Fundamentals of Music Theory 🎵 - Unit 1

Pitch and Frequency

• Pitch: The perceived highness or lowness of a sound

• Frequency: The number of vibrations per second, measured in Hertz (Hz)

• Example: A violinist tunes their instrument to Concert Pitch, which is A=440 Hz

Dynamics/Amplitude, Timbre, Articulation, and Duration

• Dynamics/Amplitude: The wave height, or loudness and softness of a sound

• Timbre: The tone color or waveform, which is unique to each instrument and voice

• Articulation: The envelope of the sound, including attack, sustain, and release

• Duration: The length of time a sound is played or held

Notation of Music

• Intervals: The building blocks of music

  • Half Step: The smallest unit of measurement, equivalent to one semitone (e.g. C to C#)

  • Whole Step: Two half steps, or one full tone (e.g. C to D)

• Clefs: Symbols used to indicate pitch ranges

  • Treble, Alto, Tenor, and Bass: The four main clefs, based on vocal ranges

  • Neutral: Used for percussion instruments

• Accidentals: Symbols used to modify pitch

  • Sharp (♯): Raises pitch by a half-step

  • Double Sharp (×): Raises pitch by a whole step

  • Flat (♭): Lowers pitch by a half-step

  • Double Flat (♭♭): Lowers pitch by a whole step

  • Natural (♮): Cancels a sharp or flat, returning to the natural pitch

Basic Notation of Music

• Stem: The vertical line of a note

• Hook/Flag: The curved part of a note

• Note Head: The oval part of a note

• Accidental: The symbol modifying the pitch

• Beam: A horizontal line connecting notes

• Measure: A division of the staff, separated by Bar Lines

• Double Bar Line: Indicates the end of a section or piece

• Ledger Lines: Lines added to the staff to notate pitches above or below the five lines

• Staff: A set of five lines and four spaces, used to notate music

• System: Multiple staves bracketed together, often used for piano music

Rhythm 🕺

• Rhythm: The relationship and duration of notes and rests

• Duration of Notes:

  • Whole Note: Four beats

  • Half Note: Two beats

  • Quarter Note: One beat

  • Eighth Note: Half a beat

  • Sixteenth Note: A quarter of a beat

• Rests: Silences in the music, with corresponding durations

• Dot: Increases the duration of a note or rest by half

• Tempo: The speed of the beat, often indicated by Italian words (e.g. Andante, Vivace)

Meter

• Meter: The organization of rhythms into groups of strong and weak beats

• Time Signature: A notation indicating the meter, with two numbers (top and bottom)

• Duple, Triple, and Quadruple: Meters with two, three, or four beats per measure, respectively

• Simple and Compound: Meter classifications, with simple meters dividing the beat into two, and compound meters dividing into three

Other Rhythmic Concepts

• Anacrusis: A pickup note before the first measure of a piece

• Syncopation: Stress on off-beat rhythms, often using dots and ties

• Hemiola: A type of syncopation in triple meter, where the beat is divided into two

Scales 🎶

• Scales: Pitches organized in whole and half step patterns

• Chromatic Scale: A scale including all 12 half steps within an octave

• Major Scale: A scale with a specific whole and half step pattern (W-W-H-W-W-W-H)

• Minor Scales: Scales with different patterns, including natural, harmonic, and melodic forms

Note: This is just a partial study guide. Please refer to the full lecture transcript for more information and examples.## Scales 🎵

Minor Pentachord and Harmonic Scales

The harmonic scale raises the 7th scale degree both when going up and coming down, making it very distinctive.

Melodic Scales

The melodic scale raises both the 6th and 7th scale degrees when going up, and becomes a natural minor scale when coming down. Notice that the melodic minor scale is asymmetrical, meaning the ascending and descending forms are different.

Parallel and Enharmonic Keys

Circle of Fifths

The circle of fifths is a tool that helps visualize and calculate scales with different numbers of sharps and flats. Each increasing sharp or flat in a key signature is a fifth above or below the previous key.

Scale Degree Names

Stability Diagram

Active tones (4th and 7th) are unstable and must resolve to a resolution tone (1st or 3rd).

Artificial Scales

Hexatonic Scale

The hexatonic scale is a 6-note scale with each note a whole step apart.

