Dissertations / Theses: 'Music in mathematics'

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Thorbjörnsson, Sofia. "Mathematics and music." Thesis, Malmö högskola, Fakulteten för lärande och samhälle (LS), 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:mau:diva-35810.

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Syftet med undersökningen är att få en uppfattning om vilka matematiska aktiviteter som genomförs och kan genomföras under sångstunder på förskolor i Sverige och om de genomförs på ett sätt så att barnen arbetar mot målen i läroplanen. Detta eftersom mycket forskning tyder på att mycket matematikinlärning kan ske under sångstunder/musiklektioner. Teori och forskning säger att musik kan utveckla matematiken hos barn på många olika sätt.Min metod var att observera en sångstund på tre förskolor i en kommun och därefter intervjua förskollärarna som höll i sångstunderna.Resultatet visade att lärarna använde en hel del matematik under sångstunderna som det är, några mer medvetna om det än andra. Det visades även att pedagogerna anser att matematiken passar bra ihop med musik. Jag kan se vilka matematiska och musikaliska aktiviteter som genomfördes.Min önskan är att pedagoger ska ge barnen mycket matematikkunskaper under en sångstund. Det märks att där finns matematik till och med om vi inte lyfter det speciellt mycket. Tänk då vad som händer när pedagogen verkligen tänker på att lägga upp det matematiskt. Det jag i synnerhet ser i resultatet är att det är enkelt att få in matematik under sångstunderna och tycker därför att vi borde passa på att göra det.
The purpose of the survey is to get an idea of what mathematical activities thats being used and can be implemented in singing while at nursery schools in Sweden and if implemented in a way so that the children are working towards the goals of the curriculum. This is because much research suggests that much mathematics learning can take place during the singing moments / music lessons. Theory and research says that music can develop mathematics in children in many different ways.My method was to observe a time of singing at three preschools in a municipality and then interviewing the preschool teachers who held the singing moments.The results showed that teachers used a lot of math in time of singing as it is, some more aware of it than others. It was also shown that teachers believe that mathematics fit well with music. I can see what mathematical and musical activities that were carried out.My wish is that teachers should give children much mathematics skills during a time of singing. It is noticeable that there are math even if we do not lift it very much. Imagine then what happens when the teacher really think about doing it mathematically. What I particularly see in the results is that it is easy to get into math in singing moments and therefore think that we should take the opportunity to do so.

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Cooke, Alexander. "Algorithmic Stochastic Music." Case Western Reserve University School of Graduate Studies / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=case1492096098674462.

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Kelley, Diana L. "Music and mathematics--is there a connection? : the effects of participation in music programs on academic achievement in mathematics /." Abstract Full Text (HTML) Full Text (PDF), 2008. http://eprints.ccsu.edu/archive/00000493/02/1949FT.htm.

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Thesis (M.S.)--Central Connecticut State University, 2008.
Thesis advisors: S. Louise Gould, Philip P. Halloran, Shelley Jones. " ... in partial fulfillment of the requirements for the degree of Master of Science in Mathematics." Includes bibliographical references (leaves 21-22). Also available via the World Wide Web.

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Molder, Nathan. "Taking Notes: Generating Twelve-Tone Music with Mathematics." Digital Commons @ East Tennessee State University, 2019. https://dc.etsu.edu/etd/3592.

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There has often been a connection between music and mathematics. The world of musical composition is full of combinations of orderings of diﬀerent musical notes, each of which has diﬀerent sound quality, length, and em phasis. One of the more intricate composition styles is twelve-tone music, where twelve unique notes (up to octave isomorphism) must be used before they can be repeated. In this thesis, we aim to show multiple ways in which mathematics can be used directly to compose twelve-tone musical scores.

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Tucker, Zoe. "Emergence and Complexity in Music." Scholarship @ Claremont, 2017. http://scholarship.claremont.edu/hmc_theses/101.

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How can we apply mathematical notions of complexity and emergence to music, and how can these mathematical ideas then inspire new musical works? Using Steve Reich's Clapping Music as a starting point, we look for emergent patterns in music by considering cases where a piece's complexity is significantly different from the total complexity of each of the individual parts. Definitions of complexity inspired by information theory, data compression, and musical practice are considered. We also consider the number of distinct musical pieces that could be composed in the same manner as Clapping Music. Finally, we present a new musical compositions to demonstrate some of these ideas.

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Cranmore, Jeff L. "Experiences and Perceptions of Students in Music and Mathematics." Thesis, University of North Texas, 2014. https://digital.library.unt.edu/ark:/67531/metadc500113/.

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Since the time of Pythagoras, philosophers, educators, and researchers have theorized that connections exist between music and mathematics. While there is little doubt that engaging in musical or mathematical activities stimulates brain activity at high levels and that increased student involvement fosters a greater learning environment, several questions remain to determine if musical stimulation actually improves mathematic performance. This study took a qualitative approach that allowed 24 high school students to express their direct experiences with music and mathematics, as well as their perceptions of how the two fields are related. Participants were divided into four equal groups based on school music participation and level of mathematic achievement, as determined by their performance on the Texas Assessment of Knowledge and Skills (TAKS). Students participated in a series of three interviews addressing their experiences in both music and mathematics, and took the Multiple Intelligences Developmental Assessment Scales (MIDAS). TAKS data and MIDAS information were triangulated with interview findings. Using a multiple intelligence lens, this study addressed the following questions: (a) How do students perceive themselves as musicians and mathematicians? (b) What experiences do students have in the fields of music and mathematics? (c) Where do students perceive themselves continuing in the fields of music and mathematics? and (d) How do students perceive the fields of music and mathematics relating to each other? Contrary to most existing literature, the students who perceived a connection between the two fields saw mathematics driving a deeper understanding of the musical element of rhythm. Not surprisingly, students with rich backgrounds in music and mathematics had a higher perception of the importance of those fields. Further, it became readily apparent that test data often played a minimal role in shaping student perceptions of themselves in the field of mathematics. Finally, it became apparent from listening to the experiences of high school students, there are many growth areas for schools in order to meet the needs of their students.

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Velamazan, Mariano. "Designing playful learning experiences : Exploring embodied mathematics through electronic music." Thesis, Umeå universitet, Designhögskolan vid Umeå universitet, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-124025.

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I present a research based project that asks for a discussion about the role of technology in education. It is a question about how to design learning experiences and how to improve the experience of learning through interactive objects. More precisely, this project tries to explore the possibilities of an embodied learning of math using music in a playful way. Superbleeper, the name of the product, is an electronic music instrument that is played using math concepts. It invites 3-6 year old children to play with the math they have to understand according to the Swedish curriculum. This math foundation for the youngest kids is about measurement, shape, patterns, time, change, quantity, sets and order. The tests carried out with children in different contexts show that electronic music can be a way to embody and enjoy the use of math concepts in a creative way.
Pedagogical Interactive Math Visualizations

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Ullrich, Ringo. "Mit Musik zur Mathematik im Unterricht der Grundschule." Doctoral thesis, Universitätsbibliothek Leipzig, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-199740.

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Jensen, Clara. "Att lära matematik genom musik:Musikintegrerad matematikundervisning." Thesis, Malmö högskola, Fakulteten för lärande och samhälle (LS), 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:mau:diva-40666.

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This literature review looks into the effects of integrating music in mathematics teaching andhow it influences the problem solving ability. A systematic search for scientific articles was madeto investigate the research area. All together 13 scientific articles were chosen, which presentedvarious ways to integrate music in mathematics teaching and which had found different resultsin their studies. Generally, the articles presented positive effects of integrating music inmathematics teaching to develop students’ problem solving ability and mathematical learning.Similarities and differences between the presented articles were compared in the results of thisstudy, which showed common features in the characters of music and mathematics. In this study,problem solving is used in a wide definition which includes arithmetic, communication,reasoning and mathematical concepts

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Perciante, Valerie Elizabeth. "Effects of Mozart music on specific mathematical testing." Theological Research Exchange Network (TREN) Access this title online, 2004. http://www.tren.com.

