AP Music Theory Course Planner
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
On Modulation —
— On Modulation — Dean W. Billmeyer University of Minnesota American Guild of Organists National Convention June 25, 2008 Some Definitions • “…modulating [is] going smoothly from one key to another….”1 • “Modulation is the process by which a change of tonality is made in a smooth and convincing way.”2 • “In tonal music, a firmly established change of key, as opposed to a passing reference to another key, known as a ‘tonicization’. The scale or pitch collection and characteristic harmonic progressions of the new key must be present, and there will usually be at least one cadence to the new tonic.”3 Some Considerations • “Smoothness” is not necessarily a requirement for a successful modulation, as much tonal literature will illustrate. A “convincing way” is a better criterion to consider. • A clear establishment of the new key is important, and usually a duration to the modulation of some length is required for this. • Understanding a modulation depends on the aural perception of the listener; hence, some ambiguity is inherent in distinguishing among a mere tonicization, a “false” modulation, and a modulation. • A modulation to a “foreign” key may be easier to accomplish than one to a diatonically related key: the ear is forced to interpret a new key quickly when there is a large change in the number of accidentals (i.e., the set of pitch classes) in the keys used. 1 Max Miller, “A First Step in Keyboard Modulation”, The American Organist, October 1982. 2 Charles S. Brown, CAGO Study Guide, 1981. 3 Janna Saslaw: “Modulation”, Grove Music Online ed. L. Macy (Accessed 5 May 2008), http://www.grovemusic.com. -
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. -
An Exploration of the Relationship Between Mathematics and Music
An Exploration of the Relationship between Mathematics and Music Shah, Saloni 2010 MIMS EPrint: 2010.103 Manchester Institute for Mathematical Sciences School of Mathematics The University of Manchester Reports available from: http://eprints.maths.manchester.ac.uk/ And by contacting: The MIMS Secretary School of Mathematics The University of Manchester Manchester, M13 9PL, UK ISSN 1749-9097 An Exploration of ! Relation"ip Between Ma#ematics and Music MATH30000, 3rd Year Project Saloni Shah, ID 7177223 University of Manchester May 2010 Project Supervisor: Professor Roger Plymen ! 1 TABLE OF CONTENTS Preface! 3 1.0 Music and Mathematics: An Introduction to their Relationship! 6 2.0 Historical Connections Between Mathematics and Music! 9 2.1 Music Theorists and Mathematicians: Are they one in the same?! 9 2.2 Why are mathematicians so fascinated by music theory?! 15 3.0 The Mathematics of Music! 19 3.1 Pythagoras and the Theory of Music Intervals! 19 3.2 The Move Away From Pythagorean Scales! 29 3.3 Rameau Adds to the Discovery of Pythagoras! 32 3.4 Music and Fibonacci! 36 3.5 Circle of Fifths! 42 4.0 Messiaen: The Mathematics of his Musical Language! 45 4.1 Modes of Limited Transposition! 51 4.2 Non-retrogradable Rhythms! 58 5.0 Religious Symbolism and Mathematics in Music! 64 5.1 Numbers are God"s Tools! 65 5.2 Religious Symbolism and Numbers in Bach"s Music! 67 5.3 Messiaen"s Use of Mathematical Ideas to Convey Religious Ones! 73 6.0 Musical Mathematics: The Artistic Aspect of Mathematics! 76 6.1 Mathematics as Art! 78 6.2 Mathematical Periods! 81 6.3 Mathematics Periods vs. -
Chapter 21 on Modal Mixture
CHAPTER21 Modal Mixture Much music of the late eighteenth and early nineteenth centuries commonly employs a type of chromaticism that cannot be said to derive from applied functions and tonicization. In fact, the chromaticism often appears to be nonfunctional-a mere coloring of the melodic and harmonic surface of the music. Listen to the two phrases of Example 21.1. The first phrase (mm. 1-8) contains exclusively diatonic harmonies, but the second phrase (mm. 11-21) is full of chromaticism. This creates sonorities, such as the A~-major chord in m. 15, which appear to be distant from the underlying F-major tonic. The chromatic harmonies in mm. 11-20 have been labeled with letter names that indicate the root and quality of the chord. EXAMPLE 21.1 Mascagni, "A casa amici" ("Homeward, friends"), Cavalleria Rusticana, scene 9 418 CHAPTER 21 MODAL MIXTURE 419 These sonorities share an important feature: All but the cadential V-I are members of the parallel mode, F minor. Viewing this progression through the lens of F minor reveals a simple bass arpeggiation that briefly tonicizes 420 THE COMPLETE MUSICIAN III (A~), then moves to PD and D, followed by a final resolution to major tonic in the major mode. The Mascagni excerpt is quite remarkable in its tonal plan. Although it begins and ends in F major, a significant portion of the music behaves as though written in F minor. This technique of borrowing harmonies from the parallel mode is called modal mixture (sometimes known simply as mixture). We have already encountered two instances of modal mixture. -