Pentatonic Scale

The pentatonic scale is a 5-note scale commonly used in Asian melodies, consisting of the tonic, super tonic, median, dominant, and submediant.

Modes

Modes are rotations of a major scale. The 7 modes are:

• Ionian

• Dorian

• Phrygian

• Lydian

• Mixolydian

• Aeolian

• Locrian

Church modes are commonly used in medieval and classical music.

There are many mnemonic devices to remember the modes, such as: "I Don't Particularly Like Modes A Lot For Each Of These Plus Locrian"

Harmonic Organization 🎵 - Unit 2

Harmony is the combination of multiple pitches sounding simultaneously, adding a vertical element to a melody. Counterpoint refers to the interweaving of multiple independent melodies.

Intervals

Intervals are the building blocks of harmony, describing the distance between two pitches. They have two components:

• Size: The numerical value of the interval (e.g., second, third, fourth, etc.)

• Quality: The type of interval (e.g., major, minor, perfect, augmented, or diminished)

"Perfect intervals are called perfect because they are the same in both major and minor keys, which is where they get their name from."

Here are the basic interval symbols:

Interval Identification

To identify intervals, compare the top note to the diatonic version of the note in the key signature scale.

• If the top note is a half step lower than the diatonic note, it's minor or diminished.

• If the top note is a half step higher than the diatonic note, it's augmented.

Doubly Augmented and Diminished Intervals

These intervals involve two half steps raised or lowered, resulting in a whole step.

Tips for Identifying Intervals

• If both notes contain accidentals, they cancel out, and the interval remains the same.

• If the top note is raised by a half step or the bottom note is lowered by a half step, it affects the interval size.

• Use the nearest key to calculate intervals if the lower note isn't a standard key.

Compound and Simple Intervals

• Compound intervals are larger than an octave. You can subtract an octave to simplify them.

• Simple intervals are smaller than an octave.

Inverting Intervals

Inverting intervals involves changing the order of the notes. Use the rule of nine to find the size and quality of the inverted interval:

• Subtract the original size from 9.

• Perfect intervals remain perfect, major turns to minor, and minor turns to major.

• Augmented turns to diminished, and vice versa.

Consonant and Dissonant Intervals

• Consonant intervals are stable and sound good (e.g., perfect fifths, major and minor thirds and sixths).

• Dissonant intervals are unstable and want to resolve to consonant intervals (e.g., major and minor seconds, major and minor sevenths, augmented and diminished intervals).

Chords

Chords are groups of three or more notes played simultaneously. Triads are three-note chords made up of two thirds intervals.

Seventh Chords

Seventh chords add another note to the triad, making them dissonant and unstable.

Chord Inversions

Chord inversions involve rearranging the notes of a chord.

Use figures and roman numerals to notate chord inversions.## Inversions and Figured Bass 🎵

Triad Inversions

• A triad in root position has the root as the lowest note.

• A triad in first inversion has the third as the lowest note, and is notated with a 6 (e.g., 6).

• A triad in second inversion has the fifth as the lowest note, and is notated with a 6/4 (e.g., 6 4).

Seventh Chord Inversions

• A seventh chord in root position has the root as the lowest note.

• A seventh chord in first inversion has the third as the lowest note, and is notated with a 6/5 (e.g., 6 5).

• A seventh chord in second inversion has the fifth as the lowest note, and is notated with a 4/3 (e.g., 4 3).

Inversion Hotline

Memorize this string of numbers to help you remember the inversion symbols: 4 6 6 4 7 6 5 4 3 4 2

Snowman Stack

Rearrange chords in a score to root position to easily identify them.

Diatonic Context 🎶

Definition of Diatonic

Diatonic refers to pitches found in the key signature.

Harmonic Function of a Triad

• Relates the chord to the scale degree in the key.

• Uses Roman numerals to represent chords in relation to the key.

Triad Qualities

Diatonic Triads in Major and Minor

Realizing Figured Bass 🎧

Steps to Realize Figured Bass

1. Organize notes in a chord stack.

2. Find and circle the bass note.

Chord Functions and Progressions 🎵

Chord Families

Common Chord Progression

Tonic → Subdominant → Dominant → Tonic (repeat)

Cadences 🎶

Definition of Cadence

A cadence is a musical phrase ending, establishing the tonal center and creating a sense of tension release.

