The Chord Numbering System
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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. -
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). -
Theory Placement Examination (D
SAMPLE Placement Exam for Incoming Grads Name: _______________________ (Compiled by David Bashwiner, University of New Mexico, June 2013) WRITTEN EXAM I. Scales Notate the following scales using accidentals but no key signatures. Write the scale in both ascending and descending forms only if they differ. B major F melodic minor C-sharp harmonic minor II. Key Signatures Notate the following key signatures on both staves. E-flat minor F-sharp major Sample Graduate Theory Placement Examination (D. Bashwiner, UNM, 2013) III. Intervals Identify the specific interval between the given pitches (e.g., m2, M2, d5, P5, A5). Interval: ________ ________ ________ ________ ________ Note: the sharp is on the A, not the G. Interval: ________ ________ ________ ________ ________ IV. Rhythm and Meter Write the following rhythmic series first in 3/4 and then in 6/8. You may have to break larger durations into smaller ones connected by ties. Make sure to use beams and ties to clarify the meter (i.e. divide six-eight bars into two, and divide three-four bars into three). 2 Sample Graduate Theory Placement Examination (D. Bashwiner, UNM, 2013) V. Triads and Seventh Chords A. For each of the following sonorities, indicate the root of the chord, its quality, and its figured bass (being sure to include any necessary accidentals in the figures). For quality of chord use the following abbreviations: M=major, m=minor, d=diminished, A=augmented, MM=major-major (major triad with a major seventh), Mm=major-minor, mm=minor-minor, dm=diminished-minor (half-diminished), dd=fully diminished. Root: Quality: Figured Bass: B. -
Many of Us Are Familiar with Popular Major Chord Progressions Like I–IV–V–I
Many of us are familiar with popular major chord progressions like I–IV–V–I. Now it’s time to delve into the exciting world of minor chords. Minor scales give flavor and emotion to a song, adding a level of musical depth that can make a mediocre song moving and distinct from others. Because so many of our favorite songs are in major keys, those that are in minor keys1 can stand out, and some musical styles like rock or jazz thrive on complex minor scales and harmonic wizardry. Minor chord progressions generally contain richer harmonic possibilities than the typical major progressions. Minor key songs frequently modulate to major and back to minor. Sometimes the same chord can appear as major and minor in the very same song! But this heady harmonic mix is nothing to be afraid of. By the end of this article, you’ll not only understand how minor chords are made, but you’ll know some common minor chord progressions, how to write them, and how to use them in your own music. With enough listening practice, you’ll be able to recognize minor chord progressions in songs almost instantly! Table of Contents: 1. A Tale of Two Tonalities 2. Major or Minor? 3. Chords in Minor Scales 4. The Top 3 Chords in Minor Progressions 5. Exercises in Minor 6. Writing Your Own Minor Chord Progressions 7. Your Minor Journey 1 https://www.musical-u.com/learn/the-ultimate-guide-to-minor-keys A Tale of Two Tonalities Western music is dominated by two tonalities: major and minor. -
Cadence in Music Version 1.9: Oct 4, 2007 12:24 Pm GMT-5
Connexions module: m12402 1 Cadence in Music Version 1.9: Oct 4, 2007 12:24 pm GMT-5 Catherine Schmidt-Jones This work is produced by The Connexions Project and licensed under the Creative Commons Attribution License ∗ Abstract A cadence is a place in a piece of music that feels like a stopping or resting point. In tonal music, cadences are classied by their chord progressions. Cadence in Music A cadence is any place in a piece of music that has the feel of an ending point. This can be either a strong, denite stopping point - the end of the piece, for example, or the end of a movement or a verse - but it also refers to the "temporary-resting-place" pauses that round o the ends of musical ideas within each larger section. A musical phrase1, like a sentence, usually contains an understandable idea, and then pauses before the next idea starts. Some of these musical pauses are simply take-a-breath- type pauses, and don't really give an "ending" feeling. In fact, like questions that need answers, many phrases leave the listener with a strong expectation of hearing the next, "answering", phrase. Other phrases, though, end with a more denite "we've arrived where we were going" feeling. The composer's expert control over such feelings of expectation and arrival are one of the main sources of the listener's enjoyment of the music. Like a story, a piece of music can come to an end by simply stopping, but most listeners will react to such abruptness with dissatisfaction: the story or music simply "stopped" instead of "ending" properly. -
