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数学

Discovery

Andrius Kulikauskas

  • ms@ms.lt
  • +370 607 27 665
  • My work is in the Public Domain for all to share freely.

Lietuvių kalba

Introduction E9F5FC

Understandable FFFFFF

Questions FFFFC0

Notes EEEEEE

Software

Komparatyvizmas, globalizacija ir dabartinių estetikos bei meno filosofijos diskursų kaita, Lietuvos kultūros tyrimų institute, siūlyti iki balandžio 25 d., vyks gegužės 5 d. Siūlyti apie muziką.


List of slides and questions

  • Title
  • Bernstein's six lectures and Chomsky: What came first, language or music? Music.
  • Bernstein's grand ideas and my questions:
  • History of evolution - abstraction of central nervous system: Where is abstraction leading us? Reclaiming concreteness.
  • Consciousness - symbolic system -
  • Apes
  • Autistic
  • Unison - clapping
  • Question - answer
  • Video - rhetoric, dialogue
  • Algebra of copyright
  • Jack loves Jill: What is the order of the transformations?
  • Video - Jack loves Jill
  • Linear and nonlinear grammar
  • House of knowledge - universal grammar of games

In 1973, Leonard Bersteing gave six lectures at Harvard University.

  • Groundbreaking as video lessons - enhanced by performances - his teaching at the key board - multimedia - form matched by content
  • Based on Chomsky and Universal Grammar and Transformation Grammar and Deep structure vs. Surface structure
  • Intuitive, conceptual and imaginative

Outline

Bernstein's grand ideas

  • Musical phonetics? Physics?
  • Chomky's syntax: transformations from deep structure to surface structure: "Jack loves Jill" - passive, negation, question - musically expressed (video)
  • Music as game
  • Metaphor
  • Music as rhetorical dialogue (video)
  • Musical transformations as rhetorical devices -
  • The requirements for ambiguity

And consider excerpts from his videos

My grand ideas

  • Evolution towards abstraction of the universe
  • Joint intentionality - synchronicity -
  • Chimpanzee sounds (video) vs. children singing (video)
  • Abstraction of sound - ability to sing in unison though in different octaves
  • Universal grammar of games [music as game]
  • Question and answer
  • Meaning - extrinsic (real world semantics) and instrinsic (musical syntax)
  • Algebra of copyright - three parsers - and their requirements
  • Linear grammar and nonlinear grammar
  • Establishing and playing with expectations - emotion
  • Syntactic - rhetorical forms

Music as rhetoric - repetition and variation

Metaphor - the common "X factor" relating A and B - a shared principle, a shared phenomenon.

What is the boundary between self and world in music? Between the known and the unknown? The old and the new?

Joint intentionality

  • A human has the freedom to intend the joint intention or their own intention.

Unison

  • The other apes don't have rhythm - they don't clap in unison - tbey have call and response - they may copy - but not perfected unison - that is the first human innovation - which creates a musical space.
  • Abstraction of pitch difference is important for singing in unity - for men and women (with different ranges) to share a melody. Animals don't abstract pitch difference.
  • Matching of pitches for harmonization with each other. How do people determine pitch? They need to attune to each other.

Question and answer

  • Garnys, garnys: Sukuria
  • "The crane, the crane has looong legs. The crane, the crane has looong legs. Run, I'd run, I would, I would, if I so should have very long legs like the crane."
  • Opening section. Closing section. Static harmony, dynamic harmony, cadence, individual chords.

Meaning

  • Language - extrinsic meaning. Music - intrinsic meaning. Math is similar to music.
  • Art - music is necessarily art - art is contrived, not related to the real world, relates to itself.
  • Language has emotive effect (poetry) but also literal effect (prose). What (primary) structure adds this literal effect?
  • Music is self-referential - as a system, it maps onto itself - thus it has a strict, well-defined structure. Whereas language references the world. But they are the same system of reference. In terms of category theory, music maps from Theory to Theory, whereas language maps from Theory to World. So music has no semantics, whereas language has semantics. Math is also important as a pure thinking about structure.
  • The particular system of music (tones, chords, etc.) is the analogue of semantics in language. And thus they are different.

Algebra of copyright - three parsers

  • Levels of parsers - Algebra of copyright
  • Consciousness can shift from one parser to another parser.
  • Semantic parser vs. syntactic parser?
  • Lowest parser: the rhythm. Verb. Lets you hear - enter a musical space.
  • Next parser: melody. Motive - Noun. Lets you hear a voice.
  • Next parser: harmony. Adjective. Lets you hear the structure amongst various melodies, voices.
  • Importance of giving the ear something to pay attention to. It is listening for normality and abnormality and distinguishing the two. Thus consonance and dissonance. If it can't hear dissonance then it feels beauty. The role of silence as the main fount of normality, consonance. Creation of tension (by dominant) and resolution. Will the dominant become a new tonic? Or will we return to the tonic? The tension of the choice. And accentuating the freedom of the choice. Retroactive sense making. The importance of cadence. The establishment of a tone in the opening can be completed by the establishment of a different tone in the ending.
  • The levels of parsers (as in the algebra of copyright) yield the six transformations and they express the nature of an established system. So the pre-systemic ways of figuring things out are what are needed to establish the parsers, and the pre-parsed atoms, thus the four levels of knowledge that ground them.
  • Harmonization of abstract systems.

Abstract structural expectations

Supposed differences

  • Structural categories are different: Subjects, Objects vs. Tonics, Dominants
  • Different kinds of hierarchical tree structure (Lerdahl & Jackendoff, 1983)
  • Opposite hemispheric bias - Neuroimaging (Zatorre), neuropsychology
  • Creation of tension (through instability) and resolution. As in stories.
  • Circle of fifths

Expectations and emotion

  • Music has emotive effect. Because it plays with expectations.
  • Poetry - unconscious speaks to conscious - by way of emotion - by way of unconscious expectations.

