An Exploration of the Relationship Between Mathematics and Music
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Mapping Inter and Transdisciplinary Relationships in Architecture: a First Approach to a Dictionary Under Construction
Athens Journal of Architecture XY Mapping Inter and Transdisciplinary Relationships in Architecture: A First Approach to a Dictionary under Construction By Clara Germana Gonçalves Maria João Soares† This paper serves as part of the groundwork for the creation of a transdisciplinary dictionary of architecture that will be the result of inter and transdisciplinary research. The body of dictionary entries will be determined through the mapping of interrelating disciplines and concepts that emerge during said research. The aim is to create a dictionary whose entries derive from the scope of architecture as a discipline, some that may be not well defined in architecture but have full meanings in other disciplines. Or, even, define a hybrid disciplinary scope. As a first approach, the main entries – architecture and music, architecture and mathematics, architecture, music and mathematics, architecture and cosmology, architecture and dance, and architecture and cinema – incorporate secondary entries – harmony, matter and sound, full/void, organism and notation – for on the one hand these secondary entries present themselves as independent subjects (thought resulting from the main) and on the other they present themselves as paradigmatic representative concepts of a given conceptual context. It would also be of interest to see which concepts are the basis of each discipline and also those which, while not forming the basis, are essential to a discipline’s operationality. The discussion is focused in the context of history, the varying disciplinary interpretations, the differing implications those disciplinary interpretations have in the context of architecture, and the differing conceptual interpretations. The entries also make reference to important authors and studies in each specific case. -
The Most Admired* What Do Clint Eastwood, Jimmy
The Most Admired* What do Clint Eastwood, Jimmy Carter, and Warren Buffett have in common? No, this isn’t a setup for a pop culture joke, but rather a partial list of the most admired Americans over age 75. Provided with the names of 23 major personalities in this age bracket and asked to select the two they most admire, Americans compile a list that is at once diverse and homogenous; topping the list are two actors, two former presidents, a man of the cloth, and a financial wizard turned philanthropist. All remarkably accomplished, but all male. Clint Eastwood ranks highest overall, with 23% rating him as their most admired public figure over age 75; among men that proportion rises to 30%, and he reaches 33% among Republicans despite his unusual 2012 GOP convention appearance, making him that group’s second highest choice. Morgan Freeman runs a close second with 21% overall, but he is the clear favorite among both African Americans (40%) and Millennials (33%). Jimmy Carter finishes third overall with 19%, but he tops Democrats’ list (33%). Similarly, George H.W. Bush is number one among Republicans (36%), and he finishes fourth overall with 17%. Rounding out the most admired list in double digits are Billy Graham (16%) and Warren Buffett (13%). Buffett’s popularity lands him in second place among college-educated adults and affluent Americans. Billy Graham is relatively well loved among those over age 50. The three most admired women cross the ideological spectrum—former First Lady Nancy Reagan (9%) on the right, Justice Ruth Bader Ginsburg (7%) on the left, and TV newswoman Barbara Walters (9%) in the middle. -
Two Conceptions of Harmony in Ancient Western and Eastern Aesthetics: “Dialectic Harmony” and “Ambiguous Harmony”
TWO CONCEPTIONS OF HARMONY IN ANCIENT WESTERN AND EASTERN AESTHETICS: “DIALECTIC HARMONY” AND “AMBIGUOUS HARMONY” Tak-lap Yeung∗ Abstract: In this paper, I argue that the different understandings of “harmony”, which are rooted in ancient Greek and Chinese thought, can be recapitulated in the name of “dialectic harmony” and “ambiguous harmony” regarding the representation of the beautiful. The different understandings of the concept of harmony lead to at least two kinds of aesthetic value as well as ideality – harmony in conciliation and harmony in diversity. Through an explication of the original meaning and relation between the concept of harmony and beauty, we can learn more about the cosmo-metaphysical origins in Western and Eastern aesthetics, with which we may gain insights for future aesthetics discourse. Introduction It is generally accepted that modern philosophy can trace itself back to two major origin points, ancient Greece in the West and China in the East. To understand the primary presuppositions of Western and Eastern philosophical aesthetics, we must go back to these origins and examine the core concepts which have had a great influence on later aesthetic representation. Inspecting the conception of “harmony”, a central concept of philosophical aesthetic thought for both the ancient Greek and Chinese world, may bring us valuable insight in aesthetic differences which persist today. In the following, I argue that the different understandings of “harmony”, which are rooted in ancient Greek and Chinese thought, can be recapitulated in the name of “dialectic harmony” and “ambiguous harmony” regarding the representation of the beautiful.1 The different understandings of the concept of harmony lead to, at least, two kinds of aesthetic value as well as ideality – harmony in conciliation and harmony in diversity. -
