Thirds Triads

Total Page：16

File Type：pdf, Size：1020Kb

Thirds Every other note in a scale makes up an interval of a third. The piano below shows thirds starting on C. There are two types of thirds. A major third is made up of four half steps and a minor third is made up of three half steps. When spelling thirds, it is important to use the enharmonic spelling that follows every other note in the scale. If you were to go up one major third from E, you would go up four half steps which would bring you the note G#/Ab. Since G# is the skip note in the scale it is used instead of Ab. It is helpful to memorize the order of third intervals from any note in a scale: Triads C E G B D F A C E G B D F A A triad is a three note chord that consists of a root, third, and fifth. The root of the chord is the name of a chord. Going up a third from the root gives you the 3rd of the chord. A third above the 3rd gives us the 5th. The type of third (major or minor) that is used between the root, 3rd, and 5th determines the quality of the chord. The name of a triad has two parts, the letter and the quality. A triad can either be major, minor, diminished, or augmented (Example: Eb minor). Below are the formulas for the four triad qualities. 5th 5th ↓5th ↑5th m3 M3 m3 M3 3rd ↓3rd ↓3rd 3rd M3 m3 m3 M3 Root Root Root Root Major Minor Dim Aug capital M is used for major and lower case m is used for minor. Let’s spell a D major triad. The root of the chord is the name of the chord, so the root of the D major triad is D. The interval between the root and the 3rd of a major triad is a major third which consists of four half steps. Four half steps up from a D is an F# or Gb. Remember that the interval of a third has to be created with every other note in the scale so we can’t use Gb. The 3rd of a D major chord is F#. The interval between the 3rd and 5th in a major triad is a minor third which consists of three half steps. Three half steps up from an F# is an A. The 5th of a D major chord is A. The D major triad is spelled D F# A where D is the root, F# is the 3rd and A is the 5th. www.shedthemusic.com.

Copy Link

Recommended publications

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.
[Show full text]
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.
[Show full text]
Hexatonic Cycles
CHAPTER Two H e x a t o n i c C y c l e s Chapter 1 proposed that triads could be related by voice leading, independently of roots, diatonic collections, and other central premises of classical theory. Th is chapter pursues that proposal, considering two triads to be closely related if they share two common tones and their remaining tones are separated by semitone. Motion between them thus involves a single unit of work. Positioning each triad beside its closest relations produces a preliminary map of the triadic universe. Th e map serves some analytical purposes, which are explored in this chapter. Because it is not fully connected, it will be supplemented with other relations developed in chapters 4 and 5. Th e simplicity of the model is a pedagogical advantage, as it presents a circum- scribed environment in which to develop some central concepts, terms, and modes of representation that are used throughout the book. Th e model highlights the central role of what is traditionally called the chromatic major-third relation, although that relation is theorized here without reference to harmonic roots. It draws attention to the contrary-motion property that is inherent in and exclusive to triadic pairs in that relation. Th at property, I argue, underlies the association of chromatic major-third relations with supernatural phenomena and altered states of consciousness in the early nineteenth century. Finally, the model is suffi cient to provide preliminary support for the central theoretical claim of this study: that the capacity for minimal voice leading between chords of a single type is a special property of consonant triads, resulting from their status as minimal perturbations of perfectly even augmented triads.
[Show full text]
Interval Cycles and the Emergence of Major-Minor Tonality
Empirical Musicology Review Vol. 5, No. 3, 2010 Modes on the Move: Interval Cycles and the Emergence of Major-Minor Tonality MATTHEW WOOLHOUSE Centre for Music and Science, Faculty of Music, University of Cambridge, United Kingdom ABSTRACT: The issue of the emergence of major-minor tonality is addressed by recourse to a novel pitch grouping process, referred to as interval cycle proximity (ICP). An interval cycle is the minimum number of (additive) iterations of an interval that are required for octave-related pitches to be re-stated, a property conjectured to be responsible for tonal attraction. It is hypothesised that the actuation of ICP in cognition, possibly in the latter part of the sixteenth century, led to a hierarchy of tonal attraction which favoured certain pitches over others, ostensibly the tonics of the modern major and minor system. An ICP model is described that calculates the level of tonal attraction between adjacent musical elements. The predictions of the model are shown to be consistent with music-theoretic accounts of common practice period tonality, including Piston’s Table of Usual Root Progressions. The development of tonality is illustrated with the historical quotations of commentators from the sixteenth to the eighteenth centuries, and can be characterised as follows. At the beginning of the seventeenth century multiple ‘finals’ were possible, each associated with a different interval configuration (mode). By the end of the seventeenth century, however, only two interval configurations were in regular use: those pertaining to the modern major- minor key system. The implications of this development are discussed with respect interval cycles and their hypothesised effect within music.
