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I:  BASIC ELEMENTS OF MUSIC THEORY


Sound and Music

  1. Definitions:

    1. Music Is Sound Organized in Time: This is the most basic definition of any kind of musical work. Any type of sounds can be used to create modern music, all that is needed is a certain time frame. Common but not required factors in music creation include a person (often called a composer) who first imagines the music, human or mechanical performers who generate the sounds, and a mechanical means of recording and reproducing them. When this happens simultaneously, it is known as a process called improvisation. However, scientists still try to figure out what qualifies as music. 

    2. Music of the Western World: Many cultures have different views on what they identify as “music”. In some cases music is such a fundamental part of their lifestyle that there is no separate, distinguished word for it. The musical traditions that developed in Europe in the past two millennia are known as “music of the Western World”.

  2. Physics of Musical Sound:

    1. Sound Waves: Sound is described as a wave of energy, characterized by both amplitude and frequency. The amplitude determines the decibel level (loudness), with higher amplitudes producing louder sounds. Frequency affects pitch, with greater frequencies resulting in higher pitches. The human ear typically hears frequencies between 20 and 20,000 cycles per second as a single tone. A pure sine wave at 440 Hz corresponds to an A above middle C, which orchestral musicians in the U.S. standardize their tuning to as "A-440." Not all sounds have a consistent frequency; for example, a dropped book produces an irregular wave pattern, resulting in non-discernible pitch. Hence, there are two types of musical sounds: pitched and non-pitched, with percussion instruments mainly providing non-pitched sounds.

    2. Instruments as Sound Sources: How is a musical sound wave produced? In the late 19th century, Curt Sachs and Erich von Hornbostel, categorized instruments into four groups, chordophones, aerophones, membranophones, and idiophones. Before Sachs and Hornbostel, Western orchestral instruments were grouped into “families.” These categories are still used for Western instruments today. They are strings, brass instruments, woodwind instruments, and percussion instruments. In some cases, keyboard instruments count as a fifth group. The first electronic instruments emerged in the early twentieth century, with the theremin being one of the most well-known. It is still used today, requiring the performer to regulate frequency with one hand and amplitude with the other by interacting with the electrical fields around its protruding bars. The next important step came after World War II, when technology had been improved, allowing musical work to be done with new equipment. Electronically generated sounds and sounds from live instruments were recorded on tape, allowing for editing, manipulation, and mechanical recombination into sound collages performed via loudspeaker. This type of composition is known as musique concrète


Pitch, Rhythm, and Harmony

  1. Pitch

    1. Pitch, Frequency, and Octaves: Pitch is the highness or lowness of a sound. When musicians speak of “a pitch” they are referring to a single tone whose highness and lowness do not change and stay constant like A-440. The musical term for the distance (or interval) between A and the next higher or next lower A is called an octave.

    2. Pitch on a Keyboard: High-sounding pitches are to the right; low sounding pitches are to the left. The distance between any two adjacent keys on the keyboard is called a half step, or semitone. A whole step is the distance between every other key. White keys are called natural keys and the symbol that represents a natural note is ♮. The signs ♯ (sharp) and ♭ (flat) indicate that a given pitch, such as A♮, has been raised or lowered, respectively, by a half step.

    3. Pitch on a Staff: Music notation uses a five-line staff as a type of ladder to indicate pitches. Each line or space on the staff is assigned to a letter of the musical alphabet—but the assignment can vary, depending on the clef symbol at the left-hand end of the staff. There are three types: treble clef, the bass clef, and the C-clef. When the C-clef indicates that the pitch C should be placed on the middle line of the staff, we call it the alto clef. But, if the C-clef is centered on the fourth line from the bottom of the staff, it is called the tenor clef.

    4. Pitch on the Grand Staff: In piano music, two bracketed staves, known as the grand staff, are used. The left hand plays the music notated on the lower staff, typically containing a bass clef, while the right hand plays the notes on the upper staff, which usually contains a treble clef. Pitches corresponding to the keyboard's white and black notes are labeled on the grand staff. It is also noted that in prose, sharp or flat symbols follow the letter (e.g., F♯, A♭), but precede the notehead when written on a staff.

