Music theory names what composers and performers do with pitch and time, so you can read music, spell it and hear it. Two habits carry most of the subject. First, count letters before you count sounds: the page tells apart notes and intervals that sound alike, and the spelling records what the music means. Second, ask whose practice a rule describes. Common-practice voice leading, strict species counterpoint and popular harmony each follow their own conventions, and none of them is a law of sound. The chapters run from notation and rhythm through scales, intervals and chords, then function, voice leading, chromatic harmony and form, and end with popular and post-tonal practice and with instruments.
Each chapter opens with the short version. Tap one to read the detail.
Reading pitch: clefs, accidentals and spelling
~2 min
A clef fixes one reference line, and you find every other note by counting from it. Sharps and flats rename a staff degree, and the key or chord decides which of two same-sounding spellings is correct.
A clef labels a single line. The treble clef marks the second line as the G above middle C, and the bass clef's two dots straddle the fourth line, the F just below middle C. A C clef turns whichever line it sits on into middle C, which keeps a part near middle C off a stack of ledger lines. Ledger lines are spaced like staff lines, so you go on naming notes by counting lines and spaces, never by how high they look.
A sharp or flat moves a staff degree a half step, and a natural cancels either one, so a natural can move a note up or down. An accidental lasts to the end of its measure. A tie carries it across the barline, but the next separate note returns to the key signature.
Spelling is where sound and page part ways. F-sharp and G-flat press the same key, yet in F-sharp major the seventh degree must be written E-sharp: a scale uses each letter once, and calling that note F would leave two Fs and no E. In the same way, C to C-sharp keeps its letter and is a chromatic half step, while C to D-flat changes letter and is a diatonic one.
The trap is spelling by ear. Choosing whichever sharp or flat looks simpler gives you the right sounds and the wrong letters, and every label you build on those letters goes wrong with them.
Rule: name a note by counting from the clef's line, and spell it so each letter appears once in its scale or chord.
Duration, meter, and rhythm that shows the beat
~2 min
Note values are proportions, so the meter and tempo decide how long any of them lasts. The time signature tells you how each beat divides, and good rhythmic notation keeps every beat visible on the page.
Each value from the whole note to the sixteenth lasts half as long as the one before. A dot makes a note one and a half times its plain length, and a second dot adds half of what the first one added. None of these lengths is absolute. The meter decides which value carries the beat and the tempo sets how fast beats come, so a quarter note in a slow piece can outlast a half note in a fast one.
Simple meters split each beat in two, so the lower number names the beat and the upper number counts beats. Compound meters split each beat in three, and the beat is a dotted note. When the top number is 6, 9 or 12, divide it by three to get the beats, so a bar of 6/8 holds six eighths but two beats at a moving tempo. Six eighths also fill a bar of 3/4, where the beat is a quarter, so the beaming must show which beat each eighth belongs to.
Syncopation is defined against the meter: a note starts on a weak position and holds through the strong one after it. A hemiola regroups the same even pulses, so two bars of triple time briefly feel like three bars of duple.
The trap is notation that adds up but hides the beat. In 6/8, a note lasting one beat and a third should be a dotted quarter tied to an eighth. A single half note has the same length and hides where the second beat starts.
Rule: write rhythms so the reader can see where every beat begins, even when it costs an extra tie.
Scales, key signatures, minor forms and modes
~2 min
Every major key is one interval pattern started on a different note, and its signature lists the sharps or flats that pattern needs. Minor raises its seventh where it needs a pull to the tonic, and each mode is the same seven notes heard from a different home.
The major scale is a fixed pattern of steps: whole, whole, half, whole, whole, whole, half. A key signature collects the sharps or flats the pattern needs. Each new sharp is the seventh degree of its key, so the tonic lies a half step above the last sharp. Each new flat is the fourth degree, so the flat before the last one names the tonic; F major, with one flat, is the case to memorize.
One signature serves two keys: a major key and its relative minor, with the same notes and a different home. A parallel minor shares the tonic instead, with three more flats or three fewer sharps.
Natural minor has a whole step from its seventh degree up to the tonic. Harmonic minor raises that seventh to a half step below the tonic, which also makes the chord on the fifth degree major. The raised note is always written as an accidental, never in the signature. Melodic minor raises the sixth and seventh on the way up and restores them on the way down.
Modes keep the notes and move the home. The white keys from C give the major scale; start the same seven notes on another white key and the two half steps fall in new places. Compare a mode with the major or natural minor scale it most resembles and find the degree that differs, such as the raised fourth of Lydian; Locrian alone differs at two degrees.
