Music Terminology
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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. -
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. -
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 -
Harmony for Bass Clef Instruments
UNDERSTANDING HARMONY FOR BASS CLEF PLAYERS Tutorials on harmony almost always use the treble clef or bass clef and treble clefs when giving examples. There are many players who can't read treble clef so this is an attempt to redress the balance. I take it for granted that the major and minor scales are known. When referring to the ascending form of the melodic minor scale which can be used in jazz to go up and down, I will call it the minor scale. For sharpened alterations to chords, I will use a + sign. For lowered alterations, a - sign. MAJOR TRIADS These consist of the root-note, the major 3rd and the perfect 5th (all to be found as steps in the major scale. MINOR TRIADS These consist of the root-note, the minor 3rd and the perfect 5th (all to be found as steps in the minor scale. The minor 3rd is a semitone lower than the major 3rd. C major triad C minor triad written C Cm H H ÜH H = H H INVERSIONS With the root-note at the bottom, the chord is in root position . If you start on the 3rd of the chord and play the root-note in a higher octave, it is called the 1st inversion. This is written like this C/E - the note after the slash is at the bottom. Similarly if you start off with the 5th and place the other notes in a higher octave it is called the 2nd inversion. This could be written as C/G. -
AP® Music Theory Syllabus Course Overview Course Objectives Course Content
AP® Music Theory Syllabus Course Overview AP® Music Theory is a rigorous course that expands upon the concepts and C-15 The course skills learned in the Introduction to Music Theory Course, and it is designed for includes, but is not limited to, study of a students who need it for career study as well as those who desire it for wide variety of vocal enrichment. [C15] and instrumental music from the standard Western tonal Course Objectives repertoires. This course is designed to develop musical skills that will lead to a thorough understanding of music composition and music theory. Students are prepared to take the AP Music Theory Exam when they have completed the course. Students planning to major in music in college may be able to enroll in an advanced music theory course, depending on individual colleges’ AP policies. Course Content 1. Review of music fundamentals, including: scales, key signatures, circle-of fifths, intervals, triads, and inversions 2. Daily ear training, including rhythmic, melodic, and harmonic dictation 3. Weekly sight singing using solfege for pitches 4. The study of modes 5. The study of figured bass 6. The study of two-part counterpoint 7. The study of four-part harmony 8. The study of seventh chords 9. The study of secondary-dominant functions 10. The study of musical form 11. The study of common compositional techniques The objectives below have been adapted from the Expanded Course Specifications posted on the AP Music Theory Home Page on AP Central®. Expanded Course Objectives 1. Identify and notate pitch in four clefs: treble, bass, alto, and tenor. -
Automatic Determination of Chord Roots
University of Innsbruck Institute of Computer Science Intelligent and Interactive Systems Automatic Determination of Chord Roots Samuel Rupprechter arXiv:1601.02546v1 [cs.SD] 11 Jan 2016 B.Sc. Thesis Supervisor: Univ.-Prof. Dr. Justus Piater 12th January 2016 Abstract Even though chord roots constitute a fundamental concept in music theory, existing models do not explain and determine them to full satisfaction. We present a new method which takes sequential context into account to resolve ambiguities and detect nonharmonic tones. We extract features from chord pairs and use a decision tree to determine chord roots. This leads to a quantitative improvement in correctness of the predicted roots in comparison to other models. All this raises the question how much harmonic and nonharmonic tones actually contribute to the perception of chord roots. i ii Contents Abstract i Contents iii List of Figures v List of Tables vii Declaration ix 1 Introduction 1 1.1 Motivation . .1 1.2 Goals . .1 1.3 Overview . .2 2 Music Theory 3 2.1 Basic Music Theory . .3 2.1.1 Musical Notation . .3 2.1.2 Notes and Pitches . .4 2.1.3 Rhythm . .4 2.1.4 Intervals . .5 2.2 Chords . .5 2.2.1 Nonharmonic Tones . .6 2.3 Chord Roots . .6 3 Determination of Chord Roots 9 3.1 Constructing Chords . .9 3.2 Existing Models . .9 3.2.1 Stacking Thirds . .9 3.2.2 Ernst Terhardt . 10 3.2.3 Richard Parncutt . 10 3.3 A New Model . 11 3.3.1 Assumptions and Representation . 11 3.3.2 Definition . -
Chord Names and Symbols (Popular Music) from Wikipedia, the Free Encyclopedia
Chord names and symbols (popular music) From Wikipedia, the free encyclopedia Various kinds of chord names and symbols are used in different contexts, to represent musical chords. In most genres of popular music, including jazz, pop, and rock, a chord name and the corresponding symbol are typically composed of one or more of the following parts: 1. The root note (e.g. C). CΔ7, or major seventh chord 2. The chord quality (e.g. major, maj, or M). on C Play . 3. The number of an interval (e.g. seventh, or 7), or less often its full name or symbol (e.g. major seventh, maj7, or M7). 4. The altered fifth (e.g. sharp five, or ♯5). 5. An additional interval number (e.g. add 13 or add13), in added tone chords. For instance, the name C augmented seventh, and the corresponding symbol Caug7, or C+7, are both composed of parts 1, 2, and 3. Except for the root, these parts do not refer to the notes which form the chord, but to the intervals they form with respect to the root. For instance, Caug7 indicates a chord formed by the notes C-E-G♯-B♭. The three parts of the symbol (C, aug, and 7) refer to the root C, the augmented (fifth) interval from C to G♯, and the (minor) seventh interval from C to B♭. A set of decoding rules is applied to deduce the missing information. Although they are used occasionally in classical music, these names and symbols are "universally used in jazz and popular music",[1] usually inside lead sheets, fake books, and chord charts, to specify the harmony of compositions. -
