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undergraduate thesis
Matematičke osnove dvanaesttonske glazbene ljestvice
Zagreb: University of Zagreb, Faculty of Electrical Engineering and Computing, 2024. urn:nbn:hr:168:234759
Đurinić, Dominik
University of Zagreb
Faculty of Electrical Engineering and Computing

Institutional repository: FER Repository

Cite this document

Đurinić, D. (2024). Matematičke osnove dvanaesttonske glazbene ljestvice (Undergraduate thesis). Zagreb: University of Zagreb, Faculty of Electrical Engineering and Computing. Retrieved from https://urn.nsk.hr/urn:nbn:hr:168:234759

Đurinić, Dominik. "Matematičke osnove dvanaesttonske glazbene ljestvice." Undergraduate thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, 2024. https://urn.nsk.hr/urn:nbn:hr:168:234759

Đurinić, Dominik. "Matematičke osnove dvanaesttonske glazbene ljestvice." Undergraduate thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, 2024. https://urn.nsk.hr/urn:nbn:hr:168:234759

Đurinić, D. (2024). 'Matematičke osnove dvanaesttonske glazbene ljestvice', Undergraduate thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, accessed 21 December 2024, https://urn.nsk.hr/urn:nbn:hr:168:234759

Đurinić D. Matematičke osnove dvanaesttonske glazbene ljestvice [Undergraduate thesis]. Zagreb: University of Zagreb, Faculty of Electrical Engineering and Computing; 2024 [cited 2024 December 21] Available at: https://urn.nsk.hr/urn:nbn:hr:168:234759

D. Đurinić, "Matematičke osnove dvanaesttonske glazbene ljestvice", Undergraduate thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, Zagreb, 2024. Available at: https://urn.nsk.hr/urn:nbn:hr:168:234759

Metadata
TitleMatematičke osnove dvanaesttonske glazbene ljestvice
Title (english)Mathematical foundations of the twelve-tone musical scale
AuthorDominik Đurinić
MentorMate Puljiz (mentor)
Committee memberMate Puljiz (predsjednik povjerenstva)
Committee memberStjepan Šebek (član povjerenstva)
Committee memberJosip Žubrinić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Electrical Engineering and Computing
Zagreb
Defense date and country2024-02-16, Croatia
Scientific / art field,
discipline and subdiscipline		TECHNICAL SCIENCES
Computing
Abstract
Glazbom dominira uređena struktura i sklad tonova koje temelji na matematičkim osnovama. Matematika nam omogućuje logičko razumijevanje elemenata i pojava u glazbi. Zvuk, kao osnovnu sastavnicu glazbe, modeliramo s pomoću sinusnog vala. Iz jednadžbe vala iščitavamo visinu i glasnoću zvuka. Pitagora za sobom ostavlja zakon malih brojeva koji definira konsonantnost tonova malih cjelobrojnih omjera frekvencija. Intervale koji izravno slijede iz zakona nazivamo prirodni intervali. Ugađanje glazbene ljestvice uključuje neki oblik temperiranja zbog povećanja njene podatnosti. Jednoliko temperiranje se ističe svojom jednostavnošću i slobodom transpozicija. Dvanaesttonska ljestvica je najzastupljenija glazbena ljestvica zapadne glazbe i njenu raspodjelu oktave na dvanaest polutonova smatramo optimalnom raspodjelom. Ljudi percipiraju zvukove ugodnim ili neugodnim. Fiziološku podlogu takve percepcije temeljimo na krivulji disonancije.
Abstract (english)
The music is dominated by an ordered structure and harmony of tones based on mathematical foundations. Mathematics allows us to logically understand the elements and phenomena in music. Sound, as a basic component of music, is modeled using a sine wave. We read the height and volume of the sound from the equation of that wave. Pythagoras left behind the law of small numbers, which defines the consonance of tones with small integer frequency ratios. Intervals that follow directly from the law are called natural intervals. Tuning a musical scale involves some form of tempering to increase its flexibility. Equal tempering stands out for its simplicity and freedom of transpositions. The twelve-tone scale is the most represented musical scale in Western music, and we consider its division of the octave into twelve semitones to be the optimal division. People perceive sounds as pleasant or unpleasant. The physiological basis of such perception is based on the dissonance curve.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:168:234759
Study programmeTitle: Computing
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka računarstva (sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka računarstva)
Type of resourceText
File originBorn digital
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Created on2024-03-28 07:46:03