Introduction to Intervals
Total Page：16
File Type：pdf, Size：1020Kb
Load more
Recommended publications
-
Common Jazz Chord Symbols Here I Use the More Explicit Abbreviation 'Maj7' for Major Seventh
Common jazz chord symbols Here I use the more explicit abbreviation 'maj7' for major seventh. Other common abbreviations include: C² C²7 CMA7 and CM7. Here I use the abbreviation 'm7' for minor seventh. Other common abbreviations include: C- C-7 Cmi7 and Cmin7. The variations given for Major 6th, Major 7th, Dominant 7th, basic altered dominant and minor 7th chords in the first five systems are essentially interchangeable, in other words, the 'color tones' shown added to these chords (9 and 13 on major and dominant seventh chords, 9, 13 and 11 on minor seventh chords) are commonly added even when not included in a chord symbol. For example, a chord notated Cmaj7 is often played with an added 6th and/or 9th, etc. Note that the 11th is not one of the basic color tones added to major and dominant 7th chords. Only #11 is added to these chords, which implies a different scale (lydian rather than major on maj7, lydian dominant rather than the 'seventh scale' on dominant 7th chords.) Although color tones above the seventh are sometimes added to the m7b5 chord, this chord is shown here without color tones, as it is often played without them, especially when a more basic approach is being taken to the minor ii-V-I. Note that the abbreviations Cmaj9, Cmaj13, C9, C13, Cm9 and Cm13 imply that the seventh is included. Major triad Major 6th chords C C6 C% w ww & w w w Major 7th chords (basic structure: root, 3rd, 5th and 7th of root's major scale) 4 CŒ„Š7 CŒ„Š9 CŒ„Š13 w w w w & w w w Dominant seventh chords (basic structure: root, 3rd, 5th and b7 of root's major scale) 7 C7 C9 C13 w bw bw bw & w w w basic altered dominant 7th chords 10 C7(b9) C7(#5) (aka C7+5 or C+7) C7[äÁ] bbw bw b bw & w # w # w Minor 7 flat 5, aka 'half diminished' fully diminished Minor seventh chords (root, b3, b5, b7). -
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. -
Naming a Chord Once You Know the Common Names of the Intervals, the Naming of Chords Is a Little Less Daunting
Naming a Chord Once you know the common names of the intervals, the naming of chords is a little less daunting. Still, there are a few conventions and short-hand terms that many musicians use, that may be confusing at times. A few terms are used throughout the maze of chord names, and it is good to know what they refer to: Major / Minor – a “minor” note is one half step below the “major.” When naming intervals, all but the “perfect” intervals (1,4, 5, 8) are either major or minor. Generally if neither word is used, major is assumed, unless the situation is obvious. However, when used in naming extended chords, the word “minor” usually is reserved to indicate that the third of the triad is flatted. The word “major” is reserved to designate the major seventh interval as opposed to the minor or dominant seventh. It is assumed that the third is major, unless the word “minor” is said, right after the letter name of the chord. Similarly, in a seventh chord, the seventh interval is assumed to be a minor seventh (aka “dominant seventh), unless the word “major” comes right before the word “seventh.” Thus a common “C7” would mean a C major triad with a dominant seventh (CEGBb) While a “Cmaj7” (or CM7) would mean a C major triad with the major seventh interval added (CEGB), And a “Cmin7” (or Cm7) would mean a C minor triad with a dominant seventh interval added (CEbGBb) The dissonant “Cm(M7)” – “C minor major seventh” is fairly uncommon outside of modern jazz: it would mean a C minor triad with the major seventh interval added (CEbGB) Suspended – To suspend a note would mean to raise it up a half step. -
The 17-Tone Puzzle — and the Neo-Medieval Key That Unlocks It
The 17-tone Puzzle — And the Neo-medieval Key That Unlocks It by George Secor A Grave Misunderstanding The 17 division of the octave has to be one of the most misunderstood alternative tuning systems available to the microtonal experimenter. In comparison with divisions such as 19, 22, and 31, it has two major advantages: not only are its fifths better in tune, but it is also more manageable, considering its very reasonable number of tones per octave. A third advantage becomes apparent immediately upon hearing diatonic melodies played in it, one note at a time: 17 is wonderful for melody, outshining both the twelve-tone equal temperament (12-ET) and the Pythagorean tuning in this respect. The most serious problem becomes apparent when we discover that diatonic harmony in this system sounds highly dissonant, considerably more so than is the case with either 12-ET or the Pythagorean tuning, on which we were hoping to improve. Without any further thought, most experimenters thus consign the 17-tone system to the discard pile, confident in the knowledge that there are, after all, much better alternatives available. My own thinking about 17 started in exactly this way. In 1976, having been a microtonal experimenter for thirteen years, I went on record, dismissing 17-ET in only a couple of sentences: The 17-tone equal temperament is of questionable harmonic utility. If you try it, I doubt you’ll stay with it for long.1 Since that time I have become aware of some things which have caused me to change my opinion completely. -
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. -
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). -
Shifting Exercises with Double Stops to Test Intonation