Chord Studies
Chord Studies 374 Chords, including: Triads Sixths Sevenths Ninths Chord Adjustments in Just Intonation Triads Sixths Sevenths Intervals and their Derivations from Equal Temperament Edited by Nikk Pilato Triads Triads are three-note chords that can be stacked in thirds (therefore, a chord such as C-F-G is not technically a triad, but rather a trichord). The three components of a triad are the root, the third, and the fifth. There are four types of triads: • Major (M3 + m3, ex: C-E-G) ! Can be expressed as C, CM, or C! • Minor (m3 + M3, ex: C-E!-G) ! Can be expressed as Cm, or C- • Diminished (m3 + m3, ex: C-E!-G!) ! Can be expressed C " • Augmented (M3 + M3m ex: C-E-G") ! Can be expressed C+ Sixth Chords A sixth chord can also be interpreted as a minor seventh chord in first inversion. Whether it should be regarded as a sixth or a minor seventh will depend on its harmonic function and context in the music. In modern music, a sixth chord is any triad with an added sixth above the root. • Major Sixth (major triad + a M6, ex: C-E-G-A) • Minor Sixth (minor Triad + a M6, ex: C-E!-G-A) There are also “special” sixth chords, such as: • Neapolitan Sixth: First inversion chord of a major triad built on the flat second (ex: In C Major, this would be F-A!-D!, where D! would be the flat second, and F the first inversion). It is notated !II6 or N6. • Augmented Sixth: Instead of a M6, these chords have an augmented sixth present along with a major third. -
Intervals Continued Compound Intervals, Inversions MUS 102 Music Fundamentals Mark Nelson, Instructor
Intervals Continued Compound Intervals, Inversions MUS 102 Music Fundamentals Mark Nelson, Instructor Compound Intervals: These intervals are greater than one octave but they function the same as intervals of an octave or less. One can merely remove the octave and what is left is essentially the interval it functions as. Example 1: This compound interval has D on the bottom and F# on the top. By moving the D up one octave to the next D, the interval can now be identified conventionally: Step 1: count the pitches – D-E-F = 3. The interval is a 3rd. Step 2: count the ½ steps – D-D#, D#-E, E-F, F-F# = 4. The interval is a Major 3rd or M3. You can also lower the F# by one octave and you would get the same interval, just one octave lower. Inversions: An inversion is when the two pitches of an interval are reversed. The total between each of the two intervals always adds up to 9. For example, a P4 and its inversion P5 is 4+5=9. Inversion possibilities: 1. Inverted intervals always invert to their opposite except perfect intervals which invert only to themselves. 2. Inversions are useful to flip pitches to allow different singers or instruments to take the high or low part. 3. Inversions have the following rules: Perfect intervals invert to Perfect intervals Major intervals invert to minor intervals (and vise versa) Diminished intervals invert to augmented intervals (and vice versa) Doubly diminished intervals invert to doubly augmented intervals. Chart of Interval Inversions Perfect, Minor, Major, Diminished and Augmented Perfect Unison Perfect -
How to Read Chord Symbols
HOW TO READ CHORD SYMBOLS The letters telling you WHICH CHORD to play – are called – CHORD QUALITIES. Chord qualities refer to the intervals between notes - which define the chord. The main chord qualities are: • Major, and minor. • Augmented, diminished, and half-diminished. • Dominant. Some of the symbols used for chord quality are similar to those used for interval quality: • m, or min for minor, • M, maj, or no symbol for major, • aug for augmented, • dim for diminished. In addition, however, • Δ is sometimes used for major, instead of the standard M, or maj, • − is sometimes used for minor, instead of the standard m or min, • +, or aug, is used for augmented (A is not used), • o, °, dim, is used for diminished (d is not used), • ø, or Ø is used for half diminished, • dom is used for dominant. Chord qualities are sometimes omitted – you will only see C or D (means to play C Major or D Major). When specified, they appear immediately after the root note. For instance, in the symbol Cm7 (C minor seventh chord) C is the root and m is the chord quality. When there are multiple “qualities” after the chord name – the accordionist will play the first “quality” for the left hand chord and “define” the other “qualities” in the right hand. The table shows the application of these generic and specific rules to interpret some of the main chord symbols. The same rules apply for the analysis of chord names. For each symbol, several formatting options are available. Except for the root, all the other parts of the symbols may be either superscripted or subscripted. -
Inversion in Music Jonathan Dimond, Phd
INTRODUCTION TO INVERSION IN MUSIC JONATHAN DIMOND, PHD C B C# A# D A D# G# E G F F# Edition: December, 2020 INTRODUCTION ..............................................................................................3 Terminology and enquiry ...........................................................................................4 INVERSION IN PITCH SPACE ...........................................................................7 INVERSION IN PITCH REGISTER ....................................................................13 INVERSION IN PITCH-CLASS SPACE ...............................................................15 Comparison of inversion in pitch space, register and pitch-class space ........................19 INVERSION IN RHYTHM ...............................................................................22 CONCLUSION ...............................................................................................29 BIBLIOGRAPHY .............................................................................................30 C B C# A# D A D# G# E G F F# INTRODUCTION Inversion is a concept that is found broadly within the musical fields of music theory, counterpoint, harmony, composition, aural training, notation, and the practice of musical instruments. It is based upon the over-arching concept of symmetry – a trait found in all the arts.1 This paper aims to alert the musician of the multitude of interpretations of the term inversion, to amalgamate different approaches and terminology into one reference document, as well as to