    5. Overtones and Partials: Very few pitches consist of a single frequency. Typically, one frequency predominates while many other frequencies are present at faint volumes. For instance, when a guitar's A string is plucked, the dominant sound wave produced is at 110 Hz, but there are numerous other waves resonating simultaneously. These include waves that are half, one-third, one-quarter, etc., the length of the string. The lowest A is termed the fundamental, being the loudest and strongest. However, it is characterized by the subtle presence of higher pitches known as partials or overtones.

    6. Equal Temperament: Generating the Twelve Pitches by Dividing the Octave: In the world of pure sound waves and overtones, pitches follow mathematical patterns. But, in the Western tradition, after about 1750, a system of tuning called equal temperament became dominant.

    7. Scales: Leading Tone, Tonic, Dominant: Western composers choose a set of seven pitches as the basis for a piece of music. When arranged in ascending order, it is known as a diatonic scale. The seventh scale degree is known as the leading tone. In the C major scale and the melodies that use it, C is the anchor, sometimes called the “resting tone” and mostly known as the tonic pitch. The fifth-scale degree, called the dominant pitch is nearly as important as the tonic because it functions like a second gravitational center that sets melodies in the 

    8. Intervals: The distance between any two pitches is called an interval. The smallest distance between any two adjacent keys on the piano is a half step (or semitone). Any interval can be performed so it is harmonic (the two pitches occur simultaneously) or melodic, with the two pitches occurring in succession(ascending or descending).

    9. Intervals of the Major Scale: A scale can be described as a succession of whole

and half steps (or major seconds and minor seconds). By using that same sequence of melodic intervals, you can create a major scale starting on any key of the piano.

  1. Minor Scales and Blues Inflections: The next most common scale is the minor scale. There are three slightly different varieties: natural (or pure) minor, harmonic minor, and melodic minor. C natural minor and Eâ™­ major are called relative major and minor because they use the same seven pitches but have different tonics. This relationship remains even when the natural minor is altered to create harmonic or melodic minor scales. In contrast, scales that start and end on the same tonic pitch are referred to as parallel. Relative scales are perceived as more closely related than parallel scales due to sharing the same collection of pitches. A scale with blues inflictions combines elements of both major and minor scales.

  2. Melody Defined; Example, Using Scale Degrees:  A melody is a series of successive pitches perceived by the ear to form a coherent whole. Only one pitch occurs at a time in a melody; if two pitches occur together, you have either harmony or counterpoint.

  3. Contour: All melodies have a contour, or profile. A conjunct melody moves smoothly, in stepwise motion(an example being “Row, Row, Row Your Boat). A disjunct melody, on the other hand, contains proportionally more leaps (intervals larger than a major second). Melodies may ascend, descend, or move in a wavelike manner. A very common contour for melodies is that of an arch.

  4. Range and Tessitura: Every instrument (including the human voice) has a range of possible pitches that it is capable of producing. The high, middle, and low parts of an instrument’s range are often called the high, middle, or low register. A melody with a high tessitura calls for more pitches in the performer’s high register than does a melody with a medium or low tessitura. music. A female singer who performs most comfortably in a high tessitura is called a soprano; a lower-register female singer is called an alto. For men, the higher register is called tenor, while a low-register male voice is a bass


  1. Rhythm - a audible collection of varying durations

    1. Beat: Beat is the steady pulse that underlies most music. Sometimes the beat is audible, sometimes not, but it is present, like the silent or ticking second hand on a mechanical clock.

    2. Tempo: The speed of the beat is called the tempo. The terms that can be used to describe the speeds of a tempo are in Italian. Tempo can slow down (ritardando) or speed up (accelerando), and it can do either gradually (poco a poco) or suddenly (subito). When there is no steady tempo—which is the same as no discernable beat—music is said to be unmetered. If there is a perceived beat, but it speeds up and slows down for expressive effect, it is called rubato.

