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III.1III.1 The Axis of SemioticsThe Axis of Semiotics
III.1.2 III.1.2 (F Oct 29) (F Oct 29) Sign SystemsSign Systems
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ar Consider music as a sign system = a Consider music as a sign system = a semioticsemiotic (= second axis of our topography) (= second axis of our topography)
Semiotics = theory of sign systems (sign: Semiotics = theory of sign systems (sign: expression/signification/contentexpression/signification/content))
Three dominant scholars:Three dominant scholars:• Charles Sanders Peirce, US philosopher: „Grammatica speculativa“ Charles Sanders Peirce, US philosopher: „Grammatica speculativa“
1865 (sign/interpretant/object)1865 (sign/interpretant/object)• Ferdinand de Saussure, Swiss linguist: „Cours de linguistique générale“Ferdinand de Saussure, Swiss linguist: „Cours de linguistique générale“
1916 (signifiant/signification/signifié)1916 (signifiant/signification/signifié)• Louis Hjelmslev Danish linguist: „La stratification du langage“ Louis Hjelmslev Danish linguist: „La stratification du langage“
1954 (expression/relation/content)1954 (expression/relation/content)Roland Barthes: „Elements of Semiology“ 1964Roland Barthes: „Elements of Semiology“ 1964
Ch.S. PeirceCh.S. PeirceCh.S. PeirceCh.S. PeirceF. de SaussureF. de SaussureF. de SaussureF. de Saussure
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Anatomy of a SemioticAnatomy of a Semiotic
CT (contents)CT (contents)
SG (signification)SG (signification)
EX (expressions)EX (expressions)
syntacticssyntactics
semanticssemantics
pragmaticspragmatics
synonymsynonym
homonymhomonym
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ExpressionExpression SignificationSignification ContentContent
LPLPanalogical
CDCD
digital
??
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1Bit 0 or 1 4 Bit 0000, 0001, ... 1111 = 16 values 0,1,2,3....15
CD has 16 Bit amplitude quantization:16 entries: 101.....1 = 1 215 + 0 214 + 1 213 + ...1 20
0,1,..., 65‘535 = 216 values
CD has 16 Bit amplitude quantization:16 entries: 101.....1 = 1 215 + 0 214 + 1 213 + ...1 20
0,1,..., 65‘535 = 216 values
2. time quantization
reading 0001110110100111001010000111110000111.....
1. amplitude quantization
binary representation of numbers:
1011 means (sign!!)
1 23 + 0 22 + 1 21 + 1 20 = 8 + 2 + 1 = 11
CD has 44‘100 samples per secondCD has 44‘100 samples per secondCD of one hour and stereo has total of
2 channels 60 minutes 60 seconds 44‘100 samples 16 amplitude Bits= 635 MByte (1 Byte = 8 Bits)
CD of one hour and stereo has total of
2 channels 60 minutes 60 seconds 44‘100 samples 16 amplitude Bits= 635 MByte (1 Byte = 8 Bits)
Polycarbonate
track width ~1μm
land pit
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harmonic analysisharmonic analysis
SignSign
ContentContent
SignificationSignification
ExpressionExpression
tonal modulationtonal modulation G G maj maj E-flatE-flat maj maj
„„score surface“score surface“
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ExpressionExpression SignificationSignification ContentContent
Harmonic Analysis Following Hugo Riemann (Function Theory)Harmonic Analysis Following Hugo Riemann (Function Theory)
three possible contentsthree possible contentsper tonality:per tonality:
T (tonic)T (tonic)D (dominant)D (dominant)S (subdominant)S (subdominant)
RiemFunRiemFunEEyy-major-major
syntactical expression:syntactical expression:RiemFunRiemFunEEyy-major-major((ChCh)) evaluate!evaluate!
ChCh
T = content of T = content of RiemFunRiemFunEEyy-major-major((ChCh) )
RiemFunRiemFunEEyy-major-major((ChCh) = T) = T
RiemFunRiemFunAAyy-major-major((ChCh) = D) = D
RiemFunRiemFunBByy-major-major((ChCh) = S) = S
Riemann theory reducesRiemann theory reducessequence of chords tosequence of chords tosequence of values T, D, Ssequence of values T, D, S(for specific but variable tonalities)(for specific but variable tonalities)
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There Is Software, e.g. Rubato/HarmoRubette for Such Analyses!There Is Software, e.g. Rubato/HarmoRubette for Such Analyses!(see www.rubato.org)(see www.rubato.org)
one chord one chord ChCh
function valuesfunction values
tonalitiestonalities
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The Harmonic PathThe Harmonic Path
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