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A Group-Theoretical Classification of Three-Tone and Four-Tone Harmonic Chords3
A GROUP-THEORETICAL CLASSIFICATION OF THREE-TONE AND FOUR-TONE HARMONIC CHORDS JASON K.C. POLAK Abstract. We classify three-tone and four-tone chords based on subgroups of the symmetric group acting on chords contained within a twelve-tone scale. The actions are inversion, major- minor duality, and augmented-diminished duality. These actions correspond to elements of symmetric groups, and also correspond directly to intuitive concepts in the harmony theory of music. We produce a graph of how these actions relate different seventh chords that suggests a concept of distance in the theory of harmony. Contents 1. Introduction 1 Acknowledgements 2 2. Three-tone harmonic chords 2 3. Four-tone harmonic chords 4 4. The chord graph 6 References 8 References 8 1. Introduction Early on in music theory we learn of the harmonic triads: major, minor, augmented, and diminished. Later on we find out about four-note chords such as seventh chords. We wish to describe a classification of these types of chords using the action of the finite symmetric groups. We represent notes by a number in the set Z/12 = {0, 1, 2,..., 10, 11}. Under this scheme, for example, 0 represents C, 1 represents C♯, 2 represents D, and so on. We consider only pitch classes modulo the octave. arXiv:2007.03134v1 [math.GR] 6 Jul 2020 We describe the sounding of simultaneous notes by an ordered increasing list of integers in Z/12 surrounded by parentheses. For example, a major second interval M2 would be repre- sented by (0, 2), and a major chord would be represented by (0, 4, 7). -
When the Leading Tone Doesn't Lead: Musical Qualia in Context
When the Leading Tone Doesn't Lead: Musical Qualia in Context Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Claire Arthur, B.Mus., M.A. Graduate Program in Music The Ohio State University 2016 Dissertation Committee: David Huron, Advisor David Clampitt Anna Gawboy c Copyright by Claire Arthur 2016 Abstract An empirical investigation is made of musical qualia in context. Specifically, scale-degree qualia are evaluated in relation to a local harmonic context, and rhythm qualia are evaluated in relation to a metrical context. After reviewing some of the philosophical background on qualia, and briefly reviewing some theories of musical qualia, three studies are presented. The first builds on Huron's (2006) theory of statistical or implicit learning and melodic probability as significant contributors to musical qualia. Prior statistical models of melodic expectation have focused on the distribution of pitches in melodies, or on their first-order likelihoods as predictors of melodic continuation. Since most Western music is non-monophonic, this first study investigates whether melodic probabilities are altered when the underlying harmonic accompaniment is taken into consideration. This project was carried out by building and analyzing a corpus of classical music containing harmonic analyses. Analysis of the data found that harmony was a significant predictor of scale-degree continuation. In addition, two experiments were carried out to test the perceptual effects of context on musical qualia. In the first experiment participants rated the perceived qualia of individual scale-degrees following various common four-chord progressions that each ended with a different harmony. -
Musicianship IV Syllabus
University of Missouri-Kansas City Conservatory of Music and Dance CONS 242: Musicianship IV Spring 2015 Credit hours: 4.0 CRN: 17576 Instructor: Dr. David Thurmaier, Associate Professor of Music Theory Office: 302 Grant Hall Phone: 235-2898 Email: [email protected] Office Hours: M, T, W from 10-10:50 and by appointment Teaching Assistant: Taylor Carmona Office: 304 Grant Hall Email: [email protected] Catalog Description Continuation of CONS 241. Study of late-nineteenth century chromaticism and analytical and compositional methods of twentieth and twenty-first century music, including set theory and twelve-tone theory. Particular attention is given to the development of critical writing skills and the creation of stylistic compositions. Prerequisite: CONS 241 Meeting Time and Location Monday-Friday, 9-9:50 am, Grant Hall 122 Required Materials Kostka, Stefan and Roger Graybill. Anthology of Music for Analysis. Upper Saddle River, NJ: Pearson Prentice Hall, 2004. Laitz, Steven G., The Complete Musician: An Integrated Approach to Tonal Theory, Analysis, and Listening. 3rd Edition. New York: Oxford University Press, 2012. Roig-Francolí, Miguel. Understanding Post-Tonal Music (text and anthology). Boston: McGraw Hill, 2007. Notebook, music paper and pens/pencils In addition, you will be required to use the Finale notation program (or equivalent) for composition assignments. This is available for personal purchase at a substantial student discount http://www.finalemusic.com. I recommend against using such free programs as Notepad, as you are not able to take advantage of the many features of Finale. Continual failure to purchase and/or bring required books will result in deductions on homework or exams. -
The Perceptual Attraction of Pre-Dominant Chords 1