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Blankenship, Ryan A. "The Golden Ratio and Fibonacci Sequence in Music." Ohio Dominican University Honors Theses / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=oduhonors1620086748612102.

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McAlpine, Kenneth B. "Applications of dynamical systems to music composition." Thesis, University of Glasgow, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.321912.

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McNeilis, Michael James. "Portfolio of compositions : pitch-class set theory in music and mathematics." Thesis, University of Liverpool, 2017. http://livrepository.liverpool.ac.uk/3009792/.

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This portfolio contains six scores of contemporary works, one electroacoustic piece submitted in concrete audio format and a critical commentary. Three additional scores are included as appendices, which present alternative arrangements of the acoustic works. An accompanying data DVD includes stereo recordings of a concert performance and four workshop performances, as well as stereo and 5.1 versions of the electroacoustic piece. With existing literature primarily focussing on pitch-class set theory as an analytical tool, this study aims to answer the question: Can set theory be used as the basis of a compositional framework to advance the creative process within the interdisciplinary field of music and mathematics? The pieces in the portfolio consider how set theory can be applied alongside mathematical principles like mutation, symmetry and proportion to inform musical networks and topologies based on material such as the octatonic scale, whole-tone scale and the all-interval tetrachords. A particular emphasis is placed on relationships between pitch-class sets in order to produce coherent compositional designs which link micro-level material to macro-level form and structure. Postcompositional evaluation of each work helps to create subsequent designs in the portfolio, and culminates in the piece Aggregation, which assesses the mathematical principles and compositional techniques developed earlier in the portfolio to encapsulate the research within a unified design and large-scale work. The results of the research establish set theory as a viable mathematical language for both the precompositional and compositional stages of the creative process, and demonstrate refinement of my own compositional methodology and musical style.

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Weiss, Mary Roy. "Background Music and Cognitive Learning Effects in Mathematics with Middle School Students." Thesis, Notre Dame of Maryland University, 2015. http://pqdtopen.proquest.com/#viewpdf?dispub=3687583.

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This quasi-experimental research study examined the cognitive effects of background music used with middle school students during mathematics classes and mathematics testing. Eight schools, nine teachers, 23 classes, and 302 students participated in the project. A series of five compact discs of Mozart selections, a specifically selected composite of 12 CD albums, was used over a period of 10 class days and one testing day. The tests were teacher-designed for use during the regular regimen of testing for their specific classes. The conditions of music and no-music were reversed so students were their own controls. Results showed a nonstatistical gain overall; however, sixth grade females had a net music gain that superseded all other male and female groupings. In addition, an incremental gain was found with those who had played instruments. Other gains/losses were noted for these conditions: if students liked or did not like background music during classes and testing, if they liked or did not like listening to music while doing homework, if they liked singing or not, and whether they felt that the music was a help or hindrance to their attention, concentration, and/or distraction. The students' perspectives concerning the quasi-experiment were reported as supplemental qualitative data which included impressions about the experiment, opinions about the experience they had, and suggestions for future experiments.

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Willis, Curt Glendale. "Impact of Music Education on Mathematics Achievement Scores Among Middle School Students." ScholarWorks, 2016. https://scholarworks.waldenu.edu/dissertations/1988.

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Music education has been shown to be related to a variety of positive outcomes, including student achievement in math. This study was conducted to explore the relationship between music education and student achievement in math. The framework for the study was Miendlarzweska and Trost's model of musical instrument training. A deidentified archival data set consisting of middle school students' (N = 116) total math scores on the Iowa Assessments was used to determine the impact of music education on students' math achievement, while controlling for students' sex and socioeconomic status. Changes in student achievement were measured by calculating math scores between the 2012-2013, 2013-2014, and 2014-2015 academic school years. The data were accessed from a private school system in the northeast United States. Results of a t test indicated that there were no differences in baseline scores between the group of students who received music education and the group of students who did not receive music education. Results of a regression model for 2013-2014 showed that music education was a significant predictor of math growth scores (p = .015). Results of a regression model for 2014-2015 indicated that only socioeconomic status was a significant predictor of math growth scores (p = .039). Implications for social change include improved stakeholder awareness of the value of music education for student achievement, which may motivate teachers to become advocates for music education and administrators to include music education in their curriculums. By increasing student access to music education, students may be helped to achieve to their fullest potential.

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Sanders, Edel Marie. "Music learning and mathematics achievement : a real-world study in English primary schools." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/283610.

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Music Learning and Mathematics Achievement: A Real-World Study in English Primary Schools Edel Marie Sanders Abstract This study examines the potential for music education to enhance children's mathematical achievement and understanding. Psychological and neuroscientific research on the relationship between music and mathematics has grown considerably in recent years. Much of this, however, has been laboratory-based, short-term or small-scale research. The present study contributes to the literature by focusing on specific musical and mathematical elements, working principally through the medium of singing and setting the study in five primary schools over a full school year. Nearly 200 children aged seven to eight years, in six school classes, experienced structured weekly music lessons, congruent with English National Curriculum objectives for music but with specific foci. The quasi-experimental design employed two independent variable categories: musical focus (form, pitch relationships or rhythm) and mathematical teaching emphasis (implicit or explicit). In all other respects, lesson content was kept as constant as possible. Pretests and posttests in standardised behavioural measures of musical, spatial and mathematical thinking were administered to all children. Statistical analyses (two-way mixed ANOVAs) of student scores in these tests reveal positive significant gains in most comparisons over normative progress in mathematics for all musical emphases and both pedagogical conditions with slightly greater effects in the mathematically explicit lessons. This investigation addresses concerns that UK and US governments' quests for higher standards in mathematics typically result in impoverished curricula with limited access to the arts. In showing that active musical engagement over time can improve mathematical achievement, as hypothesised, this work adds to a growing body of research suggesting that policy-makers and educationalists should reconsider curriculum balance.

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Baker, Jonathan Peter. "Methods of Music Classification and Transcription." BYU ScholarsArchive, 2012. https://scholarsarchive.byu.edu/etd/3330.

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We begin with an overview of some signal processing terms and topics relevant to music analysis including facts about human sound perception. We then discuss common objectives of music analysis and existing methods for accomplishing them. We conclude with an introduction to a new method of automatically transcribing a piece of music from a digital audio signal.

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Hershberger, Geoffrey D. "APPLIED TEMPERAMENT." UKnowledge, 2018. https://uknowledge.uky.edu/music_etds/126.

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The following document was created in order to promote intonation consensus in ensembles and to better facilitate learning in educational settings. Non-keyboard instruments provide musicians an opportunity to make nearly infinitesimal adjustments to pitch while performing; this creates difficulties for students and challenges even the most seasoned professionals. Non-keyboard musicians struggle their whole lives to play in tune, and even when one knows exactly where they want to place a pitch, technical difficulties can foul any musician's performance. When performing solo, the musician must choose a tuning system that is suitable for the music being performed, and attempt to realize it. When performing in ensembles, the need for consensus and a systematic approach become more apparent. When performing with keyboards, the difficulties are increased as further compromises are required. This research was conducted with the intention to assist non-keyboard instrumentalists in selecting and recreating an appropriate temperament. Additionally, the author hopes that keyboard instrumentalists will be inclined to make a consideration for the non-keyboard instruments when selecting their temperament. The following document contains information useful to those wishing to employ a consistent approach to tuning. Presented here are the acoustic phenomena that have perplexed scholars around the world for the last 2600 years. The history and science of these acoustic questions will be demonstrated and discussed.

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Stevenson-Milln, Carolyn. "Researching the development of a programme that merges mathematics and music in Grade R." Thesis, Rhodes University, 2018. http://hdl.handle.net/10962/61928.