VERY ROUGH AND PRELIMINARY DRAFT!!! Shifting Exercises with Double Stops to Test Intonation These exercises were inspired by lessons I had from 1968 to 1970 with David Smiley of the San Francisco Symphony. I don’t have the book he used, but I believe it was one those written by Dounis on the scientific or artist's technique of violin playing. The exercises were difficult and frustrating, and involved shifting and double stops. Smiley also emphasized routine testing notes against other strings, and I also found some of his tasks frustrating because I couldn’t hear intervals that apparently seemed so familiar to a professional musician. When I found myself giving violin lessons in 2011, I had a mathematical understanding of why it was so difficult to hear certain musical intervals, and decided not to focus on them in my teaching. By then I had also developed some exercises to develop my own intonation. These exercises focus entirely on what is called the just scale. Pianos use the equal tempered scale, which is the predominate choice of intonation in orchestras and symphonies (I NEED VERIFICATION THAT THIS IS TRUE). It takes many years and many types of exercises and activities to become a good violinist. But I contend that everyone should start by mastering the following double stops in “just” intonation: 1. Practice the intervals shown above for all possible pairs of strings on your violin or viola. Learn the first two first, then add one interval at a time. They get harder to hear as you go down the list for reasons having to do with the fractions: 1/2, 2/3, 3/4, 3/5, 4/5, 5/6. -
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 -
Ninth, Eleventh and Thirteenth Chords Ninth, Eleventh and Thirteen Chords Sometimes Referred to As Chords with 'Extensions', I.E
Ninth, Eleventh and Thirteenth chords Ninth, Eleventh and Thirteen chords sometimes referred to as chords with 'extensions', i.e. extending the seventh chord to include tones that are stacking the interval of a third above the basic chord tones. These chords with upper extensions occur mostly on the V chord. The ninth chord is sometimes viewed as superimposing the vii7 chord on top of the V7 chord. The combination of the two chord creates a ninth chord. In major keys the ninth of the dominant ninth chord is a whole step above the root (plus octaves) w w w w w & c w w w C major: V7 vii7 V9 G7 Bm7b5 G9 ? c ∑ ∑ ∑ In the minor keys the ninth of the dominant ninth chord is a half step above the root (plus octaves). In chord symbols it is referred to as a b9, i.e. E7b9. The 'flat' terminology is use to indicate that the ninth is lowered compared to the major key version of the dominant ninth chord. Note that in many keys, the ninth is not literally a flatted note but might be a natural. 4 w w w & #w #w #w A minor: V7 vii7 V9 E7 G#dim7 E7b9 ? ∑ ∑ ∑ The dominant ninth usually resolves to I and the ninth often resolves down in parallel motion with the seventh of the chord. 7 ˙ ˙ ˙ ˙ & ˙ ˙ #˙ ˙ C major: V9 I A minor: V9 i G9 C E7b9 Am ˙ ˙ ˙ ˙ ˙ ? ˙ ˙ The dominant ninth chord is often used in a II-V-I chord progression where the II chord˙ and the I chord are both seventh chords and the V chord is a incomplete ninth with the fifth omitted. -
Alternate Tuning Guide
1 Alternate Tuning Guide by Bill Sethares New tunings inspire new musical thoughts. Belew is talented... But playing in alternate Alternate tunings let you play voicings and slide tunings is impossible on stage, retuning is a between chord forms that would normally be nightmare... strings break, wiggle and bend out impossible. They give access to nonstandard of tune, necks warp. And the alternative - carry- open strings. Playing familiar fingerings on an ing around five special guitars for five special unfamiliar fretboard is exciting - you never know tuning tunes - is a hassle. Back to EBGDAE. exactly what to expect. And working out familiar But all these "practical" reasons pale com- riffs on an unfamiliar fretboard often suggests pared to psychological inertia. "I've spent years new sound patterns and variations. This book mastering one tuning, why should I try others?" helps you explore alternative ways of making Because there are musical worlds waiting to be music. exploited. Once you have retuned and explored a Why is the standard guitar tuning standard? single alternate tuning, you'll be hooked by the Where did this strange combination of a major unexpected fingerings, the easy drone strings, 3rd and four perfect 4ths come from? There is a the "new" open chords. New tunings are a way to bit of history (view the guitar as a descendant of recapture the wonder you experienced when first the lute), a bit of technology (strings which are finding your way around the fretboard - but now too high and thin tend to break, those which are you can become proficient in a matter of days too low tend to be too soft), and a bit of chance. -
Guitar Best Practices Years 1, 2, 3 and 4 Nafme Council for Guitar
Guitar Best Practices Years 1, 2, 3 and 4 Many schools today offer guitar classes and guitar ensembles as a form of music instruction. While guitar is a popular music choice for students to take, there are many teachers offering instruction where guitar is their secondary instrument. The NAfME Guitar Council collaborated and compiled lists of Guitar Best Practices for each year of study. They comprise a set of technical skills, music experiences, and music theory knowledge that guitar students should know through their scholastic career. As a Guitar Council, we have taken careful consideration to ensure that the lists are applicable to middle school and high school guitar class instruction, and may be covered through a wide variety of method books and music styles (classical, country, folk, jazz, pop). All items on the list can be performed on acoustic, classical, and/or electric guitars. NAfME Council for Guitar Education Best Practices Outline for a Year One Guitar Class YEAR ONE - At the completion of year one, students will be able to: 1. Perform using correct sitting posture and appropriate hand positions 2. Play a sixteen measure melody composed with eighth notes at a moderate tempo using alternate picking 3. Read standard music notation and play on all six strings in first position up to the fourth fret 4. Play melodies in the keys C major, a minor, G major, e minor, D major, b minor, F major and d minor 5. Play one octave scales including C major, G major, A major, D major and E major in first position 6.