Arpeggios - Defined & Application an Arpeggio Is the Notes of a Chord Played Individually
Arpeggios - Defined & Application An arpeggio is the notes of a chord played individually. You can get creative with arpeggios and generate all kinds of unique sounds. Arpeggios can be utilized to outline chords, create melody lines, build riffs, add notes for color, and much more - the sky is the limit! KEY POINTS: There are a few key points to consider when playing arpeggios. The first is you want to hear the arpeggio one note at a time. You don’t want the arpeggio to sound like a strummed chord. You want to hear each note of the arpeggio individually. Arpeggios are the notes that make The goal is to infer the color of the chord with the arpeggio. Kill each note after it is played by muting the strings so the notes dont bleed into each up a chord. other. Another key to good arpeggio playing is mixing arpeggios together with scales, modes, and licks. Mix them into your lead lines as per the video lessons from this course. Try creating musical phrases combining Be sure to sound arpeggios with scales and licks. each note of the arpeggio Another key point is knowing where the arpeggios “live” within a scale. You want to be able to grab arpeggios quickly. Over utilizing the same individually. You three note triads up and down the neck can often sound a bit sterile and don’t want the non-melodic. So be sure to mix the arpeggio in with other scales and licks. arpeggio to sound Often when playing arpeggios you may need to utilize the same finger for like a strummed two or more adjacent strings. -
Key Relationships in Music
LearnMusicTheory.net 3.3 Types of Key Relationships The following five types of key relationships are in order from closest relation to weakest relation. 1. Enharmonic Keys Enharmonic keys are spelled differently but sound the same, just like enharmonic notes. = C# major Db major 2. Parallel Keys Parallel keys share a tonic, but have different key signatures. One will be minor and one major. D minor is the parallel minor of D major. D major D minor 3. Relative Keys Relative keys share a key signature, but have different tonics. One will be minor and one major. Remember: Relatives "look alike" at a family reunion, and relative keys "look alike" in their signatures! E minor is the relative minor of G major. G major E minor 4. Closely-related Keys Any key will have 5 closely-related keys. A closely-related key is a key that differs from a given key by at most one sharp or flat. There are two easy ways to find closely related keys, as shown below. Given key: D major, 2 #s One less sharp: One more sharp: METHOD 1: Same key sig: Add and subtract one sharp/flat, and take the relative keys (minor/major) G major E minor B minor A major F# minor (also relative OR to D major) METHOD 2: Take all the major and minor triads in the given key (only) D major E minor F minor G major A major B minor X as tonic chords # (C# diminished for other keys. is not a key!) 5. Foreign Keys (or Distantly-related Keys) A foreign key is any key that is not enharmonic, parallel, relative, or closely-related. -
Consonance and Dissonance in Visual Music Bill Alves Harvey Mudd College
Claremont Colleges Scholarship @ Claremont All HMC Faculty Publications and Research HMC Faculty Scholarship 8-1-2012 Consonance and Dissonance in Visual Music Bill Alves Harvey Mudd College Recommended Citation Bill Alves (2012). Consonance and Dissonance in Visual Music. Organised Sound, 17, pp 114-119 doi:10.1017/ S1355771812000039 This Article is brought to you for free and open access by the HMC Faculty Scholarship at Scholarship @ Claremont. It has been accepted for inclusion in All HMC Faculty Publications and Research by an authorized administrator of Scholarship @ Claremont. For more information, please contact [email protected]. Organised Sound http://journals.cambridge.org/OSO Additional services for Organised Sound: Email alerts: Click here Subscriptions: Click here Commercial reprints: Click here Terms of use : Click here Consonance and Dissonance in Visual Music Bill Alves Organised Sound / Volume 17 / Issue 02 / August 2012, pp 114 - 119 DOI: 10.1017/S1355771812000039, Published online: 19 July 2012 Link to this article: http://journals.cambridge.org/abstract_S1355771812000039 How to cite this article: Bill Alves (2012). Consonance and Dissonance in Visual Music. Organised Sound, 17, pp 114-119 doi:10.1017/ S1355771812000039 Request Permissions : Click here Downloaded from http://journals.cambridge.org/OSO, IP address: 134.173.130.244 on 24 Jul 2014 Consonance and Dissonance in Visual Music BILL ALVES Harvey Mudd College, The Claremont Colleges, 301 Platt Blvd, Claremont CA 91711 USA E-mail: [email protected] The concepts of consonance and dissonance broadly Plato found the harmony of the world in the Pythag- understood can provide structural models for creators of orean whole numbers and their ratios, abstract ideals visual music. -
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. -