The trap is naming the key from the signature alone. One sharp fits G major or E minor, and a D-sharp leading into a closing E minor chord settles it as E minor.
Rule: read the signature for two candidate keys, then let the final chord and any raised seventh choose between them.
Intervals: letters first, size second
~2 min
An interval's number comes from counting letter names, and its quality comes from its exact size. Fixing the number from the letters first is what keeps intervals that sound alike apart.
Count the letters from the lower note to the upper one, including both ends, and you have the interval's number. Then measure its size for the quality. The lower note's major scale works as a ruler: if the upper note belongs to it, a unison, fourth, fifth or octave is perfect, and a second, third, sixth or seventh is major. Widen a major or perfect interval by a half step and it becomes augmented; narrow a minor or perfect one and it becomes diminished. A perfect interval never becomes minor.
Take E-flat up to B. The letters E, F, G, A and B make it a fifth, and the flat changes only the size. E-flat up to B-flat would be perfect, so E-flat up to B is an augmented fifth.
Inverting an interval moves its lower note up an octave. The two numbers add up to nine, the quality flips, and a perfect interval stays perfect. Intervals wider than an octave are compound, and harmony usually treats them like their simple forms.
Consonance is a style's classification, not a law of sound. Strict counterpoint classes unisons, fifths and octaves as perfect consonances, thirds and sixths as imperfect ones, and everything else as dissonant. Yet two-voice counterpoint treats the fourth as a dissonance, while at least one nineteenth-century theorist filed it in a mixed category.
The trap is starting from the keyboard. Five half steps can be a perfect fourth or an augmented third, so counting half steps first can give you the right sound with the wrong name.
Rule: fix the number from the letters, then let the half-step count choose the quality.
Triads and seventh chords
~2 min
A triad is two stacked thirds, and its four qualities come from which thirds you stack. A seventh chord adds a seventh above the root, and the bass note tells you the inversion, never the chord's name.
Put a minor third on top of a major third and you have a major triad; reverse them for minor. Two minor thirds make a diminished triad and two major thirds an augmented one, and only major and minor have a perfect fifth from root to top. To find the root, rearrange the notes into a stack of thirds. The bottom of that stack is the root, wherever it actually sounds.
Inversions are named from the bass. With the third in the bass the figure is 6, and with the fifth in the bass it is 6/4. Spacing is a separate matter: close and open position change how widely the upper voices are spread, not which chord sounds.
Built from one key's notes, a major key gives three major triads, three minor and one diminished. In harmonic minor, recheck every triad that contains the raised seventh, because its quality changes.
A seventh chord is a triad plus the seventh above its root. The dominant seventh adds a minor seventh to the major triad on the fifth degree, so its third and seventh lie a tritone apart. Its inversions carry the figures 6/5, 4/3 and 4/2, shorthand for fuller stacks of intervals above the bass.
The trap is naming a chord after its lowest note. An F major triad with A in the bass is still F major, in first inversion. Call it an A chord and every label you build on it is wrong.
Rule: stack the notes in thirds to find the root, and read the bass only for the inversion.
Labeling chords: numerals, figures and chord symbols
~2 min
A Roman numeral names a chord's root as a degree of the key, while figured-bass numbers count intervals above the bass. Settle the key, and set the decorative notes aside, before either label means anything.
Three labeling systems answer three different questions. A lead-sheet chord symbol names a chord by its own root and type, so it means the same chord in any key. A Roman numeral names the root as a degree of the key, with capital numerals for major chords and small ones for minor. Figured-bass numbers count intervals up from the written bass, not from the root, and attached to a numeral they show the inversion.
Figured bass began as a way of performing. In seventeenth- and eighteenth-century music, a chord-playing instrument such as a harpsichord or organ read the bass line and its figures and supplied the harmony.
Take the triad E-flat, G, B-flat. In B-flat major it is IV, and in A-flat major the same three notes are V. The chord symbol never changes, while the numeral follows the key.
Analysis has an order. A key signature fits two keys, so first find the tonic the music keeps returning to and closes on. Then sort chord tones from passing and neighbor tones. One study's model of pitch memory treats a note followed by a step as weaker and one that forms a consonant leap as more salient, so stepwise notes are your first candidates for decoration. Harmonic rhythm, how often the chords change, is separate from how fast the notes move.