HARMONY HAMMOND with Phillip Griffith
Art June 3rd, 2016 INCONVERSATION HARMONY HAMMOND with Phillip Griffith Harmony Hammond made her start as an artist in the feminist milieu of 1970s New York, co-founding A.I.R. Gallery, the first women’s gallery, in 1972. Her early artwork developed a feminist, lesbian, and queer idiom for painting and sculpture, especially in such celebrated works as her woven and painted Floorpieces (1973) and wrapped sculptures, like Hunkertime (1979 – 80). Since 1984, she has lived and worked in New Mexico. Her current show at Alexander Gray Associates (May 19 – June 25, 2016) showcases what she calls her “near monochrome” paintings and monotype prints on grommeted paper that Lucy Lippard has termed “grommetypes.” On the occasion of the exhibition’s opening, Hammond spoke with Phillip Griffith about martial arts, the painting body, and violence in her work. Phillip Griffith (Rail): Your paintings from this new exhibition seem appreciably different than the wrapped paintings included in your 2013 show with Alexander Gray. Harmony Hammond: Well, Things Various (2015), the earliest painting in the current exhibition, segues from the 2013 work. The visual vocabulary of grommeted straps—sometimes tied together, sometimes not—attached to the thick paint surface with pigment-covered pushpins, is the same. Only in Things Various, most of the straps hang open, untied, suggesting only the potential of connection or restraint. The new paintings continue to emphasize the material engagement of paint, but differ from the earlier work through the use of the grommeted grid as a disruptive visual strategy and the shift to what is going on beneath/below/under what we perceive as the painting surface. -
MATHEMATICS EXTENDED ESSAY Mathematics in Music
TED ANKARA COLLEGE FOUNDATION PRIVATE HIGH SCHOOL THE INTERNATIONAL BACCALAUREATE PROGRAMME MATHEMATICS EXTENDED ESSAY Mathematics In Music Candidate: Su Güvenir Supervisor: Mehmet Emin ÖZER Candidate Number: 001129‐047 Word Count: 3686 words Research Question: How mathematics and music are related to each other in the way of traditional and patternist perspective? Su Güvenir, 001129 ‐ 047 Abstract Links between music and mathematics is always been an important research topic ever. Serious attempts have been made to identify these links. Researches showed that relationships are much more stronger than it has been anticipated. This paper identifies these relationships between music and various fields of mathematics. In addition to these traditional mathematical investigations to the field of music, a new approach is presented: Patternist perspective. This new perspective yields new important insights into music theory. These insights are explained in a detailed way unraveling some interesting patterns in the chords and scales. The patterns in the underlying the chords are explained with the help of an abstract device named chord wheel which clearly helps to visualize the most essential relationships in the chord theory. After that, connections of music with some fields in mathematics, such as fibonacci numbers and set theory, are presented. Finally concluding that music is an abstraction of mathematics. Word Count: 154 words. 2 Su Güvenir, 001129 ‐ 047 TABLE OF CONTENTS ABSTRACT………………………………………………………………………………………………………..2 CONTENTS PAGE……………………………………………………………………………………………...3 -
The Market for Luca Pacioli's Summa Arithmetica
Middlesex University Research Repository An open access repository of Middlesex University research http://eprints.mdx.ac.uk Sangster, Alan, Stoner, Gregory N. and McCarthy, Patricia A. (2008) The market for Luca Pacioli’s Summa arithmetica. Accounting Historians Journal, 35 (1) . pp. 111-134. ISSN 0148-4184 [Article] This version is available at: https://eprints.mdx.ac.uk/3201/ Copyright: Middlesex University Research Repository makes the University’s research available electronically. Copyright and moral rights to this work are retained by the author and/or other copyright owners unless otherwise stated. The work is supplied on the understanding that any use for commercial gain is strictly forbidden. A copy may be downloaded for personal, non-commercial, research or study without prior permission and without charge. Works, including theses and research projects, may not be reproduced in any format or medium, or extensive quotations taken from them, or their content changed in any way, without first obtaining permission in writing from the copyright holder(s). They may not be sold or exploited commercially in any format or medium without the prior written permission of the copyright holder(s). Full bibliographic details must be given when referring to, or quoting from full items including the author’s name, the title of the work, publication details where relevant (place, publisher, date), pag- ination, and for theses or dissertations the awarding institution, the degree type awarded, and the date of the award. If you believe that any material held in the repository infringes copyright law, please contact the Repository Team at Middlesex University via the following email address: [email protected] The item will be removed from the repository while any claim is being investigated. -
