name><denotator_name><form_name><form_name>(coordinates) (coordinates)
example:example:‘‘thisChord’thisChord’
one form one form FF
A set of A set of denotators denotators of form of form FF
example:example:{p{p11,p,p22,p,p33}} F = PitchClassF = PitchClass
PowersetPowersetPowersetPowerset
Power 2Power 2
![Page 23: Guerino Mazzola (Fall 2015 © ): Introduction to Music Technology IIISymbolic Reality III.2 (We Nov 16) Denotators I—definition of a universal concept space](https://reader035.vdocuments.site/reader035/viewer/2022062423/5697bfab1a28abf838c9b2ba/html5/thumbnails/23.jpg)
Gue
rino
Maz
zola
(F
all 2
015
Gue
rino
Maz
zola
(F
all 2
015©©
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
<form_name><type>(coordinator)<form_name><type>(coordinator)
ColimitColimit
diagram ofdiagram ofn formsn forms
FF11
FFnnFFii
Gluing together spaces
Gluing together spaces
of musical objects!of musical objects!
Idea: take union of all FIdea: take union of all Fii and identify corresponding points and identify corresponding points
under the given maps.under the given maps.
![Page 24: Guerino Mazzola (Fall 2015 © ): Introduction to Music Technology IIISymbolic Reality III.2 (We Nov 16) Denotators I—definition of a universal concept space](https://reader035.vdocuments.site/reader035/viewer/2022062423/5697bfab1a28abf838c9b2ba/html5/thumbnails/24.jpg)
Gue
rino
Maz
zola
(F
all 2
015
Gue
rino
Maz
zola
(F
all 2
015©©
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
TTnn{c{c11,c,c22,...,c,...,ckk} =} = {n+c{n+c11, n+c, n+c22,..., n+c,..., n+ckk} mod 12} mod 12
(transposition by n semitones)(transposition by n semitones)
Result = set of n-transposition chord classes!Result = set of n-transposition chord classes!
ChordChordD D ==
TTnn
BTW: What would the Limit of BTW: What would the Limit of DD be?be?
<form_name><type>(coordinator)<form_name><type>(coordinator)
ColimitColimit
FF11
FFnnFFii
![Page 25: Guerino Mazzola (Fall 2015 © ): Introduction to Music Technology IIISymbolic Reality III.2 (We Nov 16) Denotators I—definition of a universal concept space](https://reader035.vdocuments.site/reader035/viewer/2022062423/5697bfab1a28abf838c9b2ba/html5/thumbnails/25.jpg)
Gue
rino
Maz
zola
(F
all 2
015
Gue
rino
Maz
zola
(F
all 2
015©©
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
—— ——
OnsetOnsetOnsetOnset LoudnessLoudnessLoudnessLoudness DurationDurationDurationDurationPitchPitchPitchPitch
NoteNoteNoteNote
STRGSTRGŸŸ
Note formNote formNote formNote form
![Page 26: Guerino Mazzola (Fall 2015 © ): Introduction to Music Technology IIISymbolic Reality III.2 (We Nov 16) Denotators I—definition of a universal concept space](https://reader035.vdocuments.site/reader035/viewer/2022062423/5697bfab1a28abf838c9b2ba/html5/thumbnails/26.jpg)
Gue
rino
Maz
zola
(F
all 2
015
Gue
rino
Maz
zola
(F
all 2
015©©
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
GeneralNoteGeneralNoteGeneralNoteGeneralNote
—— ——
OnsetOnsetOnsetOnset LoudnessLoudnessLoudnessLoudness DurationDurationDurationDurationPitchPitchPitchPitch
NoteNoteNoteNote
STRGSTRGŸŸ—— ——
DurationDurationDurationDurationOnsetOnsetOnsetOnset
PausePausePausePause
GeneralNote formGeneralNote form