Music 160A Class Notes Dr. Rothfarb October 8, 2007 Key
Music 160A class notes Dr. Rothfarb October 8, 2007 Key determination: • Large-scale form in tonal music goes hand in hand with key organization. Your ability to recognize and describe formal structure will be largely dependent on your ability to recognize key areas and your knowledge of what to expect. Knowing what to expect: • Knowing what keys to expect in certain situations will be an invaluable tool in formal analysis. Certain keys are common and should be expected as typical destinations for modulation (we will use Roman numerals to indicate the relation to the home key). Here are the common structural key areas: o V o vi • Other keys are uncommon for modulation and are not structural: o ii o iii o IV Tonicization or modulation?: • The phenomena of tonicization and modulation provide a challenge to the music analyst. In both cases, one encounters pitches and harmonies that are foreign to the home key. How then, does one determine whether a particular passage is a tonicization or a modulation? • To begin with, this is a question of scale. Tonicizations are much shorter than modulations. A tonicization may last only one or two beats, while a modulation will last much longer—sometimes for entire sections. • A modulation will have cadences. These cadences confirm for the listener that the music has moved to a new key area. A tonicization—though it might have more than two chords—will not have cadences. • A modulation will also typically contain a new theme. Tonicizations, on the other hand, are finished too quickly to be given any significant thematic material. -
CIRCLE of FIFTHS WORKSHOP a Useful Concept for When You Want to Jam with Other Instruments Or Write a Song!
CIRCLE OF FIFTHS WORKSHOP A useful concept for when you want to jam with other instruments or write a song! The Circle of Fifths shows the relationships among the twelve tones of the Chromatic Scale, their corresponding key signatures and the associated Major and Minor keys. The word "chromatic" comes from the Greek word chroma meaning "color." The chromatic scale consists of 12 notes each a half step or “semi-tone” apart. It is from the chromatic scale that every other scale or chord in most Western music is derived. Here’s the C chromatic scale going up as an example: C C# D D# E F F# G G# A A# B C In everyday terms: The Circle of Fifths is useful if you’re playing in an open jam with other instruments, e.g., guitars or fiddles around a campfire, or when you’re trying to figure out the chords of a song from scratch, or write your own song. The Circle of Fifths is a music theory picture. Each “segment” on the circle represents a note, a chord, and a key. Why is it called the Circle of Fifths? When going clockwise, each key is a fifth above the last. When going counter-clockwise, each key is a fourth above the last, so you may also hear it called the “circle of fourths”. The perfect fifth interval is said to be consonant, meaning it is a typical “pleasant sound” and sounds stable within music (the groundwork for this concept was set by Pythagoras and based on the sound frequency ratios). -
Secondary Dominant Chords.Mus
Secondary Dominants Chromaticism - defined by the use of pitches outside of a diatonic key * nonessential chromaticism describes the use of chromatic non-chord tones * essential chromaticism describes the use of chromatic chord tones creating altered chords Secondary Function Chords - also referred to as applied chords * most common chromatically altered chords * function to tonicize (make sound like tonic) a chord other than tonic * applied to a chord other than tonic and typically function like a dominant or leading-tone chord - secondary function chords can also be used in 2nd inversion as passing and neighbor chords - since only major or minor triads can function