Music Intervals
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Tonalandextratonal Functions of Theaugmented
TONAL AND EXTRATONAL FUNCTIONS OF THE AUGMENTED TRIAD IN THE HARMONIC STRUCTURE OF WEBERN'S 'DEHMEL SONGS' By ROBERT GARTH PRESTON B. Mus., Brandon University, 1982 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS in THE FACULTY OF GRADUATE STUDIES (School of Music, Music Theory) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA October 1989 © Garth Preston, 1989 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia Vancouver, Canada DE-6 (2/88) ii ABSTRACT: TONAL AND EXTRATONAL FUNCTIONS OF THE AUGMENTED TRIAD IN THE HARMONIC STRUCTURE OF WEBERN'S 'DEHMEL SONGS' The composing of the 'Dehmel Songs' marks a pivotal juncture both in Webern's oeuvre and in the history of music in general. The years that saw the birth of this cycle of five songs, 1906-8, comprise what is generally regarded as a period of transition, in the work of Schoenberg, Webern and Berg, from a 'late tonal' style of composition to an early 'atonal' style. In this study I approach the 'Dehmel Songs' from the perspective that its harmonic structure as a whole can be rendered intelligible in a theoretical way by combining a simple pitch-class-set analysis, which essentially involves graphing the pattern of recurrence of the 'augmented triad' as a motivic harmonic entity—a pattern which is in fact serial in nature-through the course of the unfolding harmonic progression, with a tonal interpretation that uses that pattern as a referential pitch-class skeleton. -
MTO 0.7: Alphonce, Dissonance and Schumann's Reckless Counterpoint
Volume 0, Number 7, March 1994 Copyright © 1994 Society for Music Theory Bo H. Alphonce KEYWORDS: Schumann, piano music, counterpoint, dissonance, rhythmic shift ABSTRACT: Work in progress about linearity in early romantic music. The essay discusses non-traditional dissonance treatment in some contrapuntal passages from Schumann’s Kreisleriana, opus 16, and his Grande Sonate F minor, opus 14, in particular some that involve a wedge-shaped linear motion or a rhythmic shift of one line relative to the harmonic progression. [1] The present paper is the first result of a planned project on linearity and other features of person- and period-style in early romantic music.(1) It is limited to Schumann's piano music from the eighteen-thirties and refers to score excerpts drawn exclusively from opus 14 and 16, the Grande Sonate in F minor and the Kreisleriana—the Finale of the former and the first two pieces of the latter. It deals with dissonance in foreground terms only and without reference to expressive connotations. Also, Eusebius, Florestan, E.T.A. Hoffmann, and Herr Kapellmeister Kreisler are kept gently off stage. [2] Schumann favours friction dissonances, especially the minor ninth and the major seventh, and he likes them raw: with little preparation and scant resolution. The sforzato clash of C and D in measures 131 and 261 of the Finale of the G minor Sonata, opus 22, offers a brilliant example, a peculiarly compressed dominant arrival just before the return of the main theme in G minor. The minor ninth often occurs exposed at the beginning of a phrase as in the second piece of the Davidsbuendler, opus 6: the opening chord is a V with an appoggiatura 6; as 6 goes to 5, the minor ninth enters together with the fundamental in, respectively, high and low peak registers. -
Intervals and Transposition
CHAPTER 3 Intervals and Transposition Interval Augmented and Simple Intervals TOPICS Octave Diminished Intervals Tuning Systems Unison Enharmonic Intervals Melodic Intervals Perfect, Major, and Minor Tritone Harmonic Intervals Intervals Inversion of Intervals Transposition Consonance and Dissonance Compound Intervals IMPORTANT Tone combinations are classifi ed in music with names that identify the pitch relationships. CONCEPTS Learning to recognize these combinations by both eye and ear is a skill fundamental to basic musicianship. Although many different tone combinations occur in music, the most basic pairing of pitches is the interval. An interval is the relationship in pitch between two tones. Intervals are named by the Intervals number of diatonic notes (notes with different letter names) that can be contained within them. For example, the whole step G to A contains only two diatonic notes (G and A) and is called a second. Figure 3.1 & ww w w Second 1 – 2 The following fi gure shows all the numbers within an octave used to identify intervals: Figure 3.2 w w & w w w w 1ww w2w w3 w4 w5 w6 w7 w8 Notice that the interval numbers shown in Figure 3.2 correspond to the scale degree numbers for the major scale. 