Music Theory for the 21st-Century Classroom Study Guide

Credits and Acknowledgements

• Author: Robert Hutchinson, University of Puget Sound.

• Date: August 17, 2020.

• Website: musictheory.pugetsound.edu.

• License: Permission is granted to copy, distribute, and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.

• Key Contributors:

  • Robert Beezer for recommending PreTeXt (formerly “MathBook XML”) as the authoring tool.

  • Jahrme Risner for coaching the author through PreTeXt commands in the terminal.

  • Gwynne Kuhner Brown for co-piloting the text and suggesting clarifications.

  • Dawn Padula (Director of Vocal Studies at the University of Puget Sound) for providing feedback on musical examples, explanations, and diagrams.

Preface to Music Theory for the 21st-Century Classroom

• Methodological Distinctions: This college music theory textbook differs from traditional versions by focusing less on four-part (SATB) voice leading and more on relating harmony to the phrase.

• Emphasis on Melodic Units: Traditional textbooks often neglect motivic analysis and analysis of melodic units smaller than the phrase. This lack of preparation often leads to students struggling to create melodies with continuity or appropriate harmonic placement.

• Concepts Taught: The curriculum covers motive, fragment, phrase, subphrase (also known as “phrase segment” or “phrase member”), and types of melodic alteration including:

  • Inversion.

  • Intervallic change.

  • Augmentation.

  • Diminution.

  • Rhythmic change.

  • Ornamentation.

  • Extension.

  • Retrograde.

• Scope: The text covers four semesters, moving from basic pitch and rhythm reading to twelve-tone technique and minimalism.

• Influence of the "Manifesto": The impetus for the book came from the College Music Society's Task Force on the Undergraduate Music Major and their document, "Transforming Music Study from its Foundations: A Manifesto for Progressive Change in the Undergraduate Preparation of Music Majors."

• Educational Philosophy: The goal is to train students as composer-performer-improvisers and arrangers, drawing from the traditions of figures like Bach, Beethoven, Charlie Parker, and Jimmy Page.

• Integration of Media: Examples include popular music, film music, and musical theater. Online versions include embedded YouTube links with specific start/stop times for pedagogical clarity.

Chapter 1: Basic Concepts

• Pitch:

  • On a standard piano, there are $88$ notes.

  • Moving to the right on a piano produces higher sounds; moving to the left produces lower sounds.

• Notation:

  • Music is written on a five-line staff (plural: staves).

  • A clef identifies a reference point for the lines of the staff.

  • Treble Clef (G clef): In treble clef, lines are $E-G-B-D-F$ (mnemonic: "Every Good Boy Does Fine") and spaces are $F-A-C-E$.

  • Bass Clef (F clef): dots surround the second line from the top (the F line). Lines are $G-B-D-F-A$ (mnemonic: "Good Boys Do Fine Always") and spaces are $A-C-E-G$ (mnemonic: "All Cows Eat Grass").

  • Ledger Lines: Used to extend the range of the staff above or below.

• Octave Registers:

  • The musical alphabet consists of seven note names: $A-B-C-D-E-F-G$.

  • An octave (abbreviated $8ve$) is the distance from a note to the next note of the same name, which is eight steps apart ($1-2-3-4-5-6-7-8$).

  • Since the musical alphabet repeats about $7$ times on a piano, numerical registers are used to specify exact pitch.

  • Middle C ($C4$): An important reference point. Register numbers change after the note $B$ (e.g., $B4$ is followed by $C5$).

  • C Clefs:

    • Alto Clef: Designates the middle line as middle C ($C4$).

    • Tenor Clef: Designates the second line from the top as middle C ($C4$).

  • Grand Staff: A treble and bass clef joined by a bracket. Middle C is notated on the ledger line below the treble staff or the ledger line above the bass staff.

• Accidentals: Symbols placed before notes to alter pitch:

  • Sharp ($\sharp$): Raises a pitch one half step.

  • Flat ($\flat$): Lowers a pitch one half step.

