Music Theory Notes

Basic Elements of Music

Sound and Music

Definition: Music is sound organized in time.
Music can be created using various sounds, not just those from musical instruments.
Essential components include a time frame, sound waves, and a perceiving mind.
Optional components: composer, performers, recording/reproduction means.
Composition and performance can occur simultaneously (improvisation or electronic composition).
Human intention and perception are crucial for music to exist.
The definition of music is debated, especially regarding birdsong or accidental sounds.
Different cultures hold varying views of music; some intertwine it with ritual, language, and dance, lacking a separate term.
Western traditions have incorporated non-Western music, and globalization has blurred cultural boundaries.
This guide focuses on the "music of the Western World," originating in Europe over the past two millennia and extending to the Americas.

The Physics of Musical Sound

Sound is a wave of energy with amplitude and frequency.
Amplitude: Affects loudness (decibel level); higher amplitude means louder sound.
Frequency: Affects pitch (highness or lowness); greater frequency means higher pitch.
Frequency between 20 and 20,000 cycles per second is audible to humans as a sustained tone.
A pure sine wave at 440 Hz sounds like A above middle C (A-440), used for orchestral tuning.
Not all sounds have regular frequencies; irregular patterns lack a discernable pitch.
Musical sounds are categorized as pitched or non-pitched.
Percussion instruments primarily produce non-pitched sounds.

Instruments as Sound Sources

Curt Sachs and Erich von Hornbostel categorized instruments into four groups:
- Chordophones: Instruments with strings (e.g., violins, harps, guitars); sound produced by vibrating strings.
- Aerophones: Wind instruments (e.g., horns, flutes); sound produced by a vibrating column of air.
- Membranophones: Instruments with a membrane stretched across a frame; membrane vibrates when struck.
- Idiophones: Instruments where the body vibrates when struck (e.g., bells, woodblocks, xylophones).
- Electrophones: Instruments that use an oscillator to create sound waves and are dependent on electricity.

Western Orchestral Instruments

Grouped into families:
- Strings: Bowed or plucked instruments.
- Brass: Metal aerophones sounded by buzzing lips.
- Woodwinds: Aerophones where air is moved by breath alone or by vibrating reeds.
- Percussion: Membranophones, idiophones, and struck chordophones (e.g., piano).
- Keyboards: Sometimes a separate category.

Early Electronic Instruments

The theremin is a well-known early electronic instrument.
Frequency is regulated with one hand, amplitude with the other, by disturbing electrical fields.

Post-World War II Electronic Music

Advances in electronics led to collaborations between scientists and composers.
Sounds were recorded on tape, edited, manipulated, and recombined to form collages.
This composition type was called musique concrète.
Basic techniques: looping and splicing, enabling compositions beyond human performance.
Centers for electronic music emerged in Rome, Paris, Cologne, and New York City.

Pitch

Pitch, Frequency, and Octaves

Pitch: Highness or lowness of a sound.
Musicians refer to a single tone with unchanging highness or lowness as "a pitch."
Halving a string's length doubles its vibration frequency, raising the pitch an octave.
Octave: The distance between a pitch and the next higher or lower occurrence of the same pitch.

Pitch on a Keyboard

High pitches are on the right, low pitches on the left.
Moving left to right is moving "up" the keyboard; right to left is moving "down."
Middle C is roughly equidistant from either end.
Black keys are in alternating groups of two and three.
Middle C is located to the left of the group of two black keys closest to the middle.
Half Step (Semitone): Distance between any two adjacent keys.
Whole Step: Distance between every other key.
Half and whole steps are basic intervals of Western scales.
White keys are called natural keys, spanning A through G.
Natural note symbol: ♮ (often omitted but sometimes included for clarity).
Sharp (#): Raises a pitch by a half step.
Flat (♭): Lowers a pitch by a half step.
A# can also be called B♭, as it's a half step below B.

Pitch on a Staff

Music notation uses a five-line staff.
Each line or space represents a letter of the musical alphabet, depending on the clef symbol.
Clef: French word for "key"; indicates how to read the staff.
Three main clefs:
- Treble Clef (G-clef): Indicates the second line from the bottom is G.
- Bass Clef (F-clef): Indicates the fourth line from the bottom is F.
- C-Clef: Centered on a line that is middle C; movable clef with different nicknames.
  - Alto Clef: C-clef centered on the middle line.
  - Tenor Clef: C-clef centered on the fourth line from the bottom.