    3. Meter: Duple, Triple, and Quadruple: All beats are of equal length, but not all beats are of equal importance. Normally, beats are grouped into measures (or more informally, bars), which are separated by bar lines. The first beat of any measure is usually the strongest, so it is customarily called the downbeat or strong beat. Meter describes the pattern of emphasis superimposed on groups of beats. In general terms, meters are duple, triple, quadruple, or irregular (also called asymmetrical). The song “Happy Birthday,” with its groupings of

three beats, is in triple meter as is shown in Figure 1–12. The first word falls before the downbeat. This is called a “pickup” or anacrusis

  1. Rhythmic Notation: A variety of symbols indicate how long a note should last. An oval note, called a whole note, is the longest. A stem can be added to symbolize that that note has been cut in half. When the note head is solid black with a stem, it is a quarter note. When a flag is added to the stem of that note, it is known as an eighth note. note. Additional flags can be added, each subdividing the value of the note by half again:

  2. Time Signature: In music notation, the meter is indicated with a time signature, which usually consists of two numbers. The lower number indicates a durational value, with 2 meaning the half note, 4 the quarter note, 8 the eighth, and 16 the sixteenth note. (This is not a fraction! Note that there is no line between the two numbers.) The upper number indicates how many of those durational values (or their equivalents) will occur in one measure. Thus, if the time signature is 6/8 , the measure will contain the combined time value of six eighth notes. Two other symbols are often used to represent the time

  3. signature: a large capital C (called “common time”) is equivalent to 4/4 time, and a vertical slash through the C indicates that the time signature is 2/2 ; this symbol is usually called “cut-time,”

  4. Simple and Compound Subdivision: Each beat is typically divided in half, known as simple subdivision (1 & 2 & 3 & or 1 & 2 & 3 & 4 &). When a beat is divided into three equal parts, it is considered compound subdivision. For instance, a 6/8 meter can be counted as 1 2 3 4 5 6 or in compound subdivision as ONE-&-a TWO-&-a. Examples like "Sumer is icumen in" and the “Irish” melody in Global Warming demonstrate compound subdivision, while “Flight of the Bumblebee” exemplifies simple subdivision. In swing music, rhythms are notated in 4/4 time but played as if in 12/8. 

  5. Mixed and Irregular Meter: Mixed meter and irregular or asymmetrical meter are variations on the grouping of beats. beats. In mixed meter, measures that have different meters occur in rapid succession. Irregular meter features measures that have different meters alternating in an irregular pattern(ex. ONE-two-three-ONE-two-three…). When two or more meters are operating simultaneously, it is referred to as a polymeter.

  6. Syncopation: Rhythm is syncopated when accented or emphasized notes fall on weak beats or in between beats. The rhythms in “Happy Birthday” are regular and coincide with the beat, so it is not considered syncopated.

  7. Polyrhythm: Polyrhythm, also called cross-rhythm, occurs when two conflicting rhythmic patterns are present simultaneously.

  8. Harmony:

  1. Harmony - occurs whenever two or more tones are sounding simultaneously.

    1. Common-Practice Tonality: Common-practice tonality (also called common-practice harmony) is the system of organizing pitch and harmony that we find intuitive today in Western cultures.

    2. Chords: A chord is three or more pitches sounding simultaneously.

      1. Triads: A triad is a three-note chord consisting of two intervals of a third and comes in four qualities: major, minor, diminished, and augmented.

        1. Major Triad (M): Has a major third interval between its lower two pitches and a minor third above.

        2. Minor Triad (m): Has a minor third on the bottom and a major third above.

        3. Diminished Triad (d): Composed of two minor thirds.

        4. Augmented Triad (A): Composed of two major thirds.

Triads are built above each note of the scale and are fundamental chords in music. In a triad, the lowest note is the root, the middle note is the third, and the highest note is the fifth.

  1. Inversions: Any pitch of a triad can be moved up or down any number of octaves. When the third of the triad is on the bottom, the chord is in first inversion. When the fifth one is on the bottom, it's in its second inversion. Any triad may be inverted. The bottom pitch determines the inversion.

  1. Keys

    1. Keys and Key Signatures: The key signature is a set of sharps or flats at the beginning of every staff that indicates the key of the music.

    2. Hierarchy of Keys: Circle of Fifths: Key signatures fall into a fascinating pattern. Remember, there are fifteen major scales. There are also fifteen minor scales. Each scale corresponds to a key of the same name. And, each major scale contains the same pitches as one of the natural minor keys. (Remember the example in Figure 1–10: C minor is the relative minor of E♭ major; E♭ is the relative major of C minor.)