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This small-scale case study explores the potential for synergy between music and mathematics learning in early childhood education whereby music can be used to help enhance children’s mathematical proficiency. Informal observations of the young learners participating in an Early Number Fun programme initiated by the South African Numeracy Chair Project suggested that many children struggled to exercise executive functioning and self-regulated skills, and struggled also with fluency in basic numeracy concepts such as understanding pattern. This case study was set up to investigate the effect of the development and implementation of a programme in which African music and mathematics learning, (particularly in relation to pattern and sequencing) were blended. The study’s core aim was to contribute to strengthening learners’ executive function and self-regulated learning competencies, both of which are important to learners’ developing agency over their own learning. An Action-Research-embedded-in-Design-Research approach was employed. This allowed an iterative process in developing a new mode of learning through blending music and mathematics. The theory of enactivism provided a theoretical framework to the study. The basic assumptions of an enactive perspective are shared understanding and joint action through engagement (as exemplified through group interaction between learner and teacher, and learning through action). The programme was developed and implemented with ongoing refinements in two Grade R classrooms. Data collected through observation, interviewing, document analysis and the keeping of a reflective research journal, are qualitative in nature. Analysis of the data indicate that the use of African block notation, as a rhythmic medium was well within reach of the participating children, such that at the end of each 16 session intervention programme, learners at both research sites demonstrated their capacity to: • Focus their attention on one activity while a different activity was taking place alongside them. • Watch, listen and only then act. • Practise their numbers through play: to count out and to write up to 16 and beyond. • Notate, read and interpret rhythmic patterns through block notation and instrumentation. The findings suggest the intervention programme could be continued over a longer period for maximum benefit, possibly through following Grade R learners through to Grade 1. The findings further suggest that fun with rhythmic, number-based patterning can assist learners’ development of executive function and self-regulated learning skills.

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Schulze, Walter. "A formal language theory approach to music generation." Thesis, Stellenbosch : University of Stellenbosch, 2010. http://hdl.handle.net/10019.1/4157.

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Thesis (MSc (Mathematical Sciences))-- University of Stellenbosch, 2010.
ENGLISH ABSTRACT: We investigate the suitability of applying some of the probabilistic and automata theoretic ideas, that have been extremely successful in the areas of speech and natural language processing, to the area of musical style imitation. By using music written in a certain style as training data, parameters are calculated for (visible and hidden) Markov models (of mixed, higher or first order), in order to capture the musical style of the training data in terms of mathematical models. These models are then used to imitate two instrument music in the trained style.
AFRIKAANSE OPSOMMING: Hierdie tesis ondersoek die toepasbaarheid van probabilitiese en outomaatteoretiese konsepte, wat uiters suksesvol toegepas word in die gebied van spraak en natuurlike taal-verwerking, op die gebied van musiekstyl nabootsing. Deur gebruik te maak van musiek wat geskryf is in ’n gegewe styl as aanleer data, word parameters vir (sigbare en onsigbare) Markov modelle (van gemengde, hoër- of eerste- orde) bereken, ten einde die musiekstyl van die data waarvan geleer is, in terme van wiskundige modelle te beskryf. Hierdie modelle word gebruik om musiek vir twee instrumente te genereer, wat die musiek waaruit geleer is, naboots.

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Rother, Sarah. "The correlation of music aptitude scores with mathematical achievement scores for high school seniors." Online version, 2000. http://www.uwstout.edu/lib/thesis/2000/2000rothers.pdf.

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Bergqvist, Johanna. "Texten i musiken där kan man hitta matematiken : En studie om matematiska begrepp i sångtexter i förskolan." Thesis, Karlstads universitet, Fakulteten för humaniora och samhällsvetenskap (from 2013), 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-26180.

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Denna studie handlar om vilken sorts matematiska begrepp som barnen i förskolan möter i sångtexter. Den har även analyserat vilken kunskap förskollärarna säger att de tror sångtexterna förmedlar och hur mycket de använder sig av sången i den dagligaverksamheten. I studien har tre kvalitativa intervjuer med pedagoger genomförts på olika förskolor, och analyser av nio sångtexter har gjorts.Frågeställningarna var: Vilka matematiska begrepp finns i de sångtexter barnen möter på förskolan? Vilka kunskaper säger pedagogerna i förskolan sig tro att sångtexterna ger barnen? Hur mycket använder sig pedagogerna av musik och sång i verksamheten? För att få reda på vilken sorts matematik och vilka begrepp som fanns i sångerna så analyserades sångtexterna och olika ”kategorier” undersöktes. De som hittades var: rumsuppfattning, tid, vikt och längd, form och räkneord. I intervjuerna framkom att barn lär sig väldigt mycket när de sjunger enligt pedagogerna. Alla pedagogerna var överens om att barnen lär sig språk och matematik genom att sjunga. Studien kom fram till att på avdelningarna där de intervjuade pedagogerna arbetar sjunger man varje dag, både spontant och inplanerat.
This study is about what kind of mathematics children in preschool encounter in song lyrics. The study has focused on what kind of knowledge preschool teachers think that the song lyrics conveys and how much they use music during the day. In the study three qualitative interviews were conducted with teachers at different preschools, and nine lyrics were analyzed. The research questions are: What mathematical concepts do children meet in song lyrics in preschool? What knowledge do teachers say they believe that the song lyrics convey to the children?How much do the teachers use music and song in their work? To find out what kind of mathematics there was in the music, lyrics were analyzed and different “categories” were found. These were: spatial perception, time, weight and length, shape and numbers. From the interviews it was concluded that teachers believe children learn very much when they sing. All teachers agreed that children can learn language and maths from song. The study concluded that in the preschool groups where the interviewed teachers work they sing every day, both spontaneously and according to schedule.

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McDonel, Jennifer S. "Exploring the relationship between music learning and mathematics learning in an interdisciplinary Pre-K curriculum." Thesis, State University of New York at Buffalo, 2013. http://pqdtopen.proquest.com/#viewpdf?dispub=3598710.

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The purpose of this study was to examine children's musical and mathematical behaviors as they participated in an interdisciplinary pre-K curriculum. Research questions were: 1. What connections—if any—do young children make between music learning and mathematics learning? 2. Is there a relationship between young children's emergent rhythm development and emergent numeracy development?

To address these questions, a concurrent embedded mixed-methods design was utilized. One intact class of 14 preschool children were observed at predetermined points throughout the Spring 2012 semester through participant observation and video footage of music classes, math activities, and other times where music was used in the curriculum. Interventions for classroom and music teachers were intended to foster developmentally appropriate practice in music and mathematics. Music aptitude and pre- and post-test measures of early music rhythm achievement and early numeracy achievement were correlated to embed a quantitative dimension.

Observed rhythm responses included movement such as (a) continuous, free-flowing motion during songs; (b) steady beat motions of bouncing, tapping, and clapping; and (c) rhythmic body motions of tapping or clapping rhythm patterns; chanted responses of (a) echoed rhythm patterns, (b) improvised rhythm patterns, and (c) parts of poems. Sung responses included singing with a light quality in initial singing range, as well as resting tone and tonal patterns. Mathematical responses included subitizing, one-to-one correspondence, counting fingers, forward and backward verbal counting, and using finger patterns to count on, and add and subtract numbers less than 10.

Limited, but supportive quantitative evidence was found regarding the relationship of early rhythm and early mathematics development. Emergent themes, community of learning and sharing, expanded social conventions, and reinforcement of learning, revolved around current thought that learning is both individually and socially constructed. That some children express themselves more readily through music and others through mathematics was supported; carefully selected song literature that meets both music learning and mathematics learning objectives can elicit observable musical and mathematical responses and may reinforce learning connections. Recommendations include replication with a design that addresses limitations of the present study and increased music and math pedagogy courses and professional development for pre-K classroom teachers.

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Burgers, Kate M. "Finding the Beat in Music: Using Adaptive Oscillators." Scholarship @ Claremont, 2011. http://scholarship.claremont.edu/hmc_theses/3.

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The task of finding the beat in music is simple for most people, but surprisingly difficult to replicate in a robot. Progress in this problem has been made using various preprocessing techniques (Hitz 2008; Tomic and Janata 2008). However, a real-time method is not yet available. Methods using a class of oscillators called relay relaxation oscillators are promising. In particular, systems of forced Hopf oscillators (Large 2000; Righetti et al. 2006) have been used with relative success. This work describes current methods of beat tracking and develops a new method that incorporates the best ideas from each existing method and removes the necessity for preprocessing.