Types of Cadences

Aural Skills 🎵 - Unit 3

Definition of Aural Skills

Aural skills refer to ear training or the identification of notes, pitches, rhythms, and intervals based on what you hear.

Components of Aural Skills

• Dictation (melodic and harmonic)

• Sight singing

• Analysis based on what you hear

Melodic Dictation

• Melodic dictation involves notating a melody played on a single staff.

• You will have both treble and bass clef melodic dictation, with one in major and one in minor, and one in simple and one in compound time.

• Skills required to excel in melodic dictation:

  • Ability to recognize pitches relative to the tonal center

  • Ability to remember the melody for a little bit and replay it in your head

  • Audition: the ability to remember part of what you heard

• Checklist for melodic dictation:

  • Look at the key signature and time signature

  • Map out possible rhythm menus in your head

  • Pace yourself and make sure you get through at least a couple of measures in each playing

Exercise: Melodic Dictation

• Fill out the rest of the melody based on the first measure provided.

• Take a screenshot or copy the staff paper and follow along with the playing.

Harmonic Dictation

• Harmonic dictation involves notating chords (between 6 and 8) on a grand staff.

• You will have to notate the soprano and bass out of the four-part voice harmony.

• Skills required to excel in harmonic dictation:

  • Ability to listen to the soprano and bass on separate playings

  • Ability to recognize chord qualities and inversions

  • Ability to recognize melodic patterns

  • Harmonic function: understanding the tonic, predominant, and dominant functions

• Techniques for harmonic dictation:

  • Listen to the bass first and then the soprano

  • Focus on the top note of the voice harmony

  • Use harmonic function to narrow down possible chords

• Tonic prolongation:

  • Four ways that first and second inversion harmonies are used:

    • Passing harmonies

    • Neighbor harmonies

    • Pedal in the bass

    • Arpeggiated harmonies

Table: Tonic Prolongation

Tips for Harmonic Dictation

• Listen to the bass and soprano separately

• Focus on the highest and lowest notes of the chords

• Use harmonic function to narrow down possible chords

• Remember that retrogression does not occur in harmonic progression

• Big changes in harmonic function usually happen on stronger beats of the measure## Harmonic Dictation 🎵

When it comes to harmonic dictation, it's essential to take advantage of your knowledge of patterns. Seventh chords are pretty obvious because you can hear the dissonance in them, like a 1-3-5-7 chord that needs resolving.

Implied Harmonies and Cadence

"Implied harmonies" refer to the harmony suggested by a particular melody or progression, even if it's not explicitly stated.

Here is a chart for implied harmonies and their relation to cadence:

Practice Exercise

Listen to a musical excerpt and try to identify the chords played. You can rewind the recording three more times to emulate the testing experience.

Multiple Choice Questions 🤔

In addition to harmonic dictation, you'll also have multiple choice questions that test your knowledge of:

• Scales and modes

• Intervals

• Chord qualities

• Rhythm

• Meter

• Tonal center and key

• Cadence

• Non-chord tones (passing and neighboring tones)

You'll also have to detect errors in musical excerpts, identifying mistakes in the score.

Performance Considerations 🎶

You'll need to recognize performance considerations such as:

• Changes in timbre (instrumentation)

• Dynamics

• Articulation

• Tempo

• Style

Take notes on the differences between two parts or phrases of an excerpt to help you answer questions.

Sight Singing 🎤

Sight singing is the last part of the free response questions. You'll have two sight singing exercises, one in treble clef and one in bass clef, one in major and one in minor, and one in simple and one in compound meter.

Tips for Sight Singing

• Reproduce the melody while maintaining tonal center (don't go off key!)

• Practice singing the scale in your head first to familiarize yourself with the context

• Identify the key (major or minor) and adjust the pitch to fit your vocal range if necessary

• Tap out the rhythm before singing to get a feel for the meter

• Hold notes to their full value and avoid rushing

Here is a checklist to help you with sight singing:

Harmonic Composition and Voice Leading for Four Voices 🎶 - Unit 4

Counterpoint and Part Writing Rules

Counterpoint: the relationship between two lines, the base and the melody.

Part Writing Rules: apply to free response questions 5, 6, and 7.