  2. d. Harmonic Progression: A harmonic progression is a series of chords or intervals that moves from tension (dissonance) toward resolution (consonance). A chain of triads, each pulling to the next, is called a chord progression. More often, some of the chords are inverted to create what is called smoother voice leading.

    1. Dissonance and Consonance: Dissonance is the quality of a pitch, interval or chord that makes it seem “unstable” or tense. Dissonance is relative. The most consonant chords are the ones that stress the lower partials on the overtone series.

    2. Diatonic Triads: Diatonic means “within the key”. A chord/melody is diatonic if no accidentals are needed other than those already indicated in the key signature. If a melody/chord borrows notes from outside the key, then it is chromatic. The tonic triad is a diatonic triad built on the tonic pitch. A diminished triad is highly unstable.

    3. The Dominant Triad’s Special Role: Other harmonies, in turn, “pull” to the dominant: these are called pre-dominant harmonies. The triads built on the second and fourth scale degrees (ii—also called the supertonic, and IV, the sub-dominant) are the most common predominant harmonies.

    4. Bass Lines: The bass line is the lowest “voice” in a series of chords. It provides the finishing touch, reinforcing the forward pull of the progression. Bass lines often, but not always, play the root of the harmony. Bass lines are usually notated in bass clef. Cadences are pausing points.

    5. The Dominant Seventh Chord: To intensify its pull to the tonic triad, the dominant triad is often turned into a dominant seventh chord, or V to the 7th.

    6. Example: A Harmonized Melody: The song “Happy Birthday” can serve to illustrate the idea of harmonic progression. In Figure 1–29, it is harmonized with diatonic triads and labeled with Roman numerals.

  3. Other Diatonic Chords: As common-practice harmony evolved after 1750, composers began to embellish triads with additional pitches, typically a sixth, seventh, or ninth above the root. These embellishments can be arranged in close or open position while maintaining the root in the bass. Besides the dominant-seventh chord, other diatonic seventh chords can enhance complexity, built by adding a seventh above the root to any diatonic triad. This addition enriches the original triad's sound without changing its function.

  4. Chromatic Harmonies and Modulation: Simple harmony is diatonic, and it uses mostly triads. Complex harmony uses more chromatic pitches, and four or more separate pitches may sound at the same time.

  5. Beyond Common Practice: Modulation and chromatic harmonies allowed composers to write music that strayed further and further from the “home base” tonic. Compositions could be longer and longer and more and more chromatic. Composers generally pursued these changes in order to be more expressive. Throughout common practice, resolution of dissonance is the driving force behind harmony. In the nineteenth century, many Romantic composers sought out new ways to portray emotion and individuality in music. Musicians use complex chromatic harmonies to express subtle emotions, often delaying resolution to the tonic. In 1910, Arnold Schoenberg proposed the 'emancipation of dissonance,' allowing music to exist without traditional resolution, leading to atonal music. He later developed the 'twelve-tone method' in 1925, using a unique tone row of twelve pitches for each piece. This approach influenced composers like Webern and Berg, and grew popular post-World War II. Other composers, such as Debussy and Stravinsky, explored unconventional harmonies, scales, and polytonality, contributing to a shift towards more static and meditative music forms.


Other Aspects of Musical Sound

  1. Texture, Counterpoint, Instrumentation, More Timbre: Besides melody, rhythm, and harmony, a number of factors greatly affect how a performance sounds. Texture, in music, describes the number of things that are going on in a singular piece. The four types of texture in Western music are monophony(single melody), homophony(two different things), polyphony(two or more separate melodies), and heterophony(two melodies are somewhat harmonie with a little variation). Instrumentation, the instrument or combination of instruments used, is among the most noticeable features of a given piece of music. Arranging is the art of taking an existing piece of music (melody, harmony, rhythm) and giving instructions as to what each individual performer should play. The timbre (also called tone color) of an acoustic guitar is affected by the size and shape of its hollow wooden body, where the sound waves produced by the strings resonate and are amplified. Instrumentalists are frequently asked to modify their timbre by using a “mute,” which not only quiets the volume but alters the tone color.