as tonic, only major or minor triads may be tonicized - Secondary function chords are labeled with two Roman numerals separated by a slash (/) * the first Roman numeral labels the function of the chord (i.e. V, V7, viiº, or viiº7) * the second Roman numeral labels the chord it is applied to - the tonicized chord * secondary function labels are read as V of __, or viiº of __, etc. Secondary Dominant Chords - most common type of secondardy function chords * always spelled as a major triad or Mm7 chord * used to tonicize a chord whose root is a 5th below (or 4th above) * can create stronger harmonic progressions or emphasize chords other than tonic Spelling Secondary Dominant Chords - there are three steps in spelling a secondary dominant chord * find the root of the chord to be tonicized * determine the pitch a P5 above (or P4 below) * using that pitch as the root, spell a -
Transfer Theory Placement Exam Guide (Pdf)
2016-17 GRADUATE/ transfer THEORY PLACEMENT EXAM guide! Texas woman’s university ! ! 1 2016-17 GRADUATE/transferTHEORY PLACEMENTEXAMguide This! guide is meant to help graduate and transfer students prepare for the Graduate/ Transfer Theory Placement Exam. This evaluation is meant to ensure that students have competence in basic tonal harmony. There are two parts to the exam: written and aural. Part One: Written Part Two: Aural ‣ Four voice part-writing to a ‣ Melodic dictation of a given figured bass diatonic melody ‣ Harmonic analysis using ‣ Harmonic Dictation of a Roman numerals diatonic progression, ‣ Transpose a notated notating the soprano, bass, passage to a new key and Roman numerals ‣ Harmonization of a simple ‣ Sightsinging of a melody diatonic melody that contains some functional chromaticism ! Students must achieve a 75% on both the aural and written components of the exam. If a passing score is not received on one or both sections of the exam, the student may be !required to take remedial coursework. Recommended review materials include most of the commonly used undergraduate music theory texts such as: Tonal Harmony by Koska, Payne, and Almén, The Musician’s Guide to Theory and Analysis by Clendinning and Marvin, and Harmony in Context by Francoli. The exam is given prior to the beginning of both the Fall and Spring Semesters. Please check the TWU MUSIc website (www.twu.edu/music) ! for the exact date and time. ! For further information, contact: Dr. Paul Thomas Assistant Professor of Music Theory and Composition [email protected] 2 2016-17 ! ! ! ! table of Contents ! ! ! ! ! 04 Part-Writing ! ! ! ! ! 08 melody harmonization ! ! ! ! ! 13 transposition ! ! ! ! ! 17 Analysis ! ! ! ! ! 21 melodic dictation ! ! ! ! ! harmonic dictation ! 24 ! ! ! ! Sightsinging examples ! 28 ! ! ! 31 terms ! ! ! ! ! 32 online resources ! 3 PART-Writing Part-writing !Realize the following figured bass in four voices. -
The Piano Improvisations of Chick Corea: an Analytical Study
Louisiana State University LSU Digital Commons LSU Historical Dissertations and Theses Graduate School 1996 The iP ano Improvisations of Chick Corea: An Analytical Study. Daniel Alan Duke Louisiana State University and Agricultural & Mechanical College Follow this and additional works at: https://digitalcommons.lsu.edu/gradschool_disstheses Recommended Citation Duke, Daniel Alan, "The iP ano Improvisations of Chick Corea: An Analytical Study." (1996). LSU Historical Dissertations and Theses. 6334. https://digitalcommons.lsu.edu/gradschool_disstheses/6334 This Dissertation is brought to you for free and open access by the Graduate School at LSU Digital Commons. It has been accepted for inclusion in LSU Historical Dissertations and Theses by an authorized administrator of LSU Digital Commons. For more information, please contact [email protected]. INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the te d directly fi-om the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overlaps. -
Secondary Dominants (Applied Dominants)