55 3711_ben01877_Ch03pp55-72.indd 55 4/10/08 3:57:29 PM The term octave refers to the number 8, its interval number. Figure 3.3 w œ œ w & œ œ œ œ Octavew =2345678=œ1 œ w8 The interval numbered “1” (two notes of the same pitch) is called a unison. Figure 3.4 & 1 =w Unisonw The intervals that include the tonic (keynote) and the fourth and fi fth scale degrees of a Perfect, Major, and major scale are called perfect. -
Andrián Pertout
Andrián Pertout Three Microtonal Compositions: The Utilization of Tuning Systems in Modern Composition Volume 1 Submitted in partial fulfilment of the requirements of the degree of Doctor of Philosophy Produced on acid-free paper Faculty of Music The University of Melbourne March, 2007 Abstract Three Microtonal Compositions: The Utilization of Tuning Systems in Modern Composition encompasses the work undertaken by Lou Harrison (widely regarded as one of America’s most influential and original composers) with regards to just intonation, and tuning and scale systems from around the globe – also taking into account the influential work of Alain Daniélou (Introduction to the Study of Musical Scales), Harry Partch (Genesis of a Music), and Ben Johnston (Scalar Order as a Compositional Resource). The essence of the project being to reveal the compositional applications of a selection of Persian, Indonesian, and Japanese musical scales utilized in three very distinct systems: theory versus performance practice and the ‘Scale of Fifths’, or cyclic division of the octave; the equally-tempered division of the octave; and the ‘Scale of Proportions’, or harmonic division of the octave championed by Harrison, among others – outlining their theoretical and aesthetic rationale, as well as their historical foundations. The project begins with the creation of three new microtonal works tailored to address some of the compositional issues of each system, and ending with an articulated exposition; obtained via the investigation of written sources, disclosure -
Generalized Interval System and Its Applications
Generalized Interval System and Its Applications Minseon Song May 17, 2014 Abstract Transformational theory is a modern branch of music theory developed by David Lewin. This theory focuses on the transformation of musical objects rather than the objects them- selves to find meaningful patterns in both tonal and atonal music. A generalized interval system is an integral part of transformational theory. It takes the concept of an interval, most commonly used with pitches, and through the application of group theory, generalizes beyond pitches. In this paper we examine generalized interval systems, beginning with the definition, then exploring the ways they can be transformed, and finally explaining com- monly used musical transformation techniques with ideas from group theory. We then apply the the tools given to both tonal and atonal music. A basic understanding of group theory and post tonal music theory will be useful in fully understanding this paper. Contents 1 Introduction 2 2 A Crash Course in Music Theory 2 3 Introduction to the Generalized Interval System 8 4 Transforming GISs 11 5 Developmental Techniques in GIS 13 5.1 Transpositions . 14 5.2 Interval Preserving Functions . 16 5.3 Inversion Functions . 18 5.4 Interval Reversing Functions . 23 6 Rhythmic GIS 24 7 Application of GIS 28 7.1 Analysis of Atonal Music . 28 7.1.1 Luigi Dallapiccola: Quaderno Musicale di Annalibera, No. 3 . 29 7.1.2 Karlheinz Stockhausen: Kreuzspiel, Part 1 . 34 7.2 Analysis of Tonal Music: Der Spiegel Duet . 38 8 Conclusion 41 A Just Intonation 44 1 1 Introduction David Lewin(1933 - 2003) is an American music theorist. -
Chapter 29 Dictation Handout