The trap is labeling every note. Count a passing tone as a chord member and you invent harmonies the music never had.
Rule: settle the key, set aside the embellishing tones, then name the root as a degree and the bass with figures.
Function, tendency tones and cadences
~2 min
In common-practice harmony, chords group into tonic, predominant and dominant roles, and dissonances such as a chord's seventh point to where the music goes next. Cadences are named by the chords that end a phrase and by the note on top.
In common-practice harmony the tonic chord is the point of rest. Dominant harmony pulls back toward it, and predominant chords such as ii and IV prepare the dominant. Root motion down a fifth is the prototype, above all when it lands on the tonic, as V to I does. Theorists treat it as central to tonal harmony, unlike other Western styles, so a progression is strong only relative to a repertoire.
Dissonance gives the motion direction. A seventh makes a chord restless, and voice-leading practice expects it to resolve by step. The dominant seventh holds a tritone between its third and seventh, which is part of why it sounds tense: the third can rise a half step to the tonic while the seventh falls a step.
Cadences mark the ends of phrases. Dominant to tonic is an authentic cadence. In C major, G to C with C both on top and in the bass is perfect; with E or G on top it is imperfect, a lighter close. A half cadence rests on V and leaves the phrase open. A deceptive cadence sends V somewhere else, most often to vi, and neither of those two ends a piece. The plagal move, IV to I, can follow an authentic close as an added confirmation.
The trap is labeling the six-four just before V as a tonic chord. A tonic chord with its fifth in the bass, placed there at a cadence, acts as a dominant decorated by a suspension. One corpus study of Beethoven's string quartets found that in major keys it moves on to the dominant, with or without its seventh, almost 80 percent of the time.
Rule: name a cadence by its last two chords and its top note, and in common-practice music hear a six-four before V as part of the dominant.
Voice leading, species counterpoint and embellishing tones
~2 min
Voice-leading rules describe how common-practice composers kept their parts independent, and species counterpoint is a strict teaching method built on similar rules. Embellishing tones are classified by how they are approached and how they leave.
Common-practice four-part writing names its voices soprano, alto, tenor and bass. A triad has only three tones, so one of them must be doubled. This style favors contrary motion, welcomes parallel thirds and sixths, and avoids parallel fifths, octaves and unisons, because two voices moving that way stop sounding like separate lines. It also keeps a note two chords share in the same voice and moves the others by small steps. These describe one style's practice, so name that style whenever you apply them.
Species counterpoint teaches the same discipline in stages, against a given melody called the cantus firmus. First species sets one note against each cantus note, opening and closing on perfect consonances and preferring thirds and sixths in between. Second species adds two notes per cantus note with a possible passing dissonance on the weak half, third species four, fourth species ties notes into suspensions, and fifth species mixes them.
Embellishing tones are named by their path. Stepping in and on in the same direction makes a passing tone, and stepping away and back makes a neighbor. A note held into a new chord and resolved down by step is a suspension, or a retardation if it rises, and a tone of the next chord sounded early is an anticipation.
The trap is doubling a note that has to move. Double the leading tone B in a G chord in C major, and when both Bs rise to C they form parallel octaves.
Rule: when you write in common-practice style, check every pair of voices for parallel perfect intervals, and classify each nonchord tone by how it arrives and how it leaves.
Applied chords, chromatic color and changing key
~2 min
An applied dominant briefly treats another chord as a tonic without leaving the key. A modulation is confirmed by a cadence in the new key, and borrowed or altered chords add color while the tonic stays put.
An applied, or secondary, dominant is the dominant of a chord other than the tonic, written V/V or V/vi. To spell one, build the target's dominant seventh as if the target were home. In C major the chord aimed at ii is the dominant seventh of D: A, C-sharp, E and G. Keep the C-sharp as written, because that raised note needs to rise into D. The piece stays in C, and D minor is tonicized only for a moment.
A modulation is different: a cadence in the new key confirms it. The nearest destinations are the five keys whose signatures differ from home by at most one sharp or flat. A pivot chord that belongs to both keys is one route, since a chord that is vi in one key is ii in the key a fifth higher. A direct modulation just begins in the new key, and respelling a chord enharmonically can reach distant keys.
Chromatic chords can also color a key without leaving it. Modal mixture borrows the lowered third, sixth and seventh degrees from the parallel minor. The Neapolitan is a major triad on the lowered second degree, normally in first inversion and heading for the dominant. Augmented sixth chords, in Italian, French and German types, also resolve to the dominant.