  2. Dynamics, Articulation, Ornamentation: Dynamics, the loudness and softness of a sound, are useful to performers and composers for expressive purposes. A gradual increase in dynamics is called a crescendo, and a gradual decrease is called a decrescendo or diminuendo. Another factor affecting the sound of a piece is articulation. Staccato indicates that the performer should shorten the duration of a note. Legato means multiple pitches are played in a smooth, connected but not overlapping manner. An accent involves more sudden sound than a staccato, and, unlike staccato, silent space before the next pitch is not required. Ornamentation refers to localized embellishments, which are often not written down.


Form in Music - Form describes how music is organized on a larger time scale—how units are combined to make larger structures. Form is the architecture of music.

  1. Perceiving Musical Form - Music takes place in time. By the time the final notes are heard, the sound waves from the beginning have long disappeared. As the listener hears a piece, he/she experiences an ebb and flow of tension and release. The main way how tension is released is through harmonic dissonance. Besides dissonance, tension can be created in other ways, including increased dynamic level, increased tempo, or increased rhythmic activity using shorter durations.

  2. Elements of Form

    1. Motive: A motive (sometimes spelled “motif”) is the smallest unit of form. A motive is best defined as the smallest identifiable recurring musical idea. A motive has a distinctive melodic and rhythmic profile(ex. The first four notes corresponding to the first four words in “Happy Birthday”).

    2. Phrase: A phrase is a cohesive musical thought (ex. The first four words in “Happy Birthday”). Phrases often come in related pairs. The first member of the pair is called the antecedent phrase(ends somewhat inconclusively), and the second is called the consequent phrase.

    3. Cadence: The term for a resting point in a piece of music is cadence. There are different types of cadences that have varying strength. this. A half cadence rests on the dominant harmony, like the first short phrase of “Happy Birthday.” A full cadence, also called an authentic cadence, uses the progression V-I, as the second short phrase of “Happy Birthday” does.

    4. Theme: A theme is a set of phrases that make a complete melody, which plays a prominent role in a longer piece of music(ex. “Happy Birthday” could be used as the main theme for a twelve minute composition of the same topic).

    5.  Introduction and Coda: Many pieces of music begin with an introduction, which is music that precedes the first main theme of the piece. It is particularly common in vocal music to have an instrumental introduction that precedes the singing. Similarly, a great many pieces end with a coda, or an outro. 

  3.  Common Forms - Musical form controls larger spans of time. Just as mystery novels, thirty-minute television sitcoms, and movie scripts tend to follow certain patterns, so does music. Balance, proportion, drama, climax, and denouement operate in musical form.

    1. Repetition: Repetition means, literally, repeating musical material, using the identical pitches, rhythms, and harmonies, or at least a very close approximation. If repeated at a different pitch level, it is called a sequence. letters. The music to a strophic song made up of a single, multi-phrased melody(ex. A A A A).

    2. Variation

      1. Theme and Variations: Theme and variations is a common way of structuring a composition, which starts with a straightforward statement of the theme, followed by sections that repeat the theme with significant changes. The differences may include variations in harmonies, accompaniment patterns, rhythms, or textures, while still maintaining the essence of the original theme. Variations are diagrammed with a “prime” mark, like A, A’, A’’, A’’’, and so on.

      2. 12-Bar Blues: The twelve-bar blues is also a variation of this form. This twelve-measure chord progression is repeated, with variations in the melodic material. Usually in a moderate or relaxed tempo, with four beats to the measure, the blues progression can be played in any key, though C, Bâ™­, and F are traditional favorites. Minor-key blues are possible but less common.

      3. Improvisation: Improvisation in soul, gospel, and jazz, especially the styles common before 1950, uses the principle of variation.

    3. Contrast

      1. Ternary and Rondo Forms: The simplest form using contrast is the three-part or ternary form, also called ABA form, in which two sections of very similar music frame a contrasting middle section that contains its very own cadence. Rondo form is also built from distinct sections, one of which keeps returning.

      2. 32-Bar Form: In mid-twentieth-century popular music, most songs contain a section of contrasting material. A melody, called the 32-bar form, was made from A-A-B-A form.