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Galante, Daniela. "THE ROLE OF THE MUSIC TO LEARN GEOMETRICAL TRANSFORMATIONS." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79850.

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This research studies the interaction among the following contexts: natural language, geometrical language and musical language and it can provide new instruments to accord didactical situations and for a deeper understanding of communication processes. It springs from the consideration that the geometrical transformations are usually used in the compositional processes and the “role of the music to learn geometrical transformations” is actually a new study. In the field of the theory of situations by G. Brousseau (1986) we can assume to be in front of a learning teaching-situation including non-teaching situation as the teacher of musical instruments, while transmitting the knowledge of musical language (theoretical-practical) didn’t have the intention to transmit the geometrical transformation.

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Blumensath, Thomas. "Bayesian modelling of music : algorithmic advances and experimental studies of shift-invariant sparse coding." Thesis, Queen Mary, University of London, 2006. http://qmro.qmul.ac.uk/xmlui/handle/123456789/3804.

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In order to perform many signal processing tasks such as classification, pattern recognition and coding, it is helpful to specify a signal model in terms of meaningful signal structures. In general, designing such a model is complicated and for many signals it is not feasible to specify the appropriate structure. Adaptive models overcome this problem by learning structures from a set of signals. Such adaptive models need to be general enough, so that they can represent relevant structures. However, more general models often require additional constraints to guide the learning procedure. In this thesis a sparse coding model is used to model time-series. Relevant features can often occur at arbitrary locations and the model has to be able to reflect this uncertainty, which is achieved using a shift-invariant sparse coding formulation. In order to learn model parameters, we use Bayesian statistical methods, however, analytic solutions to this learning problem are not available and approximations have to be introduced. In this thesis we study three approximations, one based on an analytical integral approximation and two based on Monte Carlo approximations. But even with these approximations, a solution to the learning problem is computationally too expensive for the applications under investigation. Therefore, we introduce further approximations by subset selection. Music signals are highly structured time-series and offer an ideal testbed for the studied model. We show the emergence of note- and score-like features from a polyphonic piano recording and compare the results to those obtained with a different model suggested in the literature. Furthermore, we show that the model finds structures that can be assigned to an individual source in a mixture. This is shown with an example of a mixture containing guitar and vocal parts for which blind source separation can be performed based on the shift-invariant sparse coding model.

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Green, Sarah. "An exploration of how Foundation Phase Mathematics and English can enhance teaching and learning through Music integration, according to the South African Curriculum." Diss., University of Pretoria, 2020. http://hdl.handle.net/2263/78275.

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Schools have to adjust to accommodate subjects that are 21st century appropriate in an already full curriculum. Educators feel overwhelmed and unequipped to handle all the expectations of the curriculum. Many are led to believe that Mathematics, Language and Music go hand in hand. There must be a more effective way to teach these three subjects, especially considering the biggest concern in education is always insufficient time. This study investigated the natural relationships between English, Mathematics and Life Skills in the Foundation Phase, to determine if true integration is viable. A document analysis was conducted to examine various curriculum documents including the National Curriculum, the National Protocol for Assessment Grade R – 3, and the CAPS document with the focus on Mathematics, English and Life Skills in the Foundation Phase. The findings include the potential for introducing integration of musical activities through similar topics as well as using various teaching and learning strategies that are able to construct deeper understanding. Considering the natural connections between subjects and themes, music activities can offer validity in the curriculum.
Dissertation (MMus (Music Education))-- University of Pretoria, 2020.
Music
MMus (Music Education)
Unrestricted

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Nagisetty, Vytas. "Using Music-Related Concepts to Teach High School Math." PDXScholar, 2014. https://pdxscholar.library.pdx.edu/open_access_etds/1958.

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The purpose of this research was to test a strategy which uses music-related concepts to teach math. A quasi-experimental study of two high school remedial geometry sections was conducted during a review lesson of ratio, proportion, and cross multiplication. A pretest was given to both groups. Then, Group A received normal textbook instruction while Group B received the treatment, Get the Math in Music, which is an online activity involving proportional reasoning in a music-related context. Afterwards, a posttest was given to both groups. Pretest and posttest scores were used to compare gains in subject knowledge between the groups. Then a second evaluation of the treatment was conducted. Group A received the treatment and took a post-posttest. Score gains for Group A before and after receiving the treatment were compared. After these tests, all participants took a survey to determine if their appreciation of math grew as a result of the treatment. Finally, interviews were conducted to provide better understanding of the results. The research questions of this study were: to what extent does the integration of Get the Math in Music improve students' academic performance in a remedial geometry review of ratio, proportion, and cross multiplication, and to what extent does participation in the Get the Math activity improve students' attitudes towards math? My hypotheses were that students would perform significantly better on a subject knowledge test after receiving the treatment, and that all students would have a more positive attitude towards math after receiving the treatment. Quantitative results did not triangulate to support or refute these hypotheses. Greater improvement from pretest to posttest was statistically correlated with Group B, which was the group first receiving the treatment. But later, between posttest and post-posttest Group A did not show statistically significant greater gains after receiving the treatment. Surveys results showed that students did not necessarily like math any more after the treatment. Interviews revealed that several of these students were apathetic to geometry in particular, if not to math in general. The case of one student's improvement suggested that positive teacher-student relationships are more effective than any particular method to increase academic performance and student engagement. Survey results were consistent with earlier psychological studies claiming teenagers care about music. Additional studies in the future on the merits of using music to teach high school math would be useful. Claims that proportional reasoning is challenging were supported. It would be beneficial to evaluate the treatment in an Algebra or Pre-Algebra setting when students first study proportions.

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Du, Toit Pierre Johannes. "Iannis Xenakis (1922-2001): an examination of the implementation of stochastic procedures in selected compositions." Thesis, Stellenbosch : University of Stellenbosch, 2009. http://hdl.handle.net/10019.1/1645.

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Thesis (MMus (Music))--University of Stellenbosch, 2009.
The relationship between music and mathematics has been subjected to debate for centuries. There are two schools of thought with the one viewpoint holding that the relationship between mathematics, which is conceived as an abstract and cold discipline, compared to music, which is rich with emotion, must be very limited. Arguments for this view draws, for example, on recent research which indicates that musical talent is not inherently linked to mathematical capability. On the other pole of the debate is the belief that although music and mathematics contribute to different parts of society, there is a very important inter-relationship between the two fields. Of great interest to the latter is the Greek composer Iannis Xenakis whose musical aesthetics incorporates this philosophy. As composer, Xenakis used mathematical theories as basis for his musical works. He not only incorporated well known mathematical principles such as the Golden Section into his compositions but went further and, for instance, utilized Boolean Algebra, Probability theory and Stochastic processes in his music. His composition method based on these mathematical principles became known under the term Stochastic music and forms the focus of this thesis. The research project concentrates on the early part of Xenakis’ life in order to provide insight into the development of his composition methods. The mathematical principles at the centre of his stochastic compositions receive specific rationalisation. In doing so, the most significant probability distributions (Linear, Exponential, Poisson and Normal distribution) are defined in terms of their properties and Xenakis’ use of them. The application of these distributions is considered by looking at the early works Metastaseis (in which Xenakis confronted most of his musical problems and which formed the basis for his musical style) and Achorripsis (where he fully developed their implementation). An in-depth examination of the construction of Achorripsis is performed while scrutinizing Xenakis’ calculations. Specific attention is drawn to alterations and adjustments made to the calculations. His implementation of them into the final score is furthermore examined and it is shown where he deviated between the calculations and score. The thesis concludes by considering the extent and significance of the adjustments made by the composer in the name of artistic freedom.

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Buzzelli-Clarke, Elizabeth. "The academic environment of one junior high school in northeastern Pennsylvania as perceived by the administration and the English, mathematics and music faculty an ethnography /." Open access to IUP's electronic theses and dissertations, 2008. http://hdl.handle.net/2069/71.