[Show full text]
Chords Employed in Twentieth Century Composition
Ouachita Baptist University Scholarly Commons @ Ouachita Honors Theses Carl Goodson Honors Program 1967 Chords Employed in Twentieth Century Composition Camille Bishop Ouachita Baptist University Follow this and additional works at: https://scholarlycommons.obu.edu/honors_theses Part of the Composition Commons, and the Music Theory Commons Recommended Citation Bishop, Camille, "Chords Employed in Twentieth Century Composition" (1967). Honors Theses. 456. https://scholarlycommons.obu.edu/honors_theses/456 This Thesis is brought to you for free and open access by the Carl Goodson Honors Program at Scholarly Commons @ Ouachita. It has been accepted for inclusion in Honors Theses by an authorized administrator of Scholarly Commons @ Ouachita. For more information, please contact [email protected]. Chords Formed By I nterval s Of A Third The traditional tr i ~d of t he eigh te8nth aDd n i neteenth centuries t ends to s~ un 1 trite i n t he su r roundin~s of twen tieth century d i ss onance. The c o ~poser f aces the nroble~ of i magi native us e of th e trla1 s o as t o a d d f reshness to a comnosition. In mod ern c Dmn:;sition , rna i or 8.nd minor triads are usually u s ed a s ooints of r e l axation b e f ore a nd a fter sections o f tension. Progressions of the eighte enth and n inete enth c en t u r i es we re built around t he I, IV, and V chords. All other c hords we re considered as incidenta l, serving to provide vari e t y .
[Show full text]
The Perception of Pure and Mistuned Musical Fifths and Major Thirds: Thresholds for Discrimination, Beats, and Identification
Perception & Psychophysics 1982,32 (4),297-313 The perception ofpure and mistuned musical fifths and major thirds: Thresholds for discrimination, beats, and identification JOOS VOS Institute/or Perception TNO, Soesterberg, TheNetherlands In Experiment 1, the discriminability of pure and mistuned musical intervals consisting of si multaneously presented complex tones was investigated. Because of the interference of nearby harmonics, two features of beats were varied independently: (1) beat frequency, and (2) the depth of the level variation. Discrimination thresholds (DTs) were expressed as differences in level (AL) between the two tones. DTs were determined for musical fifths and major thirds, at tone durations of 250, 500, and 1,000 msec, and for beat frequencies within a range of .5 to 32 Hz. The results showed that DTs were higher (smaller values of AL) for major thirds than for fifths, were highest for the lowest beat frequencies, and decreased with increasing tone duration. Interaction of tone duration and beat frequency showed that DTs were higher for short tones than for sustained tones only when the mistuning was not too large. It was concluded that, at higher beat frequencies, DTs could be based more on the perception of interval width than on the perception of beats or roughness. Experiments 2 and 3 were designed to ascertain to what extent this was true. In Experiment 2, beat thresholds (BTs)for a large number of different beat frequencies were determined. In Experiment 3, DTs, BTs, and thresholds for the identifica tion of the direction of mistuning (ITs) were determined. For mistuned fifths and major thirds, sensitivity to beats was about the same.