![Page 27: Guerino Mazzola (Fall 2015 © ): Introduction to Music Technology IIISymbolic Reality III.2 (We Nov 16) Denotators I—definition of a universal concept space](https://reader035.vdocuments.site/reader035/viewer/2022062423/5697bfab1a28abf838c9b2ba/html5/thumbnails/27.jpg)
Gue
rino
Maz
zola
(F
all 2
015
Gue
rino
Maz
zola
(F
all 2
015©©
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
FM-SynthesisFM-Synthesis
![Page 28: Guerino Mazzola (Fall 2015 © ): Introduction to Music Technology IIISymbolic Reality III.2 (We Nov 16) Denotators I—definition of a universal concept space](https://reader035.vdocuments.site/reader035/viewer/2022062423/5697bfab1a28abf838c9b2ba/html5/thumbnails/28.jpg)
Gue
rino
Maz
zola
(F
all 2
015
Gue
rino
Maz
zola
(F
all 2
015©©
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
NodeNodeNodeNode
FM-ObjectFM-ObjectFM-ObjectFM-Object
—— ——
AmplitudeAmplitudeAmplitudeAmplitude PhasePhasePhasePhaseFrequencyFrequencyFrequencyFrequency
FM-SynthesisFM-Synthesis
——
SupportSupportSupportSupport ModulatorModulatorModulatorModulator
FM-ObjectFM-ObjectFM-ObjectFM-Object
![Page 29: Guerino Mazzola (Fall 2015 © ): Introduction to Music Technology IIISymbolic Reality III.2 (We Nov 16) Denotators I—definition of a universal concept space](https://reader035.vdocuments.site/reader035/viewer/2022062423/5697bfab1a28abf838c9b2ba/html5/thumbnails/29.jpg)
Gue
rino
Maz
zola
(F
all 2
015
Gue
rino
Maz
zola
(F
all 2
015©©
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
NodeNodeNodeNode
FM-ObjectFM-ObjectFM-ObjectFM-Object
—— ——
AmplitudeAmplitudeAmplitudeAmplitude PhasePhasePhasePhaseFrequencyFrequencyFrequencyFrequency
FM-SynthesisFM-Synthesis
——
SupportSupportSupportSupport
FM-ObjectFM-ObjectFM-ObjectFM-Object
![Page 30: Guerino Mazzola (Fall 2015 © ): Introduction to Music Technology IIISymbolic Reality III.2 (We Nov 16) Denotators I—definition of a universal concept space](https://reader035.vdocuments.site/reader035/viewer/2022062423/5697bfab1a28abf838c9b2ba/html5/thumbnails/30.jpg)
Gue
rino
Maz
zola
(F
all 2
015
Gue
rino
Maz
zola
(F
all 2
015©©
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
??
Schenker AnalysisSchenker AnalysisGTTMGTTM
CompositionComposition
Embellishments Embellishments Embellishments Embellishments
hierarchies!hierarchies!
![Page 31: Guerino Mazzola (Fall 2015 © ): Introduction to Music Technology IIISymbolic Reality III.2 (We Nov 16) Denotators I—definition of a universal concept space](https://reader035.vdocuments.site/reader035/viewer/2022062423/5697bfab1a28abf838c9b2ba/html5/thumbnails/31.jpg)
Gue
rino
Maz
zola
(F
all 2
015
Gue
rino
Maz
zola
(F
all 2
015©©
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
macroscoremacroscoremacroscoremacroscore
nodenodenodenode
macroscoremacroscoremacroscoremacroscorescorescorescorescore
NoteNoteNoteNote FlattenFlatten
NodifyNodify
—— ——STRGSTRGŸŸ
NoteNoteNoteNote
onsetonsetonsetonset loudnessloudnessloudnessloudness durationdurationdurationdurationpitchpitchpitchpitch voicevoicevoicevoice
ŸŸ
![Page 32: Guerino Mazzola (Fall 2015 © ): Introduction to Music Technology IIISymbolic Reality III.2 (We Nov 16) Denotators I—definition of a universal concept space](https://reader035.vdocuments.site/reader035/viewer/2022062423/5697bfab1a28abf838c9b2ba/html5/thumbnails/32.jpg)
Gue
rino
Maz
zola
(F
all 2
015
Gue
rino
Maz
zola
(F
all 2