April 2021 Will Wells, Timber Creek High School C/O 2007
Black Horse Pike Regional School District Spotlight on Alumni - April 2021 Will Wells, Timber Creek High School c/o 2007 “Will graduated in 2007. Since then he has worked as a professional musician, composer, film scoring composer, arranger, and music producer. Will was a guitarist, keyboardist, and backing vocalist for the group "Imagine Dragos" and went on their world tour with them in 2015-2016. Will also was the Electronic Music Producer for the Broadway smash hit, "Hamilton." Will has also worked with famous musicians Barbara Streisand, LMFAO, Anthony Ramos, Quincey Jones, Cynthia Erivo (Star of the movie "Harriet"), Pentatonix, and many, many more! For more information, check out his website at: willwellsmusic.com Each year Will returns to Timber Creek to speak with our musicians, has brought in guest performers and conducted a song writing workshop. ~John Perkis, TC Music Education teacher 1. AA: Upon graduation, what post-secondary path did you take and why? Will: Upon graduating from Timber Creek Regional High School in 2007, I decided to attend Berklee College of Music in Boston, Massachusetts. After completing their “5- Week Summer Program” in the Summer of 2005, I knew that there was something about this institution that uniquely suited my needs, my passion, and my dreams. I was always interested in traditional and contemporary music, as well as the ever-evolving technology that was used in its creation. Berklee truly felt like the only place where I could fully immerse myself in the study of music and music technology, while being surrounded by thousands of other scholars who were passionate about music or the music industry. -
The Creative Act in the Dialogue Between Art and Mathematics
mathematics Article The Creative Act in the Dialogue between Art and Mathematics Andrés F. Arias-Alfonso 1,* and Camilo A. Franco 2,* 1 Facultad de Ciencias Sociales y Humanas, Universidad de Manizales, Manizales 170003, Colombia 2 Grupo de Investigación en Fenómenos de Superficie—Michael Polanyi, Departamento de Procesos y Energía, Facultad de Minas, Universidad Nacional de Colombia, Sede Medellín, Medellín 050034, Colombia * Correspondence: [email protected] (A.F.A.-A.); [email protected] (C.A.F.) Abstract: This study was developed during 2018 and 2019, with 10th- and 11th-grade students from the Jose Maria Obando High School (Fredonia, Antioquia, Colombia) as the target population. Here, the “art as a method” was proposed, in which, after a diagnostic, three moments were developed to establish a dialogue between art and mathematics. The moments include Moment 1: introduction to art and mathematics as ways of doing art, Moment 2: collective experimentation, and Moment 3: re-signification of education as a model of experience. The methodology was derived from different mathematical-based theories, such as pendulum motion, centrifugal force, solar energy, and Chladni plates, allowing for the exploration of possibilities to new paths of knowledge from proposing the creative act. Likewise, the possibility of generating a broad vision of reality arose from the creative act, where understanding was reached from logical-emotional perspectives beyond the rational vision of science and its descriptions. Keywords: art; art as method; creative act; mathematics 1. Introduction Citation: Arias-Alfonso, A.F.; Franco, C.A. The Creative Act in the Dialogue There has always been a conception in the collective imagination concerning the between Art and Mathematics. -
Unified Music Theories for General Equal-Temperament Systems
Unified Music Theories for General Equal-Temperament Systems Brandon Tingyeh Wu Research Assistant, Research Center for Information Technology Innovation, Academia Sinica, Taipei, Taiwan ABSTRACT Why are white and black piano keys in an octave arranged as they are today? This article examines the relations between abstract algebra and key signature, scales, degrees, and keyboard configurations in general equal-temperament systems. Without confining the study to the twelve-tone equal-temperament (12-TET) system, we propose a set of basic axioms based on musical observations. The axioms may lead to scales that are reasonable both mathematically and musically in any equal- temperament system. We reexamine the mathematical understandings and interpretations of ideas in classical music theory, such as the circle of fifths, enharmonic equivalent, degrees such as the dominant and the subdominant, and the leading tone, and endow them with meaning outside of the 12-TET system. In the process of deriving scales, we create various kinds of