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Pilkvist, Evelina. "Mattemusik på schemat : En studie av hur musiklärare och specialpedagog i matematik samarbetar för att integrera musik och matematik i sin undervisning i årskurs 1-3." Thesis, Karlstads universitet, Musikhögskolan Ingesund, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-14961.

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Bakgrunden till min studie kommer ursprungligen från mitt eget intresse att diskutera ämnesintegrerad undervisnings betydelse i skola och samhälle. Syftet med föreliggande studie är att utifrån ett multimodalt perspektiv ta reda på hur en musiklärare och en specialpedagog i matematik samarbetar för att integrera matematik och musik i sin undervisning i årskurs 1-3. Jag har använt mig av observationer och samtal för att ta reda på hur de arbetar, vilka redskap de använder sig av samt varför de arbetar som de gör. Den undervisning jag har observerat kallas mattemusik och är en utarbetad metod för ämnesintegrerat lärande. I resultatet visas att det är läroplanens mål och kunskapskrav i matematik och musik som styr undervisningen och att de två lärarna anser att det sätt som undervisningen bedrivs på även uppfyller många sociala mål som till exempel samarbetsförmåga, hänsynstagande och turtagning. Lektionerna i mattemusik utgick från ett tema och sedan arbetade lärarna tillsammans med eleverna mot den nya kunskapen ifrån många olika håll och med flera sinnen involverade. Undervisningen var i många avseenden multimodal då även momenten under lektionerna i sig själva var det. Det jag tar upp i diskussionen är bland annat avsaknaden av det taktila sinnet som inte fanns representerat i lika stor utsträckning som de visuella, auditiva och kinestetiska sinnena.
The background of my study is originally my own interest in discussing the role of crossover teaching in school and society. The purpose of this study is to discern how one music teacher and one special education teacher in mathematics work to integrate mathematics and music in their teaching in grades 1-3 from a multimodal perspective. I have used observations and conversations to determine how the teachers work, why they work the way they do, and what tools they are using. The teaching I have observed is called math-music and it is an elaborate method of crossover teaching in mathematics and music. The result shows that it is the curriculum goals and knowledge in mathematics and music that governs the teaching and that the two teachers believe that the way teaching is carried on also fulfills many social goals such as teamwork, consideration and turn-taking. The classes in math-music were based on one theme, with teachers and students working together from different perspectives, involving multiple senses. In many respects the teaching was multimodal, in which even different parts of the teaching, one by one, was multimodal in themselves. What I discuss includes the lack of the tactile sense, which was not represented as much as the visual, auditory and kinesthetic senses.

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Gäfvert, Molly, and Sofia Östensson. "”… för alla lär ju på olika vis” : En kvalitativ studie om pedagogers reflektioner och arbete med grundläggande matematik kombinerat med estetiska lärprocesser." Thesis, Södertörns högskola, Lärarutbildningen, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:sh:diva-27593.

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The purpose of this study is to investigate how teachers work with basic mathematics combined with aesthestic learning processes such as arts and music in grades F-1. The essay will compare teachers’ perceptions regarding aestethic learning processes when using art and music are used in the teaching of mathematics. We have used the following questions: Do teachers use aesthetic learning processes in the forms of arts and music in the basic teaching of mathematics and if so, how and in what way? What importance has aesthetic learning processes in the forms of arts and music in basic teaching of mathematics according to the teachers? What advantages and disadvantages do the teachers find with combinding the basic mathematics with arts and music? The study is based on a qualitative method with five interviews and eight observations. Our theoretical approach in this study is grounded on the phenomenological perspective and John Deweys progressive pedagogy about children’s learning processes. The result shows that the teachers have a positive attitude towards aesthetic learning processes when combining the basic mathematics teaching with arts and music. When comparing the different mathematics teaching methods it shows similarities and differences in the way teachers use art and music in the teaching of basic mathematics. Another result is that all of the teachers in some extent use arts in the teaching of mathematics, however there are only two teachers that combines the teaching of mathematics with music.

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Charles, James L. Jr. "Evaluating the effects of tenth grade students' music ensemble participation in relationship to the Graduation Exit Examinations mathematics and reading scores." Thesis, Capella University, 2013. http://pqdtopen.proquest.com/#viewpdf?dispub=3596099.

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The purpose of this study was to examine whether there is significant evidence suggesting that participants benefit more in their learning when musical art education is included in the curriculum. This nonexperimental correlational design was selected in anticipation that participation in the music program would lead to a greater increase in academic achievement, as measured by the Graduate Exit Examination. This study examined English Language Arts and mathematics test scores of 10^th grade participants who received instrumental music instruction and those participants who received no instrumental music instruction during the 2010-2011 academic school year. Three school districts located in southeast Louisiana participated in this study. School district 1 presented a total of 89 participants (N=89) who were administered the GEE during the 2010-2011 school year. There were 13 participants (n=13) who were members in an instrumental music ensemble during the same school year. There were 76 participants ( n=76) who were recognized as not being enrolled in an instrumental music ensemble. School district 2 presented a total of 225 participants ( N=225) who were administered the GEE during the 2010-2011 school year. Of 225 test takers, 16 participants (n=16) who were members in an instrumental music ensemble. There were 209 participants ( n=209) who were recognized as not being enrolled in an instrumental music ensemble. School district 3 presented a total of 317 participants ( N=317) who were administered the GEE during the 2010-2011 school year. Of the 317 test takers, 31 participants (n=31) were identified as members in an instrumental music ensemble. There were 286 participants (n=286) who were recognized as not be enrolled in an instrumental music ensemble. The methodology of this study consisted of comparing the mean scores of participants receiving instrumental music instruction at their school with the mean scores of participants who did not receive instrumental music instruction. Although findings of this study indicated the mean scores of instrumental music students were higher than non-instrumental music participants, results displayed no significant differences between mean scores of instrumental music participants and non-instrumental music participants where ( p< .05).

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Khoury, Imad. "Mathematical and computational tools for the manipulation of musical cyclic rhythms." Thesis, McGill University, 2007. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=101858.

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This thesis presents and analyzes tools and experiments that aim at achieving multiple yet related goals in the exploration and manipulation of musical cyclic rhythms. The work presented in this thesis may be viewed as a preliminary study for the ultimate future goal of developing a general computational theory of rhythm. Given a family of rhythms, how does one reconstruct its ancestral rhythms? How should one change a rhythm's cycle length while preserving its musicologically salient properties, and hence be able to confirm or disprove popular or historical beliefs regarding its origins and evolution? How should one compare musical rhythms? How should one automatically generate rhythmic patterns? All these questions are addressed and, to a certain extent, solved in our study, and serve as a basis for the development of novel general tools, implemented in Matlab, for the manipulation of rhythms.

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Tussing, Timothy Mark. "Analysis of Effects on Sound Using the Discrete Fourier Transform." The Ohio State University, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=osu1338371732.

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Taslakian, Perouz. "Musical rhythms in the Euclidean plane." Thesis, McGill University, 2008. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=115875.

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This thesis contains a collection of results in computational geometry that are inspired from music theory literature. The solutions to the problems discussed are based on a representation of musical rhythms where pulses are viewed as points equally spaced around the circumference of a circle and onsets are a subset of the pulses. All our results for rhythms apply equally well to scales, and many of the problems we explore are interesting in their own right as distance geometry problems on the circle.
In this thesis, we characterize two families of rhythms called deep and Euclidean. We describe three algorithms that generate the unique Euclidean rhythm for a given number of onsets and pulses, and show that Euclidean rhythms are formed of repeating patterns of a Euclidean rhythm with fewer onsets, followed possibly by a different rhythmic pattern. We then study the conditions under which we can transform one Euclidean rhythm to another through five different operations. In the context of measuring rhythmic similarity, we discuss the necklace alignment problem where the goal is to find rotations of two rhythms and a perfect matching between the onsets that minimizes some norm of the circular distance between the matched points. We provide o (n2)-time algorithms to this problem using each of the ℓ1, ℓ2, and ℓinfinity norms as distance measures. Finally, we give a polynomial-time solution to the labeled beltway problem where we are given the ordering of a set of points around the circumference of a circle and a labeling of all distances defined by pairs of points, and we want to construct a rhythm such that two distances with a common onset as endpoint have the same length if and only if they have the same label.