The Thirteenth Amendment: Modern Slavery, Capitalism, and Mass Incarceration Michele Goodwin University of California, Irvine
Cornell Law Review Volume 104 Article 4 Issue 4 May 2019 The Thirteenth Amendment: Modern Slavery, Capitalism, and Mass Incarceration Michele Goodwin University of California, Irvine Follow this and additional works at: https://scholarship.law.cornell.edu/clr Part of the Constitutional Law Commons Recommended Citation Michele Goodwin, The Thirteenth Amendment: Modern Slavery, Capitalism, and Mass Incarceration, 104 Cornell L. Rev. 899 (2019) Available at: https://scholarship.law.cornell.edu/clr/vol104/iss4/4 This Article is brought to you for free and open access by the Journals at Scholarship@Cornell Law: A Digital Repository. It has been accepted for inclusion in Cornell Law Review by an authorized editor of Scholarship@Cornell Law: A Digital Repository. For more information, please contact [email protected]. THE THIRTEENTH AMENDMENT: MODERN SLAVERY, CAPITALISM, AND MASS INCARCERATION Michele Goodwint INTRODUCTION ........................................ 900 I. A PRODIGIOUS CYCLE: PRESERVING THE PAST THROUGH THE PRESENT ................................... 909 II. PRESERVATION THROUGH TRANSFORMATION: POLICING, SLAVERY, AND EMANCIPATION........................ 922 A. Conditioned Abolition ....................... 923 B. The Punishment Clause: Slavery's Preservation Through Transformation..................... 928 C. Re-appropriation and Transformation of Black Labor Through Black Codes, Crop Liens, Lifetime Labor, Debt Peonage, and Jim Crow.. 933 1. Black Codes .......................... 935 2. Convict Leasing ........................ 941 -
Flamenco Music Theory Pdf
Flamenco music theory pdf Continue WHAT YOU NEED TO KNOW:1) Andalusian Cadence is a series of chords that gives flamenco music its characteristic sound: In Music, a sequence of notes or chords consisting of the closing of the musical phrase: the final cadences of the Prelude.3) This progression of chords consists of i, VII, VI and V chords of any insignificant scale, Ending on V chord.4) The most commonly used scale for this chord progression is the Harmonic minor scale (in C minor: B C D E F G))5) The most common keys in flamenco are the Frigian, known as Por Medio in flamenco guitar, and consisting of Dm, C, Bb. Another common key is E Phrygian, known as Por Arriba on Flamenco guitar, and consisting of Am, G, F, E. E Phrygian (Por Arriba) is often used in Solea and Fandangos Del Huelva.THE ANDALUSIAN CADENCE: Today we will discuss really common chords and sound in flamenco: Andalus Cadens! Learning more about this sound will help the audience better appreciate flamenco music, provide flamenco dancers with a better understanding of the music that accompanies them, and non-flamenco musicians some basic theory to incorporate flamenco sounds into their music. At this point, if you want to skip the theory and just listen, go to LISTENING: ANDALUSIAN CADENCE IN THE WORLD. I would recommend reading the pieces of the theory just for some context. MUSIC THEORY: CHORD PROGRESSIONThic series of four chords is so ubiquitous in flamenco that anyone who listens to it should know it when they hear it. -
Download Program Notes
Symphony No. 5 in E minor, Op. 64 Pyotr Ilyich Tchaikovsky t should come as no surprise that Pyotr Ily- background to this piece, which involved Iich Tchaikovsky approached his Fifth Sym- resignation to fate, the designs of provi- phony from a position of extreme self-doubt, dence, murmurs of doubt, and similarly since that was nearly always his posture vis- dark thoughts. à-vis his incipient creations. In May 1888 he Critics blasted the symphony at its pre- confessed in a letter to his brother Modest miere, due in part to the composer’s limited that he feared his imagination had dried up, skill on the podium; and yet the audience that he had nothing more to express in mu- was enthusiastic. Predictably, Tchaikovsky sic. Still, there was a glimmer of optimism: “I decided the critics must be right. In Decem- am hoping to collect, little by little, material ber he wrote to von Meck: for a symphony,” he wrote. Tchaikovsky spent the summer of 1888 Having played my Symphony twice in Pe- at a vacation home he had built on a forest- tersburg and once in Prague, I have come ed hillside at Frolovskoe, not far from his to the conclusion that it is a failure. There home base in Moscow. The idyllic locale ap- is something repellent in it, some over- parently played a major role in his manag- exaggerated color, some insincerity of ing to complete this symphony in the span fabrication which the public instinctive- of four months. Tchaikovsky made a habit ly recognizes. It was clear to me that the of keeping his principal patron, Nadezhda applause and ovations referred not to von Meck, informed about his compositions this but to other works of mine, and that through detailed letters, and thanks to this the Symphony itself will never please ongoing correspondence a good deal of in- the public.