NAME _______________________________________ Chapter 29 Dictation Exercises Section 1. Melodic Dictation You will hear melodies that are four measures in length. Both major and minor keys are possible. Each melody will contain altered tones. The key signature and time signature are provided to you on each blank staff. Click the Play button to hear each exercise. Before each melody begins, you will hear the notes of the entire scale played stepwise up and down, then you will hear the tempo counted off. Write each melody using the correct rhythm. 1. 2. 3. 4. 5. 6. page 1 Section 2. Interval Identification a. Thirds You will hear a variety of thirds. Listen to each interval and identify it as one of the listed qualities. A diminished third sounds identical to a major 2nd, and an augmented third sounds identical to a perfect 4th. 1. major 3rd minor 3rd diminished 3rd augmented 3rd 2. major 3rd minor 3rd diminished 3rd augmented 3rd 3. major 3rd minor 3rd diminished 3rd augmented 3rd 4. major 3rd minor 3rd diminished 3rd augmented 3rd 5. major 3rd minor 3rd diminished 3rd augmented 3rd 6. major 3rd minor 3rd diminished 3rd augmented 3rd 7. major 3rd minor 3rd diminished 3rd augmented 3rd 8. major 3rd minor 3rd diminished 3rd augmented 3rd 9. major 3rd minor 3rd diminished 3rd augmented 3rd 10. major 3rd minor 3rd diminished 3rd augmented 3rd b. Sixths You will hear a variety of sixths. Listen to each interval and identify it as one of the listed qualities. An augmented 6th sounds identical to a minor 7th. -
8.1.4 Intervals in the Equal Temperament The
8.1 Tonal systems 8-13 8.1.4 Intervals in the equal temperament The interval (inter vallum = space in between) is the distance of two notes; expressed numerically by the relation (ratio) of the frequencies of the corresponding tones. The names of the intervals are derived from the place numbers within the scale – for the C-major-scale, this implies: C = prime, D = second, E = third, F = fourth, G = fifth, A = sixth, B = seventh, C' = octave. Between the 3rd and 4th notes, and between the 7th and 8th notes, we find a half- step, all other notes are a whole-step apart each. In the equal-temperament tuning, a whole- step consists of two equal-size half-step (HS). All intervals can be represented by multiples of a HS: Distance between notes (intervals) in the diatonic scale, represented by half-steps: C-C = 0, C-D = 2, C-E = 4, C-F = 5, C-G = 7, C-A = 9, C-B = 11, C-C' = 12. Intervals are not just definable as HS-multiples in their relation to the root note C of the C- scale, but also between all notes: e.g. D-E = 2 HS, G-H = 4 HS, F-A = 4 HS. By the subdivision of the whole-step into two half-steps, new notes are obtained; they are designated by the chromatic sign relative to their neighbors: C# = C-augmented-by-one-HS, and (in the equal-temperament tuning) identical to the Db = D-diminished-by-one-HS. Corresponding: D# = Eb, F# = Gb, G# = Ab, A# = Bb. -
(Semitones and Tones). We Call These “Seconds. A
Music 11, 7/10/06 Scales/Intervals We already know half steps and whole steps (semitones and tones). We call these “seconds.” Adjacent pitch names are always called seconds, but because the space between adjacent pitch names can vary, there are different types of second: Major second (M2) = whole step = whole tone Minor second (m2) = half step = semitone In a major scale, all the seconds are major seconds (M2) except 2: E-F and B-C are minor seconds (m2). Inversion Suppose we take the two notes that make up a second, and “flip” them over—that is, lets put the lower note up an octave, so that it lies above the other note. The distance between E-D is now D-E. We say that the “inversion” of E-D is D-E, and the interval that results is not a second, but instead a seventh. More specifically, the inversion of a major second (M2) is a minor seventh (m7). There are two things to remember about inversions: 1. When an interval is inverted, their numbers add-up to 9. M2 and m7 are inversions of each other, and we can see that 2 + 7 = 9. 2. When a major interval is inverted, its quality becomes minor, and vise versa. The inversion of a M2 is a m7. Major has become minor. Likewise, the inversion of a minor second (m2) is a major seventh (M7). By these rules, we can invert other intervals, like thirds. Study the following chart: # of semitones interval name inversion # of semitones 1 m2 M7 (11) 2 M2 m7 (10) 3 m3 M6 (9) 4 M3 m6 (8) Obviously, wider intervals have more semitones between pitches. -
Music Terminology
