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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