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Thul, Eric. "Measuring the complexity of musical rhythm." Thesis, McGill University, 2008. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=116081.

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This thesis studies measures of musical rhythm complexity. Informally, rhythm complexity may be thought of as the difficulty humans have performing a rhythm, listening to a rhythm, or recognizing its structure. The problem of understanding rhythm complexity has been studied in musicology and psychology, but there are approaches for its measurement from a variety of domains. This thesis aims to evaluate rhythm complexity measures based on how accurately they reflect human-based measures. Also, it aims to compare their performance using rhythms from Africa, India, and rhythms generated randomly. The results suggest that none of the measures accurately reflect the difficulty humans have performing or listening to rhythm; however, the measures do accurately reflect how humans recognize a rhythm's metrical structure. Additionally, the results suggest a need for normalization of the measures to account for variety among cultural rhythms.

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Ujihara, Rintaro. "Multi-objective optimization for model selection in music classification." Thesis, KTH, Optimeringslära och systemteori, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-298370.

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With the breakthrough of machine learning techniques, the research concerning music emotion classification has been getting notable progress combining various audio features and state-of-the-art machine learning models. Still, it is known that the way to preprocess music samples and to choose which machine classification algorithm to use depends on data sets and the objective of each project work. The collaborating company of this thesis, Ichigoichie AB, is currently developing a system to categorize music data into positive/negative classes. To enhance the accuracy of the existing system, this project aims to figure out the best model through experiments with six audio features (Mel spectrogram, MFCC, HPSS, Onset, CENS, Tonnetz) and several machine learning models including deep neural network models for the classification task. For each model, hyperparameter tuning is performed and the model evaluation is carried out according to pareto optimality with regard to accuracy and execution time. The results show that the most promising model accomplished 95% correct classification with an execution time of less than 15 seconds.
I och med genombrottet av maskininlärningstekniker har forskning kring känsloklassificering i musik sett betydande framsteg genom att kombinera olikamusikanalysverktyg med nya maskinlärningsmodeller. Trots detta är hur man förbehandlar ljuddatat och valet av vilken maskinklassificeringsalgoritm som ska tillämpas beroende på vilken typ av data man arbetar med samt målet med projektet. Denna uppsats samarbetspartner, Ichigoichie AB, utvecklar för närvarande ett system för att kategorisera musikdata enligt positiva och negativa känslor. För att höja systemets noggrannhet är målet med denna uppsats att experimentellt hitta bästa modellen baserat på sex musik-egenskaper (Mel-spektrogram, MFCC, HPSS, Onset, CENS samt Tonnetz) och ett antal olika maskininlärningsmodeller, inklusive Deep Learning-modeller. Varje modell hyperparameteroptimeras och utvärderas enligt paretooptimalitet med hänsyn till noggrannhet och beräkningstid. Resultaten visar att den mest lovande modellen uppnådde 95% korrekt klassificering med en beräkningstid på mindre än 15 sekunder.

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Frisina, Christopher Special. "The Sound of Fractions: teaching inherently abstract representations from an aural and embodied approach." Thesis, Virginia Tech, 2019. http://hdl.handle.net/10919/89487.

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Learning fractions is the focus for much of elementary school mathematics instruction because it is important and can be difficult. Fractions constitute a system of thinking about numbers and representations that differs in important ways from counting numbers. To understand fractions requires, for example, perceiving that a symbol such as 6 is not automatically associated with a larger quantity than 5 if they are denominators. In the system that constitutes fractions, 1/5 is bigger than 1/6. When students fail to master the system of fractions by a certain age, the inherent difficulty of the concepts can become confounded with discouragement, boredom, and humiliation. Music, especially percussion, not only provides an engaging context for many students but musical patterning can also provide deep analogic experiences to fractions at embodied and representational levels. Reasonable questions about musical patterns can both motivate and guide students towards understanding the properties of systems of fractions and their representations. We utilize this possibility in a new tool and associated curriculum called Sound of Fractions (SoF). SoF incorporates three main ideas to leverage musical interest and skill to provide an alternative approach to teaching fractions: Experiencing the whole and the part at the same time is crucial to learning fractions; Drumming is a compelling, embodied, culturally-relevant activity that allows students to experience the wholes, the parts, and the relationships between them at the same time; A new computer-based representational infrastructure utilizing aural, visual, physical, and temporal components that scaffolds classroom-based activities that bridge the relationship between percussion-related and mathematics activities in such a way as to gradually bring the student towards more standard mathematical representations and usages. We conducted preliminary testing of this approach in two series of after school programs with 5th-8th grade children who were significantly behind in learning fractions. Preliminary indications are that the approach is promising and ready to be tried in more formal contexts. This work illustrates that instruction rich in representational infrastructure and domains continues to be an important component of how technology can have positive impact.
Master of Science

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Ohlsson, Patrik. "Computer Assisted Music Creation : A recollection of my work and thoughts on heuristic algorithms, aesthetics, and technology." Thesis, Kungl. Musikhögskolan, Institutionen för komposition, dirigering och musikteori, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kmh:diva-2090.

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Denna text är delvis en dokumentation av min egna resa inom datorbaserat tonsättande, specifikt inom algoritmisk komposition. Det är även ett utforskande av den tankevärld som finns i anknytning till dessa metoder – där estetiska koncept och konsekvenser diskuteras. Texten kommer huvudsakligen att beröra metoder som gynnas av eller möjliggörs av teknologi. Jag har försökt att närma mig dessa ämnen holistiskt genom att diskutera allt från estetik, teknik, till konkreta realiseringar av särskilda musikaliska idéer. Till detta tillkommer även många notexempel, lite kod, och illustrationer – specifikt för att stödja förklaringarna av, för många musikstudenter, främmande utommusikaliska koncept.

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Hughes, Jonathan. "An auditory classifier employing a wavelet neural network implemented in a digital design /." Online version of thesis, 2006. https://ritdml.rit.edu/dspace/handle/1850/2629.

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Kintz, Andrew Lane. "Nullspace MUSIC and Improved Radio Frequency Emitter Geolocation from a Mobile Antenna Array." The Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1479896813925084.

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Louati, Kaouthar. "Modèles Mathématiques pour l'Inspection Nondestructive des Pipelines." Phd thesis, Ecole Polytechnique X, 2006. http://tel.archives-ouvertes.fr/tel-00125751.

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Dans les trois premiers chapitres de ce manuscrit de thèse, On propose trois nouvelles méthodes pour l'identification et la localisation des corrosions internes dans les pipelines. La première est par impédance électrique, la deuxième est par ondes guidées ultrasoniques et la troisième est par ultrasons.
On jette les bases mathématiques de ces différentes méthodes et on présente quelques tests numériques qui montrent leur efficacité.
Notre approche rentre dans la stratégie asymptotique développée au CMAP pour la résolution des problèmes inverses d'une manière robuste et stable. On exploite l'existence d'un petit paramètre (la mesure de Hausdorff de la partie corrosive) pour extraire des données la localisation de la partie corrosive et estimer son étendue. Le tout, d'abord, à travers des formules asymptotiques des mesures dépendantes du petit paramètre, rigoureusement établies à l'aide de la méthode des équations intégrales, et ensuite, par le biais de nouveaux algorithmes non-itératifs d'inversion. La plupart de ces algorithmes sont de type MUSIC (multiple signalclassification).
Le dernier chapitre est indépendant des trois premiers. il est consacré à la reconstruction de la forme d'un objet perturbé connaissant le champ lointain électrique ou acoustique. On développe pour le cas acoustique et électrique une relation linéarisée entre le champ lointain, résultant des données sur le bord de conditions de Dirichlet comme paramètre, et la forme de la structure perturbée comme variable. Cette relation nous ouvre la voie à la reconstruction
des coefficients de Fourier de la perturbation et nous aide à la reconstruction des coefficients de Fourier de la perturbation ce qui nous mène à formuler un développement asymptotique complet de
l'opérateur Dirichlet-Neumann.