Pitch on the Grand Staff

Piano music uses two bracketed staves called the grand staff.
The left hand generally plays the lower staff (bass clef), and the right hand plays the upper staff (treble clef).

Overtones and Partials

Most pitches have one dominant frequency with fainter additional frequencies.
When a guitar's A string is plucked (110 Hz), other waves exist simultaneously (half length, one-third length, etc.).
The lowest A is the fundamental, "colored" by fainter higher pitches called partials or overtones.

Equal Temperament: Generating the Twelve Pitches by Dividing the Octave

Before 1750, pitches followed mathematical patterns.
Equal temperament adjusts mathematical ratios to divide the octave into twelve equal parts.
This system is now assumed unless otherwise stated.
The twelve pitches in ascending order form the chromatic scale.
The distance between consecutive pitches in the chromatic scale is a half step.
Enharmonic pitches: Two different labels for the same piano key (e.g., E♭ and D#).
Double-sharp ($\times$): Raises a pitch by two half steps; Double-flat ($\flat \flat$): lowers a pitch by two half steps. Rarely used.

Scales: Leading Tone, Tonic, Dominant

Composers typically choose seven pitches as the basis for a piece.
Diatonic scale: Seven pitches arranged in ascending order, following major or minor patterns.
C major scale: Common scale pattern.
When playing or writing a scale, the first pitch is repeated at the top.
The seventh scale degree is the leading tone, resolving upward to the tonic.
The tonic pitch is the anchor and point of completion (e.g., C in a C major scale).
The fifth scale degree is the dominant pitch, acting as a secondary gravitational center.

Intervals

Interval: The distance between two pitches.
The smallest interval is a half step (semitone).
Intervals are measured by the number of half steps and alphabetical letter names.
Example: C to E spans four half steps and is called a major third (M3).
Intervals can be harmonic (simultaneous) or melodic (successive).
Melodic intervals can be ascending or descending.
Major and minor ninth and tenth intervals exceed an octave.

Intervals of the Major Scale

A scale is a succession of whole and half steps (major and minor seconds).
C major scale example: C to D is a whole step (M2).
Major scale sequence: whole step-whole step-half step-whole step-whole step-whole step-half step (u-u-v-u-u-u-v).
Major scales can be created starting on any key by following the sequence of melodic intervals.

Minor Scales and Blues Inflections

Three types of minor scales: natural (pure), harmonic, and melodic.
All minor scales have a lowered third scale degree.
Natural minor: Half steps between 2-3 and 5-6.
Harmonic minor: Seventh scale degree raised by a half step.
Melodic minor: Sixth and seventh scale degrees raised ascending; restored to natural minor descending.
C natural minor and E♭ major use the same pitches, making them relative major and minor.
Parallel scales begin and end on the same tonic pitch.
A scale with blues inflections combines elements of major and minor scales.
Blues scales often feature lowered 3rd and 7th scale degrees or pitches "between the keys,"

Melody Defined with an Example Using Scale Degrees

Melody: A series of successive pitches forming a coherent whole.
Typically, only one pitch occurs at a time; simultaneous pitches create harmony or counterpoint.
Most melodies use the seven notes of a single scale.
Example: "Happy Birthday" uses specific scale degrees in the major mode.
Melodies can be transposed to any major key by maintaining the same pattern of intervals.

Contour

Contour: The profile of a melody.
Conjunct Melody: Moves smoothly in stepwise motion (half and whole steps).
Disjunct Melody: Contains more leaps (intervals larger than a major second).
Melodic direction: Ascending, descending, or wavelike manner.
Arch contour: Ascending beginning, climactic high point, and descending end.

Range and Tessitura

Range: The span of pitches an instrument or voice can produce.
Each pitch numbered from the bottom of the grand staff up.
High, middle, and low parts of an instrument's range are called registers.
Tessitura: The part of the range in which a melody lies. A high tessitura calls for high register pitches.

Rhythm

Beat

Rhythm: The way music is organized in time.
Beat: Steady pulse underlying most music; audible or silent.
Tempo: Speed of the beat.
Tempo can slow down (ritardando) or speed up (accelerando), gradually (poco a poco) or suddenly (subito).
Unmetered: Music with no steady tempo or discernable beat.
Rubato: Perceived beat that speeds up and slows down for expressive effect.