Running Head: THE PERCEPTUAL ATTRACTION OF PRE-DOMINANT CHORDS 1 The Perceptual Attraction of Pre-Dominant Chords Jenine Brown1, Daphne Tan2, David John Baker3 1Peabody Institute of The Johns Hopkins University 2University of Toronto 3Goldsmiths, University of London [ACCEPTED AT MUSIC PERCEPTION IN APRIL 2021] Author Note Jenine Brown, Department of Music Theory, Peabody Institute of the Johns Hopkins University, Baltimore, MD, USA; Daphne Tan, Faculty of Music, University of Toronto, Toronto, ON, Canada; David John Baker, Department of Computing, Goldsmiths, University of London, London, United Kingdom. Corresponding Author: Jenine Brown, Peabody Institute of The John Hopkins University, 1 E. Mt. Vernon Pl., Baltimore, MD, 21202, [email protected] 1 THE PERCEPTUAL ATTRACTION OF PRE-DOMINANT CHORDS 2 Abstract Among the three primary tonal functions described in modern theory textbooks, the pre-dominant has the highest number of representative chords. We posit that one unifying feature of the pre-dominant function is its attraction to V, and the experiment reported here investigates factors that may contribute to this perception. Participants were junior/senior music majors, freshman music majors, and people from the general population recruited on Prolific.co. In each trial four Shepard-tone sounds in the key of C were presented: 1) the tonic note, 2) one of 31 different chords, 3) the dominant triad, and 4) the tonic note. Participants rated the strength of attraction between the second and third chords. Across all individuals, diatonic and chromatic pre-dominant chords were rated significantly higher than non-pre-dominant chords and bridge chords. Further, music theory training moderated this relationship, with individuals with more theory training rating pre-dominant chords as being more attracted to the dominant. -
Affordant Chord Transitions in Selected Guitar-Driven Popular Music
Affordant Chord Transitions in Selected Guitar-Driven Popular Music Thesis Presented in Partial Fulfillment of the Requirements for the Degree Master of Arts in the Graduate School of The Ohio State University By Gary Yim, B.Mus. Graduate Program in Music The Ohio State University 2011 Thesis Committee: David Huron, Advisor Marc Ainger Graeme Boone Copyright by Gary Yim 2011 Abstract It is proposed that two different harmonic systems govern the sequences of chords in popular music: affordant harmony and functional harmony. Affordant chord transitions favor chords and chord transitions that minimize technical difficulty when performed on the guitar, while functional chord transitions favor chords and chord transitions based on a chord's harmonic function within a key. A corpus analysis is used to compare the two harmonic systems in influencing chord transitions, by encoding each song in two different ways. Songs in the corpus are encoded with their absolute chord names (such as “Cm”) to best represent affordant factors in the chord transitions. These same songs are also encoded with their Roman numerals to represent functional factors in the chord transitions. The total entropy within the corpus for both encodings are calculated, and it is argued that the encoding with the lower entropy value corresponds with a harmonic system that more greatly influences the chord transitions. It is predicted that affordant chord transitions play a greater role than functional harmony, and therefore a lower entropy value for the letter-name encoding is expected. But, contrary to expectations, a lower entropy value for the Roman numeral encoding was found. Thus, the results are not consistent with the hypothesis that affordant chord transitions play a greater role than functional chord transitions. -
The Strategic Half-Diminished Seventh Chord and the Emblematic Tristan Chord: a Survey from Beethoven to Berg
International Journal ofMusicology 4 . 1995 139 Mark DeVoto (Medford, Massachusetts) The Strategic Half-diminished Seventh Chord and The Emblematic Tristan Chord: A Survey from Beethoven to Berg Zusammenfassung: Der strategische halbverminderte Septakkord und der em blematische Tristan-Akkord von Beethoven bis Berg im Oberblick. Der halb verminderte Septakkord tauchte im 19. Jahrhundert als bedeutende eigen standige Hannonie und als Angelpunkt bei der chromatischen Modulation auf, bekam aber eine besondere symbolische Bedeutung durch seine Verwendung als Motiv in Wagners Tristan und Isolde. Seit der Premiere der Oper im Jahre 1865 lafit sich fast 100 Jahre lang die besondere Entfaltung des sogenannten Tristan-Akkords in dramatischen Werken veifolgen, die ihn als Emblem fUr Liebe und Tod verwenden. In Alban Bergs Lyrischer Suite und Lulu erreicht der Tristan-Akkord vielleicht seine hOchste emblematische Ausdruckskraft nach Wagner. If Wagner's Tristan und Isolde in general, and its Prelude in particular, have stood for more than a century as the defining work that liberated tonal chro maticism from its diatonic foundations of the century before it, then there is a particular focus within the entire chromatic conception that is so well known that it even has a name: the Tristan chord. This is the chord that occurs on the downbeat of the second measure of the opera. Considered enharmonically, tills chord is of course a familiar structure, described in many textbooks as a half diminished seventh chord. It is so called because it can be partitioned into a diminished triad and a minor triad; our example shows it in comparison with a minor seventh chord and an ordinary diminished seventh chord. -