sequences to describe facts in music theory, and we name these sequences systematically and unambiguously with the aim to facilitate future research. - 1 - 1. INTRODUCTION Keyboard configuration and combinatorics The concept of key signatures is based on keyboard-like instruments, such as the piano. If all twelve keys in an octave were white, accidentals and key signatures would be meaningless. Therefore, the arrangement of black and white keys is of crucial importance, and keyboard configuration directly affects scales, degrees, key signatures, and even music theory. To debate the key configuration of the twelve- tone equal-temperament (12-TET) system is of little value because the piano keyboard arrangement is considered the foundation of almost all classical music theories. -
How to Read Music Notation in JUST 30 MINUTES! C D E F G a B C D E F G a B C D E F G a B C D E F G a B C D E F G a B C D E
The New School of American Music How to Read Music Notation IN JUST 30 MINUTES! C D E F G A B C D E F G A B C D E F G A B C D E F G A B C D E F G A B C D E 1. MELODIES 2. THE PIANO KEYBOARD The first thing to learn about reading music A typical piano has 88 keys total (including all is that you can ignore most of the informa- white keys and black keys). Most electronic tion that’s written on the page. The only part keyboards and organ manuals have fewer. you really need to learn is called the “treble However, there are only twelve different clef.” This is the symbol for treble clef: notes—seven white and five black—on the keyboard. This twelve note pattern repeats several times up and down the piano keyboard. In our culture the white notes are named after the first seven letters of the alphabet: & A B C D E F G The bass clef You can learn to recognize all the notes by is for classical sight by looking at their patterns relative to the pianists only. It is totally useless for our black keys. Notice the black keys are arranged purposes. At least for now. ? in patterns of two and three. The piano universe tends to revolve around the C note which you The notes ( ) placed within the treble clef can identify as the white key found just to the represent the melody of the song. -
18.703 Modern Algebra, Permutation Groups
5. Permutation groups Definition 5.1. Let S be a set. A permutation of S is simply a bijection f : S −! S. Lemma 5.2. Let S be a set. (1) Let f and g be two permutations of S. Then the composition of f and g is a permutation of S. (2) Let f be a permutation of S. Then the inverse of f is a permu tation of S. Proof. Well-known. D Lemma 5.3. Let S be a set. The set of all permutations, under the operation of composition of permutations, forms a group A(S). Proof. (5.2) implies that the set of permutations is closed under com position of functions. We check the three axioms for a group. We already proved that composition of functions is associative. Let i: S −! S be the identity function from S to S. Let f be a permutation of S. Clearly f ◦ i = i ◦ f = f. Thus i acts as an identity. Let f be a permutation of S. Then the inverse g of f is a permutation of S by (5.2) and f ◦ g = g ◦ f = i, by definition. Thus inverses exist and G is a group. D Lemma 5.4. Let S be a finite set with n elements. Then A(S) has n! elements. Proof. Well-known. D Definition 5.5. The group Sn is the set of permutations of the first n natural numbers. We want a convenient way to represent an element of Sn. The first way, is to write an element σ of Sn as a matrix. -
Permutation Group and Determinants (Dated: September 16, 2021)
Permutation group and determinants (Dated: September 16, 2021) 1 I. SYMMETRIES OF MANY-PARTICLE FUNCTIONS Since electrons are fermions, the electronic wave functions have to be antisymmetric. This chapter will show how to achieve this goal. The notion of antisymmetry is related to permutations of electrons’ coordinates. Therefore we will start with the discussion of the permutation group and then introduce the permutation-group-based definition of determinant, the zeroth-order approximation to the wave function in theory of many fermions. This definition, in contrast to that based on the Laplace expansion, relates clearly to properties of fermionic wave functions. The determinant gives an N-particle wave function built from a set of N one-particle waves functions and is called Slater’s determinant. II. PERMUTATION (SYMMETRIC) GROUP Definition of permutation group: The permutation group, known also under the name of symmetric group, is the group of all operations on a set of N distinct objects that order the objects in all possible ways. The group is denoted as SN (we will show that this is a group below). We will call these operations permutations and denote them by symbols σi. For a set consisting of numbers 1, 2, :::, N, the permutation σi orders these numbers in such a way that k is at jth position. Often a better way of looking at permutations is to say that permutations are all mappings of the set 1, 2, :::, N onto itself: σi(k) = j, where j has to go over all elements. Number of permutations: The number of permutations is N! Indeed, we can first place each object at positions 1, so there are N possible placements.