The trap is calling every accidental a change of key. A single chromatic note may only tonicize one chord, so wait for a cadence in the new key before you rename the key.
Rule: an accidental can tonicize a chord, but only a confirming cadence in the new key makes a modulation.
Phrases, periods and form
~2 min
A phrase ends with a cadence, and two phrases with a lighter then a stronger cadence make a period. Larger forms are plans of keys, departures and returns more than sequences of tunes.
A phrase is the smallest unit that completes a musical idea, and a cadence marks its end. Most phrases last four measures, but length never defines one, and a phrase can grow to ten measures or more when its cadence is held back. A period pairs an antecedent that ends lightly with a consequent that answers it with a conclusive cadence, usually eight measures in all. In an elision, one measure ends one phrase and begins the next.
Binary form has two parts. In the classic plan the first moves from the home key to a related key, usually the dominant, and the second works back. A rounded binary brings the opening idea back before the end, and ternary form makes that return central: a statement, a contrasting middle, then the statement again. A minuet and trio is a large ternary, with the minuet played again after the trio. A rondo brings its main theme back after each contrasting episode.
Sonata form is a key plan first. The exposition presents two main themes in two keys, linked by a modulating bridge. The development breaks the material into fragments and moves through many keys. The recapitulation restates both themes in the home key, so the bridge has to be rewritten.
The trap is reading form from tunes alone. A second part with no new theme can still complete a binary form, because the move away from home and back is what defines its halves.
Rule: find the cadences first, then trace the keys, because a form is where the music goes and how it returns.
Popular harmony, the blues frame and music without a key
~2 min
Popular styles work with chord symbols, loops and song sections rather than four-part rules, and post-tonal music organizes pitch without a tonic. Each repertoire is judged by its own practice.
A chord symbol names a root and a chord type and leaves the voicing to the player. The symbol A7 means an A dominant seventh, the notes A, C-sharp, E and G, the same four notes that served as the applied dominant to ii in C. In jazz, players commonly add extensions or substitute other chords. A loop repeats a short chord pattern through a song. In one study of a large multi-genre corpus, the most frequent four-chord strings were just two chords a fifth apart, alternating.
One model of improvisation treats the twelve-bar blues as a shared frame. Each pass through its twelve bars is a chorus, and an improvised solo is a string of choruses over the same progression. Song analysis labels sections such as intro, verse, pre-chorus, chorus, bridge and outro, and a strophic song sings every verse to the same music.
Music can also do without a key. Atonal music tends to avoid any pitch center. Schoenberg's twelve-tone technique, devised around 1920, builds a piece from a row of tones and aims to treat all twelve as equals, so none becomes a tonic; a row can also appear reversed, upside down, or both. In Debussy's melodies, one study remarks in passing, a note that is stressed and held can take on a brief tonic quality.
The trap is grading one repertoire by another's rules. A blues chorus is not a faulty chorale, and a twelve-tone row is not a scale with wrong notes; each follows its own practice.
Rule: before you judge a progression, name the style whose practice it follows.
Instruments, transposition and score reading
~2 min
Orchestral instruments group by how they produce sound, and a transposing instrument's written note differs from its sounding note by a fixed interval. Reading a full score means applying each part's interval as you go.
The orchestra groups its instruments into strings, woodwinds, brass and percussion, by how each produces its tone. A full score gives every part its own staff in a customary order: woodwinds at the top, then brass, timpani and percussion, harp, and the strings at the bottom.
Some instruments transpose. An instrument named in a key sounds that note when it reads a written C, so a clarinet in B-flat sounds a whole step lower than written and a clarinet in A sounds a minor third lower. To write a part, move every note by the instrument's interval and move the key signature with it. Music meant to sound in five flats goes to the B-flat clarinet in three flats, a whole step higher, and six sharps of sound come from three sharps on the page for the clarinet in A.
Register changes color. An instrument has a practical orchestral range and a wider one a soloist may reach, and its tone shifts across it: Rimsky-Korsakov heard the flute's low register as dull and cold and its highest one as brilliant.
Performance marks are relative too. Dynamics run from ppp to fff, yet each mark says only that one passage is louder than another, and an accent in a soft passage asks for less force than the same accent in a loud one.
The trap is reading a transposing part at face value. Play a B-flat clarinet's written notes on the piano as printed and you sound a whole step higher than the clarinet does.
Rule: find each part's key, apply its interval, and move the signature along with the notes.
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