Dr. Barbara Murphy University of Tennessee School of Music SECONDARY DOMINANTS (APPLIED DOMINANTS) DEFINITION: A secondary dominant is an altered chord having a dominant or leading tone relationship to a chord in the key other than the tonic. An altered chord is a chord containing at least one tone that is foreign to the key. Using secondary dominants results in the tonicization of the chord of resolution. Tonicization is the process of emphasizing a chord by making it seem like the tonic for a relatively short period of time. Usually this is accomplished by embellishing the chord with a chord that has a dominant or leading tone relationship to it (a secondary dominant). ANALYSIS: Secondary dominants are analyzed as 'x/y' where: x is one of : V, V7, viio, viio/ 7, viio7 y is a major or minor triad in the key. y can be one of: Major key: ii, iii, IV, V, vi minor key: iv, V, VI y can not be a diminished or augmented triad since diminished and augmented triads do not act as tonic triads. RESOLUTION: 1. Normal resolution: x/y resolves normally to y. 2. Irregular resolution: x/y may resolve to a chord that is a substitution (primary or secondary) for y. 3. Deceptive resolution: x/y may resolve to the chord whose root is a third below the root of the y chord. PART-WRITING: The part-writing of a secondary dominant is essentially the same as for the diatonic dominant or leading tone chords: For V and V7: 1. root resolves down a fifth to the root of the next chord (normal resolution). -
1 Lesson JJJ – Applied Chords Introduction: Very Frequently, When Analyzing Tonal Music, You Will Encounter Chords That Includ
1 Lesson JJJ – Applied Chords Introduction: Very frequently, when analyzing tonal music, you will encounter chords that include non-diatonic pitches. Some of them, like those discussed in Lesson III, arise from voice-leading procedures and expand a reference sonority. We will now look at another set of sonorities, known as applied chords , which also enrich the harmonic vocabulary by incorporating chromatically altered pitches. Applied chords are ones modeled on familiar dominant-function chords (V, V 7, vii o, vii o7 , and vii Ø7) and suggest a momentary, pseudo-tonic function for a chord other than the global tonic 1. Momentarily highlighting such a pseudo-tonic by means of a pseudo-dominant chord is called tonicization . In this lesson, we will first discuss the difference between modulation and tonicization. That distinction is essential for understanding how applied chords work. We will then look at several examples of applied dominant chords and applied leading-tone chords, and will discuss associated voice-leading issues. Modulation vs. tonicization: As mentioned above, tonicization occurs when a chord other than the global tonic is heard momentarily, or in passing, as a rival tonic. By contrast, a modulation establishes a new key more enduringly, generally as a sign of large-scale structural organization, sometimes even leading to a change in key signature. Tonicization and modulation are most clearly differentiated by duration and structural significance. A tonicization is brief, lasting from two or three chords to a phrase, and is not a factor in a work’s overall structure. A modulation, on the other hand, takes hold for a longer period, usually prevailing for an entire section, and is a factor in a work’s overall structure. -
Consonance & Dissonance
UIUC Physics 406 Acoustical Physics of Music Consonance & Dissonance: Consonance: A combination of two (or more) tones of different frequencies that results in a musically pleasing sound. Why??? Dissonance: A combination of two (or more) tones of different frequencies that results in a musically displeasing sound. Why??? n.b. Perception of sounds is also wired into (different of) our emotional centers!!! Why???/How did this happen??? The Greek scholar Pythagoras discovered & studied the phenomenon of consonance & dissonance, using an instrument called a monochord (see below) – a simple 1-stringed instrument with a movable bridge, dividing the string of length L into two segments, x and L–x. Thus, the two string segments can have any desired ratio, R x/(L–x). (movable) L x x L When the monochord is played, both string segments vibrate simultaneously. Since the two segments of the string have a common tension, T, and the mass per unit length, = M/L is the same on both sides of the string, then the speed of propagation of waves on each of the two segments of the string is the same, v = T/, and therefore on the x-segment of string, the wavelength (of the fundamental) is x = 2x = v/fx and on the (L–x) segment of the string, we have Lx = 2(L–x) = v/fLx. Thus, the two frequencies associated with the two vibrating string segments x and L – x on either side of the movable bridge are: v f x 2x v f Lx 2L x - 1 - Professor Steven Errede, Department of Physics, University of Illinois at Urbana-Champaign, Illinois 2002 - 2017.