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Souza, Luciana Gastaldi Sardinha. "Uma abordagem didático-pedagógica da racionalidade matemática na criação musical." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/48/48134/tde-21012013-142634/.

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A presente tese se ocupa, do ponto de vista didático-pedagógico, em estudar a presença da racionalidade matemática na criação musical. A linguagem matemática é uma poderosa ferramenta que pode ser utilizada para compreender estruturas subjacentes às composições. Com o intuito de defender essa característica, são apresentados, neste trabalho, conceitos e estruturas matemáticas passíveis de analisar algumas obras musicais, como a teoria de conjuntos de Forte, a qual permite, por exemplo, tratar translações e inversões por meio do conceito de função matemática. Essa mesma teoria possibilitou ainda analisar algumas composições do século XX, como as de Almeida Prado e Rodolfo Coelho de Souza. A presença da razão áurea é pesquisada na obra de Mozart, Villa Lobos, Bartók e Debussy. Exemplos de autossimilaridade na música são apresentados analisando-se composições de Bach e Rodolfo Coelho de Souza. São estudados diversos tipos de simetria e feitas algumas aplicações em correlação com a música. É verificado que funções transposição (T) e inversão (TnI) formam um grupo com a operação composição. São definidas as funções P, L e R que têm como elementos do domínio e da imagem acordes maiores e menores e é mostrado como essas funções, juntamente com a operação composição geram o grupo PLR. São analisados alguns Choros de Pixinguinha e algumas Canções dos Beatles, como Octopuss Garden e verifica-se que tais composições apresentam este grupo PLR de funções no seu encadeamento. Demonstra-se que os grupos T/TnI e PLR são isomorfos ao grupo diedral D12, oferecendo aos graduandos em matemática um exemplo representativo do rico potencial da interface matemática/música, no caso via uma aplicação em música da Teoria de Grupos. O forte caráter interdisciplinar do presente trabalho se fundamenta, do ponto de vista didático-pedagógico, em textos de Olga Pombo e Ivani Fazenda. Uma tentativa de reintegrar a música à educação pode ser verificada pela aprovação do Projeto de Lei 2732/2008, o qual determina a obrigatoriedade do ensino musical na Educação Básica. Assim sendo, um importante resultado deste trabalho é a proposta de uma disciplina, a ser oferecida na graduação, voltada tanto para estudantes de música como de matemática, que contribua, de alguma maneira, com a formação desses profissionais, oferecendo-lhes subsídios para atuar no ensino médio ao integrar essas duas disciplinas. Tal disciplina tem o intuito de gerar um vasto campo de trocas de experiências entre os alunos, os quais poderão se apropriar de novos conhecimentos proporcionados pela união dessas áreas do conhecimento.
This thesis deals, in didactic-pedagogical terms, with the study of the presence of mathematical reasoning at the musical creation. The mathematical language is a powerful tool that can be used to understand structures underlying the compositions. In order to defend this characteristic, concepts and mathematical structures capable of analyzing some musical compositions, as the theory of sets of Forte are presented in this work, allowing, for example, treating translations and inversions through the concept of mathematical function. This same theory enabled the detailed analysis of particular twentieth centurys compositions, such as works by Almeida Prado and Rodolfo Coelho de Souza. The presence of the Golden Ratio is investigated in the works of Mozart, Villa Lobos, Bartók and Debussy. Examples of self-similarity in music are presented through the analysis of compositions by Bach and by Rodolfo Coelho de Souza. Specific types of symmetry are studied and some applications in correlation with music are realized. The fact that transpositions (T) and inversions (TnI) functions form a group with the compositions operation is verified. The functions P, L and R, whose domain and image elements are major and minor chords, are defined, and a detailed description is given on how these functions generate the PLR group through the composition operation. Cries by Pixinguinha and Beatles songs such as Octopuss Garden are analyzed and the fact that these compositions have the PLR group in their chaining can be verified. According to the demonstration, the groups T/TnI and PLR are isomorphic to the dihedral group D12, offering to the undergraduate mathematics students an example of the rich potential of the mathematics/music interface, in this case, through an application of the Groups Theory in music. The strong interdisciplinary character of this work is based, in didactic-pedagogical terms, on Olga Pombo\'s and Ivani Fazenda\'s texts. An attempt to reintegrate music to the standard education can be verified through the approval of the Law project 2732/2008, which stipulates the mandatory teaching of music in Basic Education. This way, an important result of this work is the proposal of a subject, to be offered at an undergraduate level to both students of music and mathematics, which contributes to the their professional training, offering them tools to integrate these two subjects when acting in high school. This subject aims to generate a wide range ofexperience exchange between students, who can expand their knowledge through the combination of these two subject matters.

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du, Plessis Janine. "Transformation Groups and Duality in the Analysis of Musical Structure." Digital Archive @ GSU, 2008. http://digitalarchive.gsu.edu/math_theses/66.

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One goal of music theory is to describe the resources of a pitch system. Traditionally, the study of pitch intervals was done using frequency ratios of the powers of small integers. Modern mathematical music theory offers an independent way of understanding the pitch system by considering intervals as transformations. This thesis takes advantage of the historical emergence of algebraic structures in musicology and, in the spirit of transformational theory, treats operations that form mathematical groups. Aspects of Neo-Riemannian theory are explored and developed, in particular the T/I and PLR groups as dual. Pitch class spaces, such as 12, can also be defined as torsors. In addition to surveying the group theoretical tools for music analysis, this thesis provides detailed proofs of many claims that are proposed but seldom supported.

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Cohen, Nathann. "Three years of graphs and music : some results in graph theory and its applications." Phd thesis, Université Nice Sophia Antipolis, 2011. http://tel.archives-ouvertes.fr/tel-00645151.

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Cette thèse présente différents aperçus de problèmes de mathématiques discrètes en lien avec la théorie des graphes. Elle s'intéresse en particulier à la coloration de graphes, i.e. l'assignation de couleurs aux sommets (ou arêtes) d'un graphes sous certaines contraintes locales, notamment l'exclusion de motifs. Pour différents types de coloration (choisissabilité des sommets, des arêtes, coloration acyclique ou linéaire, ...), un état de l'art est présenté, accompagné de résultats d'existence sur les graphes planaires ou leurs sous-classes, ayant pour but de minimiser le nombre de couleurs nécessaires pour un degré maximum ou un degré moyen maximum (Mad) donnés. Cette thèse traite également de décompositions induites de graphes, et démontre qu'il existe pour tout graphe $H$ une suite infinie de graphes denses dont les arêtes peuvent être partitionnées en copies induites de $H$. Cette preuve requiert le formalisme des hypergraphes, pour lesquels un autre résultat de décomposition est démontré, i.e. une décomposition optimale de l'hypergraphe complet 3-régulier en hypergraphes $\alpha$-acycliques. La troisième parti porte sur des questions algorithmiques. Elles consistent en problèmes d'optimisation ou d'existence, motivés par le routage d'information dans les réseaux, analysés par le formalisme classique de complexité algorithmique, ou traitent de la recherche de sous-graphes dans le formalisme de la complexité paramétrée. Dans une quatrième partie sont considérés des problèmes de comptage issus de la chimie, suivis de la présentation de Programmes Linéaires Entiers utilisés dans le logiciel de mathématiques Sage.

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McCorkle, Tricia Dawn. "Math, music, and membranes: A historical survey of the question "can one hear the shape of a drum"?" CSUSB ScholarWorks, 2005. https://scholarworks.lib.csusb.edu/etd-project/2933.

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In 1966 Mark Kac posed an interesting question regarding vibrating membranes and the sounds they make. His article entitled "Can One Hear the Shape of a Drum?", which appeared in The American Mathematical Monthly, generated much interest and scholarly debate. The evolution of Kac's intriguing question will be the subject of this project.

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Pillão, Delma. "A pesquisa no âmbito das relações didáticas entre matemática e música: estado da arte." Universidade de São Paulo, 2009. http://www.teses.usp.br/teses/disponiveis/48/48134/tde-09032010-115909/.