Sources

Books

  • VGTU: Tonal Pitch Space, Fred Lerdahl, 2001
  • Fred Lerdahl, writings
  • The Relationship Between Music and Language
  • Krumhansi 1979
  • Aniruddh Patel, music cognition, brain responses, syntax, at Rice University.
  • Fred Lehrdal video
  • Leonard Bernstein - Musical Syntax
  • Rohrmeier. Musical syntax and its cognitive implications.
  • Towards a generative syntax of tonal harmony.
  • Meyer, 1956. Emotion & Meaning in Music.
  • Huron, 2006. Sweet Anticipation.
  • "Chills research" (Sloboda, Zatorre)
  • Granroth-Wilding, M & Steedman, M. (2012) Statistical Parsing for Harmonic Analysis of Jazz Chord Sequences. In Proceedings of the International Computer Music Conference (ICMC).
  • Haas, W.B. de, Rohrmeier, M., Veltkamp, R.C. & Wiering, F. (2009). Modeling Harmonic Similarity Using a Generative Grammar of Tonal Harmony. In Proceedings of theInternational Conference on Music Information Retrieval (ISMIR).
  • Lerdahl, F. & Jackendoff, R. (1983). A Generative Theory of Tonal Music. Cambridge, MA.
  • Patel, A.D. (2008). Music, Language, and the Brain. Oxford University Press, New York.
  • Rebuschat, P., Rohrmeier, M., Cross, I., Hawkins (2011) Eds. Language and Music as Cognitive Systems. Oxford University Press
  • Rohrmeier, M. (2011). Towards a generative syntax of tonal harmony. Journal of Mathematics and Music, 5 (1), pp. 35-53.
  • Steedman, M. (1996). The Blues and the Abstract Truth: Music and Mental Models. In A. Garnham and J. Oakhill, (eds.), Mental Models In Cognitive Science. Mahwah, NJ: Erlbaum, 305-318.

II) Musical Syntax

  • 32 min. Jack Loves Jill - chord
  • irresolution - question
  • minor - negation
  • 35 min. Deletion
  • 44 min. musical prose - Hannon
  • 46 min. converting prose into poetry
  • 48 min. inversions
  • 1:11 upbeat vs. downbeat - deletion

III) Musical Semantics

  • metaphor
  • 20 min. "playing is the very stuff of music" - "the game of notes" Stravinsky: le jeu de ... musical puns and anagrams - a continuing game of anagrams - constant rearrangement made rich by horizontal and vertical structurs, melodic, harmonic and contrapuntal anagrams - variety of high and low registers, durations, meters - a super game of sonic anagrams - release energy, exercise purposes, to compete, to show off, to establish intimacy and other affective functions.
  • 23 min. Music means what? Our thesis: music has intrinsic meanings of its own generated by a constant stream of metaphors which are all forms of musical transformations.
  • 30 min. Beethoven dialogue - drama of pleading and refusal.
  • 32 min. a totally metaphoric language
  • 40 min. musical figure of speech - more direct - with greater force - than linguistic figure of speech - relating tonic to dominant and vice versa
  • 45 min. repetition in poetry as the source of time
  • 47 min. alliteration - repetition of single notes - anaphora - use of identical phrases - repetition of multiple notes
  • 49 min. chiasmos - reversing the elements - AB vs. BA repetition subjected to reversal
  • 51 min. rhetoric or poetic devices - musical transformations

IV) Delights and dangers of ambiguity

  • Rhythmic ambiguity, chromatic ambiguity - ambiguity of key
  • 1:49 The tritone

1973 metais Harvardo universitetas įrašė šešias dirigento L.Bernšteino paskaitas apie "Neatsakytą klausimą", kaip vystosi muzika? Įkvėptas kalbotyrininko N.Chomskio atradimų, jisai ieškojo muzikos gramatikos, jos fonologijos, sintaksės ir semantikos. Jisai pabrėžė muzikos žaismingumą. Muzikos žaidimą grindė lūkesčių išvystymu, pažeidimu ir atstatymu su tikslu išplėtoti daugiaprasmiškumą, nusakyti lygtį - palyginimą ir žaisti su palyginimo viena ir kita puse.

Aš savo ruožtu įsivaizduosiu, kaip žmonės priešistoriniais laikais išsiskyrė nuo kitų homonidų savo sugebėjimu, kaip Tomasello pastebėjo, užsiimti bendru reikalu ("joint intentionality"). Mano manymu, lygiagrečiai išsivystė žmonių nesąmoningas sugebėjimas savo kūnus derinti, ir kartu polinkis bendram reikalui susikaupti, kaip nesugeba šimpanzės arba autistai. Manau, tokią darną palaikė dainavimas, kas skatino išvystyti balso stygas ir išplėsti kalbos galimybes. Ryškėjant bendram reikalui žmonės ėmė žaisti žaidimus, kurti vaizduotės pasaulius, į kuriuos įžengdavo bendru klausimu ir iš kurio išeidavo bendru atsakymu. Pristatysiu žaidimų gramatika, kurią išmąsčiau tirdamas Silicio slėnio įmonių kūrybinius žaidimus. Žaidimas plėtoja neatsakytą klausimą, tad šios mintys suskamba su L.Bernšteino "Neatsakytu klausimu" ir jo įžvalgomis apie muzikos gramatiką.

MusicalSyntax


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Puslapis paskutinį kartą pakeistas 2018 gegužės 04 d., 10:09
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