015©©
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
The denoteX notation for forms and denotators The denoteX notation for forms and denotators
![Page 33: Guerino Mazzola (Fall 2015 © ): Introduction to Music Technology IIISymbolic Reality III.2 (We Nov 16) Denotators I—definition of a universal concept space](https://reader035.vdocuments.site/reader035/viewer/2022062423/5697bfab1a28abf838c9b2ba/html5/thumbnails/33.jpg)
Gue
rino
Maz
zola
(F
all 2
015
Gue
rino
Maz
zola
(F
all 2
015©©
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
1.1. FormsForms
Name:.TYPE(Coordinator);Name:.TYPE(Coordinator);
• Name = word (string)Name = word (string)
• TYPE = one of the following:TYPE = one of the following:- Simple- Simple- Limit- Limit- Colimit- Colimit- Powerset- Powerset
• Coordinator = one of the following:Coordinator = one of the following:- TYPE = Simple: STRING, Boole, - TYPE = Simple: STRING, Boole, ŸŸ, , —— - TYPE = Limit, Colimit: A sequence F- TYPE = Limit, Colimit: A sequence F11,... F,... Fnn of form names of form names
- TYPE = Powerset: One form name F- TYPE = Powerset: One form name F
![Page 34: Guerino Mazzola (Fall 2015 © ): Introduction to Music Technology IIISymbolic Reality III.2 (We Nov 16) Denotators I—definition of a universal concept space](https://reader035.vdocuments.site/reader035/viewer/2022062423/5697bfab1a28abf838c9b2ba/html5/thumbnails/34.jpg)
Gue
rino
Maz
zola
(F
all 2
015
Gue
rino
Maz
zola
(F
all 2
015©©
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
2.2. DenotatorsDenotators
Name:@FORM(Coordinates);Name:@FORM(Coordinates);
• Name = word (string)Name = word (string)
• FORM = name of a defined formFORM = name of a defined form
• Coordinates = x, which looks as follows:Coordinates = x, which looks as follows:- FORM:.Simple(F), then x is an element of F - FORM:.Simple(F), then x is an element of F
(STRING, Boole, (STRING, Boole, ŸŸ, , ——))
- FORM:.Powerset(F), then x = {x- FORM:.Powerset(F), then x = {x11,, xx22,, xx33,... x,... xkk}}
xxi i = F-denotators, = F-denotators, only names only names
xxii::
- FORM:.Limit(F- FORM:.Limit(F11,... F,... Fnn), then x = (x), then x = (x11, x, x22, x, x33,... x,... xnn))
x xi i = F= Fii-denotators, i = 1,...n-denotators, i = 1,...n
- FORM:.Colimit(F- FORM:.Colimit(F11,... F,... Fnn), then x = denotator of one F), then x = denotator of one Fi i
(i>x, (i>x, only names x:only names x:) )
![Page 35: Guerino Mazzola (Fall 2015 © ): Introduction to Music Technology IIISymbolic Reality III.2 (We Nov 16) Denotators I—definition of a universal concept space](https://reader035.vdocuments.site/reader035/viewer/2022062423/5697bfab1a28abf838c9b2ba/html5/thumbnails/35.jpg)
Gue
rino
Maz
zola
(F
all 2
015
Gue
rino
Maz
zola
(F
all 2
015©©
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
): I
ntro
duct
ion
to M
usic
Tec
hnol
ogy
Exercise:Exercise:
• A FM form and a denotator for this function:A FM form and a denotator for this function:
f(t) = -12.5 sin(2f(t) = -12.5 sin(25t+3)+cos(t -sin(65t+3)+cos(t -sin(6t+sin(t+sin(t+89))) t+89)))
NodeNodeNodeNode
FM-ObjectFM-ObjectFM-ObjectFM-Object
—— ——
AmplitudeAmplitudeAmplitudeAmplitude PhasePhasePhasePhaseFrequencyFrequencyFrequencyFrequency
——
SupportSupportSupportSupport
FM-ObjectFM-ObjectFM-ObjectFM-Object