Meter: Duple, Triple, and Quadruple

Beats are of equal length but not equal importance.
Measures (Bars): Groups of beats separated by bar lines.
Downbeat: The first, strongest beat of a measure.
Meter: Pattern of emphasis superimposed on groups of beats (duple, triple, quadruple, irregular).
Duple Meter: Groups of two beats (STRONG-weak).
Triple Meter: Three-beat pattern (STRONG-weak-weak).
Quadruple Meter: Four-beat pattern (1-strongest, 3-second strongest, 2 & 4-weak).
Listeners sometimes treat duple as quadruple and vice versa.
Irregular (Asymmetrical) Meters: Groupings that cannot be divided into two, three, or four beats.
Common: Five-beat or seven-beat measures.
Pickup (Anacrusis): When the first word falls before the downbeat.

Rhythmic Notation

Symbols indicate note duration.
Whole note: longest symbol used.
Half note: oval plus stem is half as long as the whole note.
Quarter note: A half as long as a half note
Adding a flag to the stem halves the quarter note duration, creating an eighth note.
Additional flags subdivide the value by half again (sixteenth, thirty-second notes, etc.).
Flagged notes can use beams for easier reading.
A dot adds half the original value to a note.
Tie: A curved line connecting notes of the same pitch, combining their values.
Symbols for silence are rests, following a similar hierarchy as note values.

Time Signature

Indicates the meter in music notation.
Two numbers: lower number indicates durational value (2-half note, 4-quarter note, 8-eighth), and the upper number indicates how many of those values occur in one measure.
Common time (C) is equivalent to $\frac{4}{4}$ , cut-time (\cent;) is equivalent to $\frac{2}{2}$ .

Simple and Compound Meter

Simple subdivision: Each beat divided in half.
Compound subdivision: Beat divided into three equal parts.
Example: $\frac{6}{8}$ meter counted 123456 or ONE-&-a TWO-&-a.

Mixed and Irregular Meter

Mixed meter measures that have different meters occur in rapid succession.
Irregular Meter: Different meters alternating in an irregular pattern.
Steady beat grouped unpredictably (e.g., seven beats: ONE-two-three ONE-two ONE-two).
Polymeter: Two or more meters operating simultaneously.

Syncopation

Syncopation occurs when accented notes fall on weak beats or in between beats.

Polyrhythm

Also called cross-rhythm.
Polyrhythm occurs when two conflicting rhythmic patterns are present simultaneously.
Common examples: two against three and three against four.

Rhythm: Summary

Rhythm is a collection of varying durations and is always audible.
Beat is a regular underlying pulse, not always audible but felt or imagined.
Meter is the grouping of beats and associated patterns of strong and weak beats.

Harmony

Common-Practice Tonality

Harmony occurs whenever two or more tones are sounding simultaneously.
Common-practice tonality :Organization of pitch and harmony intuitive in Western cultures.
Developed in Europe, codified by about 1750.
Conventions govern nearly all music in the Western world.

Chords

Chord: Three or more pitches sounding simultaneously.
Most common chords don't use adjacent pitches.

Triads

Triad: Three-note chord consisting of two intervals of a third.
Qualities: major (M), minor (m), diminished (d), and augmented (A).
Major triad (M): Major third interval between lower pitches, minor third between upper pitches.
Minor triad (m): Minor third on the bottom, major third above.
Diminished triad (d): Two minor thirds.
Augmented triad (A): Two major thirds.
Basic piece chords are triads built above each scale note.
Root: Lowest note of a triad.
Third: Middle note.
Fifth: Highest note.
Root Position: The chord with the root on the bottom.

Inversion

Inversion occurs When the third of the triad is on the bottom: the chord is in first inversion.
When the fifth is on the bottom: it is in second inversion.
First inversion indicated by a "6" after the chord symbol.
Second inversion indicated by a “6/4” .

Keys

Key: The world of pitch relationships where a piece or substantial section of music takes place.
The gravitational center of a key is the tonic pitch which in turn lends its name to the entire key.
"Key" as the set of seven notes or scale has been selected for use in that piece-NOT the piano key!
The tonic becomes the entire keys name e.g. The key of A
A triad may be inverted but, will not change the keys chord classification.

Key Signatures

Key Signature: Set of sharps or flats at the beginning of every staff, indicating the key of the music.
Signals which seven pitches make up the scale by indicating which pitches will be raised or lowered.
Raising All Fs in the entire composition with an F# at the beginning of the piece, unless otherwise indicated, (which would be done with a natural sign in front of the individual note).
G major, and E minor-each scale corresponds and relates to another.

Hierarchy of Keys: Circle of Fifths

Key signatures follow a pattern.
There are fifteen major scales and fifteen minor scales.
Each scale corresponds to a key of the same name.
Each major scale contains the same pitches as one of the natural minor keys.