[Show full text]
The Consecutive-Semitone Constraint on Scalar Structure: a Link Between Impressionism and Jazz1
The Consecutive-Semitone Constraint on Scalar Structure: A Link Between Impressionism and Jazz1 Dmitri Tymoczko The diatonic scale, considered as a subset of the twelve chromatic pitch classes, possesses some remarkable mathematical properties. It is, for example, a "deep scale," containing each of the six diatonic intervals a unique number of times; it represents a "maximally even" division of the octave into seven nearly-equal parts; it is capable of participating in a "maximally smooth" cycle of transpositions that differ only by the shift of a single pitch by a single semitone; and it has "Myhill's property," in the sense that every distinct two-note diatonic interval (e.g., a third) comes in exactly two distinct chromatic varieties (e.g., major and minor). Many theorists have used these properties to describe and even explain the role of the diatonic scale in traditional tonal music.2 Tonal music, however, is not exclusively diatonic, and the two nondiatonic minor scales possess none of the properties mentioned above. Thus, to the extent that we emphasize the mathematical uniqueness of the diatonic scale, we must downplay the musical significance of the other scales, for example by treating the melodic and harmonic minor scales merely as modifications of the natural minor. The difficulty is compounded when we consider the music of the late-nineteenth and twentieth centuries, in which composers expanded their musical vocabularies to include new scales (for instance, the whole-tone and the octatonic) which again shared few of the diatonic scale's interesting characteristics. This suggests that many of the features *I would like to thank David Lewin, John Thow, and Robert Wason for their assistance in preparing this article.
[Show full text]
11 – Music Temperament and Pitch
11 – Music temperament and pitch Music sounds Every music instrument, including the voice, uses a more or less well defined sequence of music sounds, the notes, to produce music. The notes have particular frequencies that are called „pitch“ by musicians. The frequencies or pitches of the notes stand in a particular relation to each other. There are and were different ways to build a system of music sounds in different geographical regions during different historical periods. We will consider only the currently dominating system (used in classical and pop music) that was originated in ancient Greece and further developed in Europe. Pitch vs interval Only a small part of the people with normal hearing are able to percieve the absolute frequency of a sound. These people, who are said to have the „absolute pitch“, can tell what key has been hit on a piano without looking at it. The human ear and brain is much more sensitive to the relations between the frequencies of two or more sounds, the music intervals. The intervals carry emotional content that makes music an art. For instance, the major third sounds joyful and affirmative whereas the minor third sounds sad. The system of frequency relations between the sounds used in music production is called music temperament . 1 Music intervals and overtone series Perfect music intervals (that cannot be fully achieved practically, see below) are based on the overtone series studied before in this course. A typical music sound (except of a pure sinusiodal one) consists of a fundamental frequency f1 and its overtones: = = fn nf 1, n 3,2,1 ,..
[Show full text]
4.1.9 Alterations of Chord Extensions
22 High-Yield Music Theory, Vol. 4: Jazz Theory Section 4.1.9 A LTERATIONS OF C HORD E XTENSIONS Unaltered An extension (ninth, eleventh, or thirteenth) is unaltered if it follows the extensions major scale built on the root of that chord. Extensions may be lowered or raised a half step by changing the accidental. Lowered extensions are Natural nine flatted, and raised extensions are sharped. So a natural ninth (or natural Flat nine nine) follows the major scale built on the chord root, a flatted ninth (or flat Sharp nine nine) means a lowered ninth, and a sharped ninth (or sharp nine) means a raised ninth. Remember: a ninth is the same as a second. §9 b9 #9 = minor 3rd w bw #w bw && & w w w w Natural eleven An eleventh is the same as a fourth. A natural eleventh (or natural eleven) Sharp eleven always means follow the major scale, and sharp eleventh (or sharp eleven) means raise the eleventh a half step, regardless of the accidentals used. §11 #11 = b5 &&bw w #w w Natural thirteen A thirteenth is the same as a sixth. A natural thirteenth (or natural Sharp thirteen thirteen) always means major sixth, and flat thirteenth (or flat thirteen) means lowered thirteenth, regardless of the accidentals used. §13 b13 = #5 w bw &&#w w w w Flat eleven Flat eleven and sharp thirteen are never used. A flat eleven is the same as a Sharp thirteen major third, and a sharp thirteen is the same as a minor seventh. b11 = major 3rd #13 = minor 7th #w bw & bw & w w w w Volume 4, Chapter 1: Jazz Theory Fundamentals 23 Spelling Depending on the root, unaltered (natural) extensions may actually use alterations naturals, flats, sharps, or even double flats or double sharps.