      3. Verse-Chorus Form: In the early days of popular music, the most popular formal architecture was the verse-chorus (or verse-refrain) form. It consists of multiple verses, each with different words, and a repetitive chorus, or refrain. This form is often diagrammed as a-B-a-B (etc.), with the upper-case “B” indicating that both the melody and the words repeat. During the verses, it is only the melody that repeats. (An example of verse-chorus form appears in “Big Yellow Taxi”

    4. Development

      1. Fugue: Fugue is not actually a standard form, but a technique. However, the form of many classical pieces is determined by the way the composer uses fugal technique, rather than by any of the other forms described here. A fugue usually has a single theme, called a fugue subject, which the composer develops using the technique of imitative counterpoint. When there is a companion theme, it is called a countersubject. Imitation, the approximate repetition of a melodic idea at a different pitch level, is central to fugal technique.

      2. Sonata Form: Sonata form is a standard form that has been used for the first movements of many Western classical compositions, beginning around 1730. The sonata form consists of three main sections: exposition, development, and recapitulation, typically structured in two sections. The exposition introduces two main musical ideas, the first in the tonic key and the second modulated to a different key, often characterized by a key change marked by increased rhythmic activity and dynamics. The development section is harmonically unstable, exploring and varying material from the exposition. It features irregular phrases and unexpected changes, culminating in a half cadence. The recapitulation restores order by returning to Idea #1 and presenting Idea #2 in the original key, concluding the movement. Sonata form, prevalent in many Classical compositions, is often referred to as 'first-movement form.'


Which Is the Real Music? Scores, Recordings, and Performance

Music theory traditionally describes pieces of music as if they were fixed objects. However, it is important to remember that (most) music is performed by living people. Music notation is able to convey some things precisely—pitch relationships, rhythms, instrumentation, and to some degree phrasing, dynamics, and articulation. Yet it also has obvious limitations. We cannot know how smoothly people in the 1870s performed a “legato” phrase. Historians have found written comments suggesting that the exact pitch for concert A may have varied as much as a minor third in either direction from today’s A440—which even today is not universally adopted. Recording technology has allowed us to preserve far more information than notation allows, but this too

is limited in different ways. An entire subfield called “performance practice” exists to address the question, how did the music really sound? Perhaps critics like Christopher Small have it right when they propose that in addition to marveling at the intricate structure of Western music, we should also study the human activity he calls “Musicking.”


SECTION I SUMMARY:


Sound and Music

  • Music is sound organized in time.


Pitch, Rhythm, Harmony

  • Developed over centuries in the Western world, common-practice tonality is the widely accepted system for describing the relationships among pitches and harmonies.

  • Pitch is the highness or lowness of a sound. It is the basic building block for melody and harmony. Harmony occurs when two or more pitches sound simultaneously.

  • The octave occurs naturally in the overtone series. Western tradition divides it into twelve equal intervals called half steps.

  • Melody is a coherent succession of pitches perceived as a whole, with a beginning, middle, and end.

  • Major and minor scales are sets of seven different pitches arranged in a specific pattern of whole and half steps within a single octave.

  • The beat is the steady, regular pulse underlying most music. Tempo is the speed of the beat.

  • Meter groups beats into regular patterns of strong and weak beats.

  • Rhythm is the series of durations of varying lengths that overlie the beat.

  • Nearly all Western music is built upon the need for dominant harmony to resolve to the tonic, or resting tone.

  • A key is a hierarchical set of harmonic and melodic pitch relationships organized around a tonic and using one of the thirty major and minor scales.

  • Diatonic music uses pitches from only a single scale; music is chromatic when it uses accidentals (sharps and flats) to add pitches from outside the key, or to change keys.

  • The triad is the most basic type of chord. It consists of two stacked thirds.

  • Some composers in the last 120 years have sought to expand and even overturn common- practice tonality.


Other Aspects

  • Texture, counterpoint, dynamics, articulation, and ornamentation are important features that can distinguish otherwise similar musical sounds.


Form

  • Tension and release, memory and anticipation, and continuity and contrast are fundamental to the listener’s musical experience.

  • Motives, phrases, cadences, and themes are the smallest building blocks of form.

  • Musical material may be repeated, varied, developed, or contrasted with different material to create longer forms; it can be framed by an introduction and/or a coda.

  • Common forms include strophic, theme and variations, twelve-bar blues, ternary (ABA), rondo, thirty-two-bar form, verse-chorus, fugue, and sonata form.


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