Scales, Tunings and Notations
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Tonality in My Molto Adagio
Estonian Academy of Music and Theatre Jorge Gómez Rodríguez Constructing Tonality in Molto Adagio A Thesis Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy (Music) Supervisor: Prof. Mart Humal Tallinn 2015 Abstract The focus of this paper is the analysis of the work for string ensemble entitled And Silence Eternal - Molto Adagio (Molto Adagio for short), written by the author of this thesis. Its originality lies in the use of a harmonic approach which is referred to as System of Harmonic Classes in this thesis. Owing to the relatively unconventional employment of otherwise traditional harmonic resources in this system, a preliminary theoretical framework needs to be put in place in order to construct an alternative tonal approach that may describe the pitch structure of the Molto Adagio. This will be the aim of Part 1. For this purpose, analytical notions such as symmetric pair, primary dominant factor, harmonic domain, and harmonic area will be introduced before the tonal character of the piece (or the extent to which Molto Adagio may be said to be tonal) can be assessed. A detailed description of how the composer envisions and constructs the system will follow, with special consideration to the place the major diatonic scale occupies in relation to it. Part 2 will engage in an analysis of the piece following the analytical directives gathered in Part 1. The concept of modular tonality, which incorporates the notions of harmonic area and harmonic classes, will be put forward as a heuristic term to account for the use of a linear analytical approach. -
Martin Pfleiderer
Online publications of the Gesellschaft für Popularmusikforschung/ German Society for Popular Music Studies e. V. Ed. by Eva Krisper and Eva Schuck w w w . gf pm- samples.de/Samples17 / pf l e i de r e r . pdf Volume 17 (2019) - Version of 25 July 2019 BEYOND MAJOR AND MINOR? THE TONALITY OF POPULAR MUSIC AFTER 19601 Martin Pfleiderer While the functional harmonic system of major and minor, with its logic of progression based on leading tones and cadences involving the dominant, has largely departed from European art music in the 20th century, popular music continues to uphold a musical idiom oriented towards major-minor tonality and its semantics. Similar to nursery rhymes and children's songs, it seems that in popular songs, a radiant major affirms plain and happy lyrics, while a darker minor key underlines thoughtful, sad, or gloomy moods. This contrast between light and dark becomes particularly tangible when both, i.e. major and minor, appear in one song. For example, in »Tanze Samba mit mir« [»Dance the Samba with Me«], a hit song composed by Franco Bracardi and sung by Tony Holiday in 1977, the verses in F minor announce a dark mood of desire (»Du bist so heiß wie ein Vulkan. Und heut' verbrenn' ich mich daran« [»You are as hot as a volcano and today I'm burning myself on it«]), which transitions into a happy or triumphant F major in the chorus (»Tanze Samba mit mir, Samba Samba die ganze Nacht« [»Dance the samba with me, samba, samba all night long«]). But can this finding also be transferred to other areas of popular music, such as rock and pop songs of American or British prove- nance, which have long been at least as popular in Germany as German pop songs and folk music? In recent decades, a broad and growing body of research on tonality and harmony in popular music has emerged. -
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. -
Development of Musical Scales in Europe
RABINDRA BHARATI UNIVERSITY VOCAL MUSIC DEPARTMENT COURSE - B.A. ( Compulsory Course ) (CBCS) 2020 Semester - II , Paper - I Teacher - Sri Partha Pratim Bhowmik History of Western Music Development of musical scales in Europe In the 8th century B.C., The musical atmosphere of ancient Greece introduced its development by the influence of then popular aristocratic music. That music was melody- based and the root of that music was rural folk-songs. In each and every country, the development of music was rooted in the folk-songs. The European Aristocratic Music of the Christian Era had been inspired by the developed Greek music. In the 5th century B.C. the renowned Greek Mathematician Pythagoras had first established a relation between science and music. Before him, the scale of Greek music was pentatonic. Pythagoras changed the scale into hexatonic pattern and later into heptatonic pattern. Greek musicians applied the alphabets to indicate the notes of their music. For the natural notes they used the alphabets in normal position and for the deformed notes, the alphabets turned upside down [deformed notes= Vikrita svaras]. The musical instruments, they had invented are – Aulos, Salpinx, pan-pipes, harp, lyre, syrinx etc. In the western music, the term ‘scale’ is derived from Latin word ‘scala’, ie, the ladder; scale means an ascent or descent formation of the musical notes. Each and every scale has a starting note, called ‘tonic note’ [‘tone - tonic’ not the Health-Tonic]. In the Ancient Greece, the musical scale had been formed with the help of lyre , a string instrument, having normally 5 or 6 or 7 strings. -
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. -
Playing Harmonica with Guitar & Ukulele