  • Double Sharp ($\times$): Raises a pitch two half steps (one whole step).

  • Double Flat ($\flat\flat$): Lowers a pitch two half steps (one whole step).

  • Natural ($\natural$): Cancels previous accidentals within a measure or from a key signature.

• Enharmonic Notes: Two notes that sound the same but are written differently (e.g., $C\sharp 4 = D\flat 4$, $C = B\sharp$, $E = F\flat$).

Chapter 2: Major Scales and Key Signatures

• Half Steps and Whole Steps:

  • Half Step: The distance from one note to the next nearest note on a piano keyboard.

  • Whole Step: Consists of two half steps.

• The Major Scale:

  • A major scale is built of two tetrachords (four-note segments) joined by a whole step.

  • The pattern of intervals is: $W-W-H$ (lower tetrachord) + $W$ (connection) + $W-W-H$ (upper tetrachord).

  • All major scales must use all notes of the musical alphabet in order without skipping or repeating names.

• Major Key Signatures:

  • Key signatures are placed at the beginning of a piece to indicate which sharps or flats are consistently used.

  • There are $15$ major key signatures.

  • Order of Sharps: $F-C-G-D-A-E-B$ (mnemonic: "Fast Cars Go Dangerously Around Every Bend").

  • Order of Flats: $B-E-A-D-G-C-F$ (the word "BEAD" plus "Greatest Common Factor").

  • Identifying Major Keys:

    • Sharps: The key is a half step above the last sharp in the signature.

    • Flats: The key is the second-to-last flat in the signature (with $F$ major as the exception having one flat).

• The Circle of Fifths:

  • Clockwise (ascending fifths) adds sharps: $C(0)-G(1\sharp)-D(2\sharp)-A(3\sharp)-E(4\sharp)-B(5\sharp)-F\sharp(6\sharp)-C\sharp(7\sharp)$.

  • Counterclockwise (descending fifths) adds flats: $C(0)-F(1\flat)-B\flat(2\flat)-E\flat(3\flat)-A\flat(4\flat)-D\flat(5\flat)-G\flat(6\flat)-C\flat(7\flat)$.

  • Overlap: $B$ major is enharmonically same as $C\flat$ major; $F\sharp$ same as $G\flat$; $C\sharp$ same as $D\flat$.

Chapter 3: Minor Scales and Key Signatures

• Types of Minor Scales:

  • Natural Minor: Corresponds exactly to the minor key signature. In relation to major, it has a lowered $3rd$, $6th$, and $7th$ scale degree.

  • Harmonic Minor: A natural minor scale with a raised $7th$ scale degree ($\hat{7}$).

  • Melodic Minor: Ascending, it has a raised $6th$ ($\hat{6}$) and $7th$ ($\hat{7}$) scale degree. Descending, it is identical to the natural minor scale.

• Minor Key Relationships:

  • Parallel Minor: A minor scale that shares the same tonic (1st scale degree) as a major scale (e.g., $C$ major and $C$ minor). To find the key signature, add three flats to the parallel major signature.

  • Relative Minor: A minor scale that shares the same key signature as a major scale. The relative minor starts on the $6th$ scale degree of the relative major, or three half steps below the relative major tonic.

• Scale Degree Names:

  1. $\hat{1}$: Tonic

  2. $\hat{2}$: Supertonic

  3. $\hat{3}$: Mediant

  4. $\hat{4}$: Subdominant

  5. $\hat{5}$: Dominant

  6. $\hat{6}$: Submediant

  7. $\hat{7}$: Leading Tone (if a half step below tonic) or Subtonic (if a whole step below tonic).

Chapter 4: Basics of Rhythm

• Time Signatures:

  • Top Number: Indicates "how many" beats or pulses.

  • Bottom Number: Indicates "of what" (the durational value of the beat).

    • $2 =$ half note.

    • $4 =$ quarter note.

    • $8 =$ eighth note.

    • $16 =$ sixteenth note.