List of Symbols
List of Symbols a atmosphere speed of sound a exponent in approximate thrust formula ac aerodynamic center a acceleration vector a0 airfoil angle of attack for zero lift A aspect ratio A system matrix A aerodynamic force vector b span b exponent in approximate SFC formula c chord cd airfoil drag coefficient cl airfoil lift coefficient clα airfoil lift curve slope cmac airfoil pitching moment about the aerodynamic center cr root chord ct tip chord c¯ mean aerodynamic chord C specfic fuel consumption Cc corrected specfic fuel consumption CD drag coefficient CDf friction drag coefficient CDi induced drag coefficient CDw wave drag coefficient CD0 zero-lift drag coefficient Cf skin friction coefficient CF compressibility factor CL lift coefficient CLα lift curve slope CLmax maximum lift coefficient Cmac pitching moment about the aerodynamic center CT nondimensional thrust T Cm nondimensional thrust moment CW nondimensional weight d diameter det determinant D drag e Oswald’s efficiency factor E origin of ground axes system E aerodynamic efficiency or lift to drag ratio EO position vector f flap f factor f equivalent parasite area F distance factor FS stick force F force vector F F form factor g acceleration of gravity g acceleration of gravity vector gs acceleration of gravity at sea level g1 function in Mach number for drag divergence g2 function in Mach number for drag divergence H elevator hinge moment G time factor G elevator gearing h altitude above sea level ht altitude of the tropopause hH height of HT ac above wingc ¯ h˙ rate of climb 2 i unit vector iH horizontal -
Chords Employed in Twentieth Century Composition
Ouachita Baptist University Scholarly Commons @ Ouachita Honors Theses Carl Goodson Honors Program 1967 Chords Employed in Twentieth Century Composition Camille Bishop Ouachita Baptist University Follow this and additional works at: https://scholarlycommons.obu.edu/honors_theses Part of the Composition Commons, and the Music Theory Commons Recommended Citation Bishop, Camille, "Chords Employed in Twentieth Century Composition" (1967). Honors Theses. 456. https://scholarlycommons.obu.edu/honors_theses/456 This Thesis is brought to you for free and open access by the Carl Goodson Honors Program at Scholarly Commons @ Ouachita. It has been accepted for inclusion in Honors Theses by an authorized administrator of Scholarly Commons @ Ouachita. For more information, please contact [email protected]. Chords Formed By I nterval s Of A Third The traditional tr i ~d of t he eigh te8nth aDd n i neteenth centuries t ends to s~ un 1 trite i n t he su r roundin~s of twen tieth century d i ss onance. The c o ~poser f aces the nroble~ of i magi native us e of th e trla1 s o as t o a d d f reshness to a comnosition. In mod ern c Dmn:;sition , rna i or 8.nd minor triads are usually u s ed a s ooints of r e l axation b e f ore a nd a fter sections o f tension. Progressions of the eighte enth and n inete enth c en t u r i es we re built around t he I, IV, and V chords. All other c hords we re considered as incidenta l, serving to provide vari e t y . -
Expanded Tonality: the Rt Eatment of Upper and Lower Leading Tones As Evidenced in Sonata "Undine,” IV by Carl Reinecke Joshua Blizzard University of South Florida
University of South Florida Scholar Commons Graduate Theses and Dissertations Graduate School 7-13-2007 Expanded Tonality: The rT eatment of Upper and Lower Leading Tones As Evidenced in Sonata "Undine,” IV by Carl Reinecke Joshua Blizzard University of South Florida Follow this and additional works at: https://scholarcommons.usf.edu/etd Part of the American Studies Commons Scholar Commons Citation Blizzard, Joshua, "Expanded Tonality: The rT eatment of Upper and Lower Leading Tones As Evidenced in Sonata "Undine,” IV by Carl Reinecke" (2007). Graduate Theses and Dissertations. https://scholarcommons.usf.edu/etd/638 This Thesis is brought to you for free and open access by the Graduate School at Scholar Commons. It has been accepted for inclusion in Graduate Theses and Dissertations by an authorized administrator of Scholar Commons. For more information, please contact [email protected]. Expanded Tonality: The Treatment of Upper and Lower Leading Tones As Evidenced in Sonata "Undine,” IV by Carl Reinecke by Joshua Blizzard A thesis submitted in partial fulfillment of the requirements for the degree of Master of Music College of Visual and Performing Arts University of South Florida Major Professor: Ann Hawkins, M.A. Kim McCormick, D.M.A. David A. Williams, Ph.D. Date of Approval: July 13, 2007 Keywords: tonic substitution, wedge, prolongation, delayed resolution, chromaticism © Copyright 2007, Joshua Blizzard Dedication To my wife for her tireless support of me both emotionally and monetarily, to my Aunt Susie who played a significant role in my musical development from my youth, to my parents who worked to instill a sense of discipline in my studies, and, ultimately, to the glory of God, without whom nothing is possible. -