• Stem Direction: for each of the four parts, the stem of the note goes up for Soprano and Tenor, and down for Alto and Bass.

• Contrapuntal Character: the linear movement implied by chords and figured bass.

Motion and Types of Motion

• Motion: the direction of the melody in relation to the bass line.

• Contrary Motion: when the melody moves in the opposite direction of the bass.

• Oblique Motion: when one voice remains on the same note and the other moves.

• Similar Motion: when the bass and the soprano both move in the same direction, but with different intervals.

• Parallel Motion: when both the bass and the soprano move in the same direction, with the same intervals.

Things to Avoid in Composition

• Parallel Fifths and Octaves: avoid writing parallel fifths and octaves between any voices.

• Unequal Fifths: avoid using unequal fifths in the common practice era.

• Crossing Voices: avoid writing a higher part lower than a lower part.

• Doubling Tendency Tones: avoid doubling tendency tones, especially the leading tone.

• Doubling the Seventh of a Chord: avoid doubling the seventh of a chord.

Resolution Rules

• Scale Degree 7: resolves upward to 1.

• Scale Degree 4: resolves downward to 3.

• The Seventh of a Chord: resolves downward or holds until it can.

Checklist for Part Writing to Figured Bass

Harmonic Progression (Chord Leading)

• Circle Progression: a progression of chords that moves by diatonic fifths.

• Progression by Thirds and Seconds: a progression of chords that moves up and down by a third or second.

• Inversions: weaken the function of chords in terms of the tonic, subdominant, and dominant.

Types of Chords

• Six-Four Chords: have a lot of uses, including passing tones, neighbor tones, and arpeggios, but be careful not to mess up.

• Mode Mixtures: use chords not found in the key, usually borrowing from a parallel major or minor.

Accidentals and Figured Bass

• Accidentals: used in figured bass to indicate changes in chord quality.

• Mode Mixtures: use chords not found in the key, usually borrowing from a parallel major or minor.

Secondary Dominance

• Secondary Dominance: a chord that temporarily takes over the function of the tonic.

• Notation: a Roman numeral followed by a slash and another Roman numeral, indicating the temporary tonic and the scale degree above it.

Rules of Progression and Retrogression

• Progression: moving from stable to unstable and back to stable.

• Retrogression: moving from unstable to stable.

I hope this helps! Let me know if you have any questions or need further clarification. 😊## Harmonic Rhythm and Chord Progressions 🎶

Harmonic Rhythm: Refers to how often you change the root of your chords.

Important Rules to Remember:

• Never follow a five chord with a four or two six or a two six five.

• Never follow a six with a one, as it is an example of going from unstable to stable, which is bad for harmonic rhythm.

Chord Change Frequencies:

• Generally, it is recommended to change the root of chords in quarter notes or half notes.

• Eighth notes are unnecessary and can be considered quick and extra.

Melodic Scale Harmonization

Scale Degree Harmonization Diagram:

This diagram shows the chord combinations that can be used to harmonize each scale degree or solfege note.

Steps to Harmonize a Melody for Free Response Questions:

1. Identify the scale degrees of the notes of the melody.

2. Fill in the cadences first, as they make up most of the points for this question.

   • Cadence Rules:

     • Cadences can only end with one, four, or five.

     • Use root position chords for the last two chords in each cadence.

3. Keep it straightforward by avoiding inversions and non-chord tones.

4. Use seventh chords when possible.

5. Harmonize everything else using implied harmonies and connecting the dots.

6. Sing it in your head and go through everything to make sure it sounds like a melody from the common practice period.

Tips to Achieve the Highest Score on Composition Effort Cues

Common Mistakes to Avoid:

• Missing a chord or omitting an accidental can lead to a significant loss of points.

• The Triangle Effect: A mistake in one area can affect other aspects of the grading, leading to a greater loss of points.

• Avoid parallel fifths and eighths, as they are heavily emphasized in the grading guidelines.

Grading Guidelines:

• It is highly recommended to review the grading guidelines to understand where points can be lost.

• Note that the case of Roman numerals (e.g., capitalization) does not affect grading.

Additional Tips:

• Avoid spending too much brain power on insignificant details during the test.

• Use the grading guidelines to your advantage to maximize your score.