Dissertation Index

Author: Djordjevic, Michael, L.

Title: Discrete Tone Relations Determined by the Hearing Phenomenon within Five-Dimensional Sound-Musical Continuum

Institution: Radio Belgrade, Hilandarska 2, 11000 Belgrade, Serbia, YU

Begun: January 1990

Completed: June 1995


I. Theory
Five-Dimensional Sound-Musical Continuum materializes itself into objective Sound Space and subjective Musical Space defined as MOS-Musical Organisation of Sound. Sound-Musical Space is defined as union of the sets: A the set of parameters related to the sound signal at its source, B the set of parameters of the sound signal with a listener. A and B interactions with binary relations of ordered pairs represents the new set C. MOS defined as set X implicates Y as set of aural, final psychological perception of music.

II. Experiments
Quantum of Hearing Discrimination was elaborated in experiments MATEST 1 and 2 with values in cents ranged from 3-7, extreme 2, being constant along the greater part of the frequency spectrum, 4 cents. Unit called Unitary Distance was defined. Phase Space Cell signifies distribution of DTR within the Sound-Musical Space as matrix. MATEST 2 included several different tonal systems for comparison and DTR system justification.

III. Practice DTR-Discrete
Tone Relations: 1. Hearing discrimination 2. Temperament 3. Intonation 4. Musical abilities 5. Compositional organization of DTR 6.Ortography and notation 7. Reproductive medium with its limits 8. Constructing new musical instruments 9. Aesthetics and axiology

Keywords: discrete, tone, relations, DTR, UD, unitary, distance, STTR, PSC, phase, space, cells, QHd, quantum, hearing, discrimination, phenomenon, sound, musical, continuum, fivedimensional, matest, system


I. Theoretical aspects:

1. General conception of universal sound-musical manifestation
2. Materialization of sound-musical continuum into union of sets of all musical parameters,
3. Defining of tone pitches and their relations on the base of quantum theory i.e. discrete atributs of sound-musical space,
4. Presentation of discrete tone relations system and its implications in regard to hearing phenomenon

II. Experimental aspects:

5. Experimental determination of hearing threshold value and quantum of hearing discrimination within the range of discrete tone pitches and their relations
6. Projection of discrete tone relation systems and selection of its optimal variants
7. Testing of discrete tone relations system in relation to already existing tone systems and proofs of its universality, validity and practical benefits

III. Practical aspects:

8. Practical application of discrete tone relations from the aspect of contemporary musical science
9. Discrete tone relations application from the aspect of reproductive musical media,
10. Systematization of theoretical and practical results of discrete tone relations phenomenon research, Summary, Literature, Application of references towards fundamental theses of dissertation.


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