ABAGANON MATERIAL MUSIC THEORY OF DODECAPHONIC EQUAL TEMPERAMENT MUSIC INTRODUCTION PG.3 RHYTHM PG.4 PITCH PG.14 MELODY PG.35 COMPOSITION PG.42 PHYSICS PG.52 PHILOSOPHY PG.67 CLASSICAL PG.76 JAZZ PG.92 BOOK DESIGN This book was designed with a few things in mind. Primarily, it was written to adapt to the way musicians and composers learn and think. Usually, they learn in hierarchies, or in other words, they put everything into groups. This form of learning and thinking comes from the tasks that musicians typically have to perform. They memorize groups of rhythms, pitches, motor skills, sounds, and more. This allows them to learn larger amounts of information. An example of this type of learning and thinking can be found in the way that most people memorize a phone number. Usually they will memorize it in groups of 3 + 3 + 4 (this is typical in the United States, although some people from other nationalities will group the numbers differently). You can see this grouping in the way phone numbers are written: (123) 456-7890. By learning in this way, a person is essentially memorizing three bits of information, instead of ten individual pieces. This allows the brain to memorize far more material. To fit with this style of learning, the book’s chapters have been set to cover distinctly separate areas of music, which makes it easier to locate certain topics, as well as keep related ideas close together. This style is different from other textbooks, which often use chapters as guides that separate different musical topics by difficulty of comprehension. -
Exploration of an Adaptable Just Intonation System Jeff Snyder
Exploration of an Adaptable Just Intonation System Jeff Snyder Submitted in partial fulfillment of the requirements of the degree of Doctor of Musical Arts in the Graduate School of Arts and Sciences Columbia University 2010 ABSTRACT Exploration of an Adaptable Just Intonation System Jeff Snyder In this paper, I describe my recent work, which is primarily focused around a dynamic tuning system, and the construction of new electro-acoustic instruments using this system. I provide an overview of my aesthetic and theoretical influences, in order to give some idea of the path that led me to my current project. I then explain the tuning system itself, which is a type of dynamically tuned just intonation, realized through electronics. The third section of this paper gives details on the design and construction of the instruments I have invented for my own compositional purposes. The final section of this paper gives an analysis of the first large-scale piece to be written for my instruments using my tuning system, Concerning the Nature of Things. Exploration of an Adaptable Just Intonation System Jeff Snyder I. Why Adaptable Just Intonation on Invented Instruments? 1.1 - Influences 1.1.1 - Inspiration from Medieval and Renaissance music 1.1.2 - Inspiration from Harry Partch 1.1.3 - Inspiration from American country music 1.2 - Tuning systems 1.2.1 - Why just? 1.2.1.1 – Non-prescriptive pitch systems 1.2.1.2 – Just pitch systems 1.2.1.3 – Tempered pitch systems 1.2.1.4 – Rationale for choice of Just tunings 1.2.1.4.1 – Consideration of non-prescriptive -
Chord and It Gives It It's Name
Interval Functions • In any chord, each interval has a ‘job’ or ‘function’ • The root is the most fundamental part of the chord and it gives it it’s name and ‘tone’ or pitch • The third is what makes the chord sound happy or sad. • The fifth ‘bulks’ up the chord • The seventh adds the ‘spice’ on top of the chord Intervals (Advanced) • Perfect intervals are the 4, 5 and 8 (octave). These are intervals whose frequencies divide into neat fractions. • Perfect Intervals are considered ‘consonant’ as opposed to ‘dissonant’ ROUGHWORK Note Frequency Note Frequency A1 28 A4 220 C B1 31 B4 247 G C1 33 C4 262 D1 37 D4 294 E1 41 E4 330 F1 44 F4 349 33 G1 49 G4 392 A2 55 A5 440 49 B2 62 B5 494 C2 65 C5 523 D2 73 D5 587 E2 82 E5 659 F2 87 F5 698 2 G2 98 G5 784 A3 110 A6 880 3 B3 123 B6 988 C3 131 C6 1047 D3 147 D6 1175 E3 165 E6 1319 F3 175 F6 1397 G3 196 G6 1568 • Non-perfect intervals are 2, 3, 6 and 7. They can be either a major or minor interval. Interval Name Interval Alternate Name Unison 0 Aug Diminished Second Minor Second Dim m2 Majo Augmented Unison r Major Second Minor M2 Aug Diminished Third Minor Third Dim m3 Majo Augmented Second r Major Third Minor M3 Aug Diminished Fourth Perfect Fourth Dim 4 Aug Augmented Third Diminished Fifth/Augmented Fourth Dim Tritone Aug Diminished Fifth/Augmented Fourth Perfect Fifth Dim 5 Aug Diminished Sixth Minor Sixth Minor m6 Majo Augmented Fifth r Major Sixth Dim M6 Majo Diminished Seventh r Minor Seventh Minor m7 Aug Augmented Sixth Major Seventh Minor M7 Aug Diminished Octave Perfect Octave Dim Octave -
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.