[Show full text]
On the Notation and Performance Practice of Extended Just Intonation
On Ben Johnston’s Notation and the Performance Practice of Extended Just Intonation by Marc Sabat 1. Introduction: Two Different E’s Like the metric system, the modern tempered tuning which divides an octave into 12 equal but irrational proportions was a product of a time obsessed with industrial standardization and mass production. In Schönberg’s words: a reduction of natural relations to manageable ones. Its ubiquity in Western musical thinking, epitomized by the pianos which were once present in every home, and transferred by default to fixed-pitch percussion, modern organs and synthesizers, belies its own history as well as everyday musical experience. As a young musician, I studied composition, piano and violin. Early on, I began to learn about musical intervals, the sound of two tones in relation to each other. Without any technical intervention other than a pitch-pipe, I learned to tune my open strings to the notes G - D - A - E by playing two notes at once, listening carefully to eliminate beating between overtone-unisons and seeking a stable, resonant sound-pattern called a “perfect fifth”. At the time, I did not know or need to know that this consonance was the result of a simple mathematical relationship, that the lower string was vibrating twice for every three vibrations of the upper one. However, when I began to learn about placing my fingers on the strings to tune other pitches, the difficulties began. To find the lower E which lies one whole step above the D string, I needed to place my first finger down.
[Show full text]
MTO 12.3: Duffin, Just Intonation in Renaissance Theory and Practice
Volume 12, Number 3, October 2006 Copyright © 2006 Society for Music Theory Ross W. Duffin ABSTRACT: Just intonation has a reputation as a chimerical, theoretical system that simply cannot work in practice. This is based on the assessment of most modern authorities and supported by misgivings expressed during the Renaissance when the practice was supposedly at its height. Looming large among such misgivings are tuning puzzles printed by the 16th-century mathematician, Giovanni Battista Benedetti. However, Renaissance music theorists are so unanimous in advocating the simple acoustical ratios of Just intonation that it seems clear that some reconciliation must have occurred between the theory and practice of it. This article explores the basic theory of Just intonation as well as problematic passages used to deny its practicability, and proposes solutions that attempt to satisfy both the theory and the ear. Ultimately, a resource is offered to help modern performers approach this valuable art. Received June 2006 Introduction | Theoretical Background | Benedetti's Puzzles | Problematic Passages | Is Just Tuning Possible? A New Approach | Problem Spots in the Exercises | Rehearsal Usage | Conclusion Introduction The idea . that one can understand the ratios of musical consonances without experiencing them with the senses is wrong. Nor can one know the theory of music without being versed in its practice. [1] So begins the first of two letters sent by the mathematician Giovanni Battista Benedetti to the composer Cipriano de Rore in 1563. Subsequently publishing the letters in 1585,(1) Benedetti was attempting to demonstrate that adhering to principles of Just intonation, as championed most famously by Gioseffo Zarlino,(2) would, in certain cases, cause the pitch of the ensemble to migrate.
[Show full text]
Mathematics and Music: Using Group Theory to Qualify N-Note Tonal Systems
Mathematics and Music: Using Group Theory to Qualify N-Note Tonal Systems By Kristie Kennedy Senior Honors Thesis Appalachian State University Submitted to the Honors College in partial fulfillment of the requirements for the degree of Bachelor of Science May 2015 Approved by: _____________________________________________________ Vicki Klima, Ph.D., Thesis Director _____________________________________________________ William Harbinson, Ph.D., Second Reader _____________________________________________________ Leslie Sargent Jones, Ph.D., Director, The Honors College Abstract In this senior thesis we examine the relationship between math, speciﬁcally group theory, and tonal music systems. In particular, we examine the 12-note tonal system of western music and identify some of its fundamental properties. From there we establish criteria that an alternative tonal system must meet to be considered an acceptable alternative to the 12-note tonal system. We build a mathematical model for n-note tonal systems using cyclic groups of order n. Ultimately we conclude that in order for an n-note tonal system to be acceptable, the system must be composed of n notes where n is divisible by 4, but not divisible by 8. 1 Introduction Within this project we set criteria for acceptable alternatives to the 12-note tonal system and determine which n-note tonal systems meet these criteria. In section 2 we introduce the basic musical terms we will use throughout the paper. In section 3 we review literature that introduces cyclic groups to the study of tonal systems. We use section 4 to introduce the basic concepts of cyclic groups and how they correspond to the 12-note tonal system. Section 5 sets out our criteria for alternative tonal systems.
[Show full text]