• Durational Symbols:

  • Whole note ($w$), Half note ($\dot{h}$), Quarter note ($q$), Eighth note ($e$), Sixteenth note ($s$), Thirty-second note.

  • Rare values include the double whole note (Breve) and the $64th$ note.

• Dots and Ties:

  • Tie: Links two notes of the same pitch to create a new duration.

  • Slur: Connects notes of different pitches for smooth (legato) playing.

  • Single Dot: Increases the note's duration by half.

  • Double Dot: The second dot adds half the value of the first dot (one quarter of the original duration).

• Meter Classification:

  • Number of Beats: Duple ($2$), Triple ($3$), Quadruple ($4$).

  • Division of Beats:

    • Simple Meter: Beats divide into two parts. Top numbers are $2$, $3$, or $4$.

    • Compound Meter: Beats divide into three parts. Top numbers are $6$, $9$, or $12$. The beat value is always a dotted note.

• Tuplets: Groupings that divide a beat in a way not normally found in a specific meter (e.g., a triplet in a simple meter, or a duplet in a compound meter).

• Notation Standards: Rhythms should be beamed to clearly show where each beat begins.

• Syncopation: Occurs when notes on weak beats or weak parts of beats are emphasized and strong beats are de-emphasized. Strong beats in $4/4$ are beats $1$ and $3$.

Chapter 5: Intervals

• Types of Intervals:

  • Harmonic: Notes sounded simultaneously (vertical).

  • Melodic: Notes sounded one after another (horizontal).

• Naming Conventions: Includes numeric size and quality.

  • Numeric Size: Count note names between the two pitches. Odd numbers (unison, $3rd$, $5th$, $7th$) move line-to-line or space-to-space. Even numbers ($2nd$, $4th$, $6th$, $8ve$) move line-to-space.

  • Perfect Quality: Unison, $4th$, $5th$, $8ve$.

  • Major/Minor Quality: $2nd$, $3rd$, $6th$, $7th$.

• Measurement Standards:

  • Perfect Intervals: Natural-to-natural, flat-to-flat, or sharp-to-sharp, except between $B$ and $F$ ($B-F\sharp$ is a P5; $B\flat-F$ is a P5).

  • Minor vs. Major: A minor interval is one half step smaller than a major interval of the same numerical size.

  • Augmented (+): One half step larger than perfect or major.

  • Diminished ($\circ$): One half step smaller than perfect or minor.

• Half Steps per Interval:

  • $m2 = 1$ half step.

  • $M2 = 2$ half steps.

  • $m3 = 3$ half steps.

  • $M3 = 4$ half steps.

  • $P4 = 5$ half steps.

  • $Tritone (+4/\circ 5) = 6$ half steps.

  • $P5 = 7$ half steps.

  • $m6 = 8$ half steps.

  • $M6 = 9$ half steps.

  • $m7 = 10$ half steps.

  • $M7 = 11$ half steps.

  • $P8 = 12$ half steps.

• Interval Inversion:

  • $Perfect \rightarrow Perfect$.

  • $Major \leftrightarrow Minor$.

  • $Augmented \leftrightarrow Diminished$.

  • $Numeric Rule: (Original Size) + (Inverted Size) = 9$.

Chapter 6: Triads

• Triad Construction: Three notes stacked in thirds.

  • Root: The lowest note when stacked in thirds.

  • Third: The middle note.

  • Fifth: The highest note.

• Triad Qualities:

  • Major: $M3$ interval + $m3$ interval ($P5$ between root and fifth).

  • Minor: $m3$ interval + $M3$ interval ($P5$ between root and fifth).

  • Diminished: $m3$ interval + $m3$ interval ($\circ 5$ between root and fifth).

  • Augmented: $M3$ interval + $M3$ interval ($+5$ between root and fifth).

• Lead-Sheet Symbols:

  • Major: Just the root name ($C$).

  • Minor: Root + "m" ($Cm$).

  • Diminished: Root + "$\circ$" ($C\circ$).

  • Augmented: Root + "+" ($C+$).