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Esta dissertação tem como objetivo desenvolver um estado da arte da produção acadêmica no âmbito da relação entre matemática e música na área de educação, no Brasil, no período de 1990 a 2008. A partir do objeto de estudo dissertações de mestrado e teses de doutorado identificadas por meio do banco de teses da Capes foi construído um diretório de pesquisas sobre o tema, na tentativa de compreender o que tem sido estudado por estes pesquisadores, buscando conhecer suas principais preocupações e perspectivas, bem como as dificuldades e tensões que precisam ser observadas no âmbito dos estudos educacionais voltados para a utilização de música no ensino de matemática. Inicialmente, foi realizado o mapeamento geral da produção, tendo por base seus resumos. Após esta etapa foi realizada a leitura dos principais estudos. A análise de conteúdo, definida por Bardin (2000), configurou-se como o principal o procedimento metodológico que orientou a presente pesquisa, possibilitando a realização de uma investigação de cunho qualitativo. O referencial teórico utilizado pautou-se nos estudos de autores como Ferreira (1999; 2002), DAmbrósio (1986; 1990; 1993; 1999; 2004; 2005; 2006), Cortella (1998), Morin (2006), Biembengut (2002), Conrado (2005), Brejo (2007) entre outros, a fim de localizar e aprofundar as questões trazidas pelos estudos. Desse modo, este estudo busca destacar o valor, o papel e o significado dos trabalhos acadêmicos em torno dos estudos didáticos que envolvem música e matemática, procurando contribuir para a ampliação das pesquisas acadêmicas nesta área de estudos.
This dissertation aims at developing a State of the Art of the academic production in the context of the interrelationships between mathematics and music with an educational approach in Brazil, during the period from 1990 to 2008. From the object of study dissertations of Master and theories of Doctorate identified, by database of Thesis from CAPES it was built a directory of research on such a subject, in order to try to understand what has been studied by these researchers. This thesis also tries to understand their main concerns and perspectives, as well as the difficulties and tensions which are present in the educational studies toward the use of music in mathematics education. Initially, the general mapping of all the production was developed based on the abstract of each research. After this, it was read the main searches on this subject. The content analysis is defined by Bardin (2000), configured itself as the main methodological procedure that oriented this research, enabling the achievement of an inquiry with a qualitative approach. The theoretical framework used is guided by the studies of authors such as Ferreira (1999, 2002), D\'Ambrosio (1986, 1990, 1993, 1999, 2004, 2005, 2006), Cortella (1998), Morin (2006), Biembengut (2002), Conrad (2005), Brejo (2007) among others to find and to develop the issues brought by the studies. Thus, this study aims to stand out the value, the role and the meaning of academic works toward didactical studies involving music and mathematics, in order to widen the academic research in this area of study.

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Mbusi, Nokwanda Princess. "An investigation into the use of traditional Xhosa dance to teach mathematics: a case study in a Grade 7 class." Thesis, Rhodes University, 2012. http://hdl.handle.net/10962/d1003499.

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This study seeks to explore mathematical concepts embedded in traditional Xhosa dance and how these concepts can be incorporated into a learning programme for the teaching and learning of mathematics. The study seeks to gain insight into whether learners could benefit from the implementation of such a learning programme. Learners from a Grade 7 class in a rural school performed traditional Xhosa dances and their performances were captured through video recording. The video recordings were then observed and analysed to determine the mathematical concepts embedded in the dances. These concepts were then linked to those found in the Grade 7 mathematics curriculum. A learning programme integrating mathematical concepts from the dance activities with mathematical concepts from the Grade 7 curriculum was then designed. The learning programme contained mathematical problem solving activities that required learners to re-enact the dance performances in order to find the required solutions. The learning programme was then implemented with the learners over a period of three weeks. During the implementation, learners’ behaviour towards the learning experience was observed, their engagement with the problem solving activities as well as their strategies for solving the problems, were carefully observed. Also, their interactions with each other were noted. After the implementation of the learning programme, focus group interviews were held with learners to determine their opinions, attitudes and feelings about their experience of learning mathematics through traditional Xhosa dance. Key findings indicated that traditional Xhosa dance can be used as a medium for learning many concepts in the mathematics curriculum; the use of the dance gave learners an opportunity to learn mathematics from a familiar context and to participate actively and collaboratively in their learning. Also, it emerged that the use of dance to teach mathematics had potential to help improve learners’ attitudes towards mathematics. Conclusions were reached that the dance had potential for use as a means for the meaningful learning of mathematics. However, limitations and challenges with the study were identified, such as its limited replicability in other mathematics classrooms.

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Prado, Luis Antonio Gagliardi. "Matemática, física e música no renascimento: uma abordagem histórico-epistemológica para um ensino interdisciplinar." Universidade de São Paulo, 2010. http://www.teses.usp.br/teses/disponiveis/48/48134/tde-28092010-095901/.

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Durante o Renascimento ocorre uma retomada do pensamento racional em que o conhecimento clássico é revisitado e reorganizado pelo homem. Há uma contestação à razão pitagórica nos intervalos musicais. Vincenzo Galilei se opõe à maneira que Pitágoras relacionou os intervalos musicais através de razões de números naturais. Dá-se então, uma revolução sobre as idéias científicas que influenciaram a música. Vincenzo Galilei rompe com a visão pitagórica e passa a testar experimentalmente relações musicais supostamente corretas e começa a reescrever a teoria musical a partir de fundamentos experimentais. Seu filho Galileu, por sua vez, coloca a física dentro de um enfoque experimental e prático. Com este novo enfoque a concepção pitagórica da música se vê ameaçada. As relações entre a física, a matemática e a música se intensificam e o estudo da música nesta época tem um caráter particularmente interessante sob o ponto de vista interdisciplinar. Através de um enfoque histórico-epistemológico, busca-se estudar a importância da interdisciplinaridade no ensino de maneira geral, em especial da matemática, física e música, e de propor algumas oficinas interdisciplinares em que essas três disciplinas, possam de algum modo estar presentes. O aprendizado focado em mais de uma disciplina através de uma atividade interdisciplinar nem sempre é fácil e pode representar um obstáculo epistemológico, uma vez que saímos de nossa zona de conforto. Tais oficinas, portanto, têm também por objetivo instigar o aluno e convidá-lo a ter um enfoque reflexivo e crítico, assim como perceber o desafio que é enxergar e estudar fenômenos através de enfoques diferentes. Espera-se, dessa maneira, enriquecer o potencial de aprendizado através de uma complementação do ensino tradicionalmente feito através de disciplinas separadas, pela inclusão da interdisciplinaridade, quando possível.
During the Renaissance there is a resumption of the rational thought in which classical knowledge is revisited and rearranged by man. There is a contestation that challenges the Pythagorean intervals. Vincenzo Galilei opposed the way that Pythagoras listed the musical intervals by ratios of natural numbers. It was then established a revolution of scientific ideas that influenced music. Vincenzo Galilei breaks the Pythagorean view and starts to test experimentally musical relationships that were supposedly correct and begins to write a new music theory based on experimental foundations. His son Galileo, in turn, puts physics within a practical an experimental approach. Due to this new approach, the Pythagorean concept of music is threatened. The relationships between physics, mathematics and music are intensified and the study of music at this time has a particularly interesting character from an interdisciplinary point of view. Through a historical and epistemological approach, this work studies the importance of interdisciplinary education in general, especially in mathematics, physics and music, and aims at suggesting some interdisciplinary workshops such that these three disciplines can somehow be present. Learning involving more than one subject through an interdisciplinary activity is not always easy and may represent an epistemological obstacle since we go out of our comfort zone. These workshops therefore also aim at instigating the students as well as inviting them to take a reflective and critical approach, and realize how challenging is to see and study phenomena through different points of view. It is hoped in this way to enrich the learning potential through a complementation of the education process, traditionally done by separate subjects, by the inclusion of interdisciplinary activities whenever possible.

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Dissertations / Theses on the topic 'Music in mathematics'

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