Playing Harmonica with Guitar & Ukulele IT’S EASY WITH THE LEE OSKAR HARMONICA SYSTEM... SpiceSpice upup youryour songssongs withwith thethe soulfulsoulful soundsound ofof thethe harmonicaharmonica alongalong withwith youryour GuitarGuitar oror UkuleleUkulele playing!playing! Information all in one place! Online Video Guides Scan or visit: leeoskarquickguide.com ©2013-2016 Lee Oskar Productions Inc. - All Rights Reserved Major Diatonic Key labeled in 1st Position (Straight Harp) Available in 14 keys: Low F, G, Ab, A, Bb, B, C, Db, D, Eb, E, F, F#, High G Key of C MAJOR DIATONIC BLOW DRAW The Major Diatonic harmonica uses a standard Blues tuning and can be played in the 1st Position (Folk & Country) or the 2 nd Position (Blues, Rock/Pop Country). 1 st Position: Folk & Country Most Folk and Country music is played on the harmonica in the key of the blow (exhale) chord. This is called 1 st Position, or straight harp, playing. Begin by strumming your guitar / ukulele: C F G7 C F G7 With your C Major Diatonic harmonica Key of C MIDRANGE in its holder, starting from blow (exhale), BLOW try to pick out a melody in the midrange of the harmonica. DRAW Do Re Mi Fa So La Ti Do C Major scale played in 1st Position C D E F G A B C on a C Major Diatonic harmonica. 4 4 5 5 6 6 7 7 ©2013-2016 Lee Oskar Productions Inc. All Rights Reserved 2nd Position: Blues, Rock/Pop, Country Most Blues, Rock, and modern Country music is played on the harmonica in the key of the draw (inhale) chord. -
GRAMMAR of SOLRESOL Or the Universal Language of François SUDRE
GRAMMAR OF SOLRESOL or the Universal Language of François SUDRE by BOLESLAS GAJEWSKI, Professor [M. Vincent GAJEWSKI, professor, d. Paris in 1881, is the father of the author of this Grammar. He was for thirty years the president of the Central committee for the study and advancement of Solresol, a committee founded in Paris in 1869 by Madame SUDRE, widow of the Inventor.] [This edition from taken from: Copyright © 1997, Stephen L. Rice, Last update: Nov. 19, 1997 URL: http://www2.polarnet.com/~srice/solresol/sorsoeng.htm Edits in [brackets], as well as chapter headings and formatting by Doug Bigham, 2005, for LIN 312.] I. Introduction II. General concepts of solresol III. Words of one [and two] syllable[s] IV. Suppression of synonyms V. Reversed meanings VI. Important note VII. Word groups VIII. Classification of ideas: 1º simple notes IX. Classification of ideas: 2º repeated notes X. Genders XI. Numbers XII. Parts of speech XIII. Number of words XIV. Separation of homonyms XV. Verbs XVI. Subjunctive XVII. Passive verbs XVIII. Reflexive verbs XIX. Impersonal verbs XX. Interrogation and negation XXI. Syntax XXII. Fasi, sifa XXIII. Partitive XXIV. Different kinds of writing XXV. Different ways of communicating XXVI. Brief extract from the dictionary I. Introduction In all the business of life, people must understand one another. But how is it possible to understand foreigners, when there are around three thousand different languages spoken on earth? For everyone's sake, to facilitate travel and international relations, and to promote the progress of beneficial science, a language is needed that is easy, shared by all peoples, and capable of serving as a means of interpretation in all countries. -
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. -
10 - Pathways to Harmony, Chapter 1
Pathways to Harmony, Chapter 1. The Keyboard and Treble Clef Chapter 2. Bass Clef In this chapter you will: 1.Write bass clefs 2. Write some low notes 3. Match low notes on the keyboard with notes on the staff 4. Write eighth notes 5. Identify notes on ledger lines 6. Identify sharps and flats on the keyboard 7.Write sharps and flats on the staff 8. Write enharmonic equivalents date: 2.1 Write bass clefs • The symbol at the beginning of the above staff, , is an F or bass clef. • The F or bass clef says that the fourth line of the staff is the F below the piano’s middle C. This clef is used to write low notes. DRAW five bass clefs. After each clef, which itself includes two dots, put another dot on the F line. © Gilbert DeBenedetti - 10 - www.gmajormusictheory.org Pathways to Harmony, Chapter 1. The Keyboard and Treble Clef 2.2 Write some low notes •The notes on the spaces of a staff with bass clef starting from the bottom space are: A, C, E and G as in All Cows Eat Grass. •The notes on the lines of a staff with bass clef starting from the bottom line are: G, B, D, F and A as in Good Boys Do Fine Always. 1. IDENTIFY the notes in the song “This Old Man.” PLAY it. 2. WRITE the notes and bass clefs for the song, “Go Tell Aunt Rhodie” Q = quarter note H = half note W = whole note © Gilbert DeBenedetti - 11 - www.gmajormusictheory.org Pathways to Harmony, Chapter 1. -
Use of Scale Modeling for Architectural Acoustic Measurements
Gazi University Journal of Science Part B: Art, Humanities, Design And Planning GU J Sci Part:B 1(3):49-56 (2013) Use of Scale Modeling for Architectural Acoustic Measurements Ferhat ERÖZ 1,♠ 1 Atılım University, Department of Interior Architecture & Environmental Design Received: 09.07.2013 Accepted:01.10.2013 ABSTRACT In recent years, acoustic science and hearing has become important. Acoustic design tests used in acoustic devices is crucial. Sound propagation is a complex subject, especially inside enclosed spaces. From the 19th century on, the acoustic measurements and tests were carried out using modeling techniques that are based on room acoustic measurement parameters. In this study, the effects of architectural acoustic design of modeling techniques and acoustic parameters were investigated. In this context, the relationships and comparisons between physical, scale, and computer models were examined. Key words: Acoustic Modeling Techniques, Acoustics Project Design, Acoustic Parameters, Acoustic Measurement Techniques, Cavity Resonator. 1. INTRODUCTION (1877) “Theory of Sound”, acoustics was born as a science [1]. In the 20th century, especially in the second half, sound and noise concepts gained vast importance due to both A scientific context began to take shape with the technological and social advancements. As a result of theoretical sound studies of Prof. Wallace C. Sabine, these advancements, acoustic design, which falls in the who laid the foundations of architectural acoustics, science of acoustics, and the use of methods that are between 1898 and 1905. Modern acoustics started with related to the investigation of acoustic measurements, studies that were conducted by Sabine and auditory became important. Therefore, the science of acoustics quality was related to measurable and calculable gains more and more important every day. -
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. -
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.