• Inverted Triads:

  • Root Position: Root is the lowest (bass) note.

  • First Inversion: Third is in the bass.

  • Second Inversion: Fifth is in the bass.

  • Slash Chords: Notation like $C/E$ means a $C$ major triad with an $E$ in the bass.

• Sus Chords:

  • Sus4: A perfect $4th$ replaces the $3rd$.

  • Sus2: A major $2nd$ replaces the $3rd$.

Chapter 7: Roman Numerals and Cadences

• Roman Numeral System: Used to represent chords relative to a key.

  • Uppercase = Major.

  • Lowercase = Minor.

  • Lowercase + $\circ$ = Diminished.

  • Uppercase + $+$ = Augmented.

• Diatonic Chords in Major: $I - ii - iii - IV - V - vi - vii^{\circ}$ .

• Diatonic Chords in Minor: Due to scale variations, most common are: $i - ii^{\circ} - III - iv - V - VI - VII$ and $vii^{\circ}$.

  • $VII$ is built on the subtonic (natural minor scale).

  • $vii^{\circ}$ is built on the leading tone (harmonic minor scale).

• Cadence Types:

  • Authentic (AC): Ends with $V-I$.

  • Plagal (PC): Ends with $IV-I$.

  • Deceptive (DC): Ends with $V-vi$ (or any chord other than $I$).

  • Half (HC): A phrase ending specifically on the $V$ chord.

Chapter 8: Seventh Chords

• Construction: A triad plus a note a third above the fifth (forming a seventh with the root).

• Five Common Types:

  1. Major Seventh (Maj7): Major triad + major seventh.

  2. Dominant Seventh (Major-Minor Seventh, 7): Major triad + minor seventh.

  3. Minor Seventh (m7): Minor triad + minor seventh.

  4. Half-Diminished Seventh ($\emptyset 7$): Diminished triad + minor seventh.

  5. Fully-Diminished Seventh ($\circ 7$): Diminished triad + diminished seventh.

• Diatonic Roman Numerals:

  • Major: $IM7 - ii7 - iii7 - IVM7 - V7 - vi7 - vii^{\emptyset}7$.

  • Minor: $i7 - ii^{\emptyset}7 - IIIM7 - iv7 - V7 - VIM7 - vii^{\circ}7$.

• Special Chords: The $IV/\hat{5}$ chord (e.g., $F/G$ in $C$ major) often substitutes for the $V7$ chord in pop music; it is also labeled as $G9sus4$.

Chapter 9: Harmonic Progression and Function

• Circle of Fifths Progression: $I-IV-vii^{\circ}-iii-vi-ii-V-I$.

  • In minor: $i-iv-VII-III-VI-ii^{\circ}-V-i$.

  • Characterized by sequence: a musical idea repeated at a different pitch level.

• Harmonic Rhythm: The rate at which the chords change.

• Shorter Progressions:

  • $ii-V-I$: Found heavily in jazz and the Great American Songbook.

  • $vi-ii-V-I$: Last four chords of the circle.

  • $I-vi-ii-V$: Known as the "1950s progression."

• Harmonic Function:

  1. Tonic (ton.): Stability ($I, i$).

  2. Dominant (dom.): Tends toward tonic ($V, vii^{\circ}$).

  3. Pre-dominant (pre-dom.): Tends toward dominant ($IV, ii$).

  4. Tonic Prolongation (ton. prol.): Occurs usually after tonic ($vi, iii$).

• Exceptions:

  • $IV$ acts as Tonic Prolongation when moving to $I$ (Plagal cadence).

  • $I/5th$ acts as Dominant when moving to $V$.

• Subtonic Chord (2VII): Ubiquitous in rock music (e.g., $A-G-F-G$ in $A$ minor).

• Best-Seller Progression: $I-V-vi-IV$. Rotations include $vi-IV-I-V$ and $IV-I-V-vi$. Examples include "Someone Like You" (Adele) and "All About That Bass" (Meghan Trainor).