The Death and Resurrection of Function
THE DEATH AND RESURRECTION OF FUNCTION A Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By John Gabriel Miller, B.A., M.C.M., M.A. ***** The Ohio State University 2008 Doctoral Examination Committee: Approved by Dr. Gregory Proctor, Advisor Dr. Graeme Boone ________________________ Dr. Lora Gingerich Dobos Advisor Graduate Program in Music Copyright by John Gabriel Miller 2008 ABSTRACT Function is one of those words that everyone understands, yet everyone understands a little differently. Although the impact and pervasiveness of function in tonal theory today is undeniable, a single, unambiguous definition of the term has yet to be agreed upon. So many theorists—Daniel Harrison, Joel Lester, Eytan Agmon, Charles Smith, William Caplin, and Gregory Proctor, to name a few—have so many different nuanced understandings of function that it is nearly impossible for conversations on the subject to be completely understood by all parties. This is because function comprises at least four distinct aspects, which, when all called by the same name, function , create ambiguity, confusion, and contradiction. Part I of the dissertation first illuminates this ambiguity in the term function by giving a historical basis for four different aspects of function, three of which are traced to Riemann, and one of which is traced all the way back to Rameau. A solution to the problem of ambiguity is then proposed: the elimination of the term function . In place of function , four new terms—behavior , kinship , province , and quality —are invoked, each uniquely corresponding to one of the four aspects of function identified. -
Ebook Download Guitar Chords & Scales: an Easy Reference for Acoustic Or Electric Guitar
GUITAR CHORDS & SCALES: AN EASY REFERENCE FOR ACOUSTIC OR ELECTRIC GUITAR PDF, EPUB, EBOOK Hal Leonard Corp | 56 pages | 01 Feb 2003 | Hal Leonard Publishing Corporation | 9780634052736 | English | none Guitar Chords & Scales: An Easy Reference for Acoustic or Electric Guitar PDF Book I've got you covered. Free printable guitar chord chart. Related Searches. View Product. Guitar Chords Deluxe Guitar Educational. Recommended Scales. Fast loading desktop and mobile experience Auto-resume across devices Quick search, note taking and bookmarking for easy reference Responsive book design, so things look great on mobile too New books being added regularly This convenient reference features a clear, concise, simple and visual approach to keyboard and guitar chords. Play on. As you'll quickly learn the more connected you come with your guitar, tuning is vitally important to your success in playing. Whatever guitar you pick, make sure it inspires you. After that turn on your metronome and move between the chords. It syncs automatically with your account and allows you to read online or offline wherever you are. Account Options Sign in. Use a metronome at first when you are able to change between them without it. Thank you. This is true, if your child is between the ages of , a smaller guitar can work. Advertising seems to be blocked by your browser. So I bought the same book and went though the chord shapes once a day for a couple of months. Start making music. Acoustic guitars are often considered harder to learn. They are quick and easy to use. Arpeggio Information. Chords for Keyboard and Guitar - A Pocket. -
MTO 22.2: Reenan, Types and Applications of P3,0 Seventh-Chord Transformations
Volume 22, Number 2, June 2016 Copyright © 2016 Society for Music Theory 3,0 Samuel Reenan and Richard Bass NOTE: The examples for the (text-only) PDF version of this item are available online at: http://www.mtosmt.org/issues/mto.16.22.2/mto.16.22.2.reenan_bass.php KEYWORDS: Harmony, Chromaticism, Neo-Riemannian Theory, Parsimonious Voice Leading ABSTRACT: The expression P3,0 refers to one class of parsimonious voice-leading transformations between seventh chords introduced in a 1998 article by Jack Douthett and Peter Steinbach as Pm,n (Journal of Music Theory 42 (2): 241–63). In addition to tones that may be held in common, the subscripts indicate the number of voices that move by half step (m) or whole step (n) in connecting one seventh chord to the next. P3,0 designates a transformation in which one of the chord members is held in common while each of the other three moves by half step. P3,0 transformations produce some of the most striking chromatic harmonic progressions in the late Romantic repertoire. This study focuses on aspects of P3,0 transformations that include 1) their place in the broader context of neo-Riemannian voice-leading transformations; 2) their properties and a specific means of notating all possible P3,0 types; 3) explications of how the various types are integrated within late nineteenth-century harmonic practice and interact with traditional tonal harmony; and 4) analytic applications that demonstrate how P3,0 transformations operate within and contribute to musical structure, including the opening of the Prelude to Wagner’s Tristan und Isolde, and a complete song (“Ruhe, meine Seele!” op.