Music Theory curriculum

The staff gives you five lines and the spaces between and around them. Ledger lines extend it upward or downward, and they must be spaced exactly like the staff lines, because you identify a note by counting lines, not by judging how high it looks: a note on the first ledger line above the treble staff is A however it is drawn.

A clef labels a single line, and you find every other note by stepping from it. The treble clef curls around the second line, making it the G above middle C; the bass clef's two dots straddle the fourth line, the F just under middle C. Both signs grew out of the letters G and F, so the line they mark matters more than their exact shape.

The C clef turns whichever line it sits on into middle C. On the middle line it makes the alto staff, and on the fourth line the tenor staff, and both remain in regular use in orchestral parts. Its job is to keep a part that lives around middle C inside the staff instead of on a stack of ledger lines.

Piano music joins a treble staff and a bass staff into one great staff, with room for a single ledger line between them. Middle C sits on that line, written either just below the treble staff or just above the bass staff. The two spellings are the same key on the piano, so the staff you see it on is a reading convenience, not a different pitch.

Octave numbers change at each C, not at A, so every B belongs with the C below it rather than the C above it. Older books name the same octaves with words instead, calling the octave from middle C upward the one-lined octave, so check which system a source uses before trusting a label.

With one part on a staff, notes below the middle line take stems up and notes above it take stems down; a note on the line may go either way, whichever looks tidier. When two parts share one staff the rule gives way: every stem of the upper part points up and every stem of the lower part points down, so you can follow each line even where they cross.

Tenor parts are commonly written on the treble staff and sung an octave lower than the notes show, so the reading is the familiar treble one while the sound sits in the male range. Older vocal scores gave the tenor a C clef instead, a practice that has largely disappeared in favor of the treble staff.

The black keys come in alternating groups of two and three, and that pattern is your map: find C as the white key just left of each pair of black keys, and the white keys to its right run D, E, F, G, A and B. A black key takes its name from either neighbor, sharp of the lower or flat of the upper.

Modern tuning divides the octave into equal half steps, and a whole step is simply two of them, so a whole step always has exactly one key, black or white, between its two notes. You will also see half tone and whole tone for the same sizes, but half step and whole step are less ambiguous.

A sharp or flat changes which pitch a line or space stands for, a half step above or below what it otherwise means. Strictly it renames the staff degree rather than bending a note: F to F-sharp is as real a step as B to C. A natural can therefore move a note either way: it lowers a note the key had sharped and raises one the key had flatted, returning it to its plain letter.

F-sharp and G-flat press the same key, but they are not interchangeable on the page. A scale uses each letter once, so in F-sharp major the seventh degree has to be written E-sharp: calling it F would give the scale two Fs and no E. The key, chord or scale decides the spelling, and the sound alone never does.

A double sharp raises a plain note by a whole step, but you usually meet it on a note the key has already sharped. G-sharp minor's signature sharps F, so raising its seventh degree for harmonic minor takes F double-sharp. Writing G instead would skip the letter F and leave the scale with two Gs.

An accidental governs the rest of its measure. If the altered note is tied across the barline, the alteration lasts through the tied value, but the next separate note on that line or space is back to the key signature unless the sign is repeated. Many writers add a reminder sign in the following bar anyway, because readers expect one.

C to C-sharp and C to D-flat are the same half step in sound. The first keeps its letter, so it is a chromatic half step and counts as an augmented unison; the second moves to the next letter, so it is a diatonic half step, a minor second. Count letters first, because the letters, not the sound, decide which interval you write.

Each value from the whole note to the sixteenth lasts half as long as the one before, and each has a rest of the same length. Because the halving never changes, two notes of one value always fill exactly the time of one note of the next longer value, which is the check to run whenever you add up a bar.

A note's shape tells you how long it lasts compared with the other notes, not for how many seconds: a half note is always twice a quarter in the same piece. 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.

A single dot makes a note one and a half times its plain length, and a double dot makes it seven-fourths, so a double-dotted half equals a half, a quarter and an eighth tied together. Writers avoid a dot that would carry an off-beat note through the next accented beat; a tie shows that beat to the eye.

A tie joins two notes of the same pitch into one sound whose length is their sum, and you play only the first. A slur over different pitches asks you to connect them, in one bow or one breath, and in songs it shows several notes sung to one syllable. Two equal pitches under a slur are still struck twice unless a tie joins them.

Beams should show you where each beat begins. In 6/8 the six eighths of a bar are beamed as two groups of three, because the bar has two beats, while in 3/4 the same six eighths may share one beam or go in pairs. In vocal music, notes sung to separate syllables traditionally get separate flags rather than a beam.

A triplet fits three notes into the time of two of the same kind, and a group of five takes the time of four. A duplet runs the other way: two notes take the time of three of their own kind, so they move more slowly than the notes around them. A small number over the group tells you which division to use.

A whole rest stands for a full silent measure in any meter, so in 3/4 it lasts three beats, not four. Inside a bar, write silence beat by beat: a single rest should not cover parts of two beats, even where one note of the same length would be fine, and longer silences in a part are shown as a multimeasure rest with the number of bars written over it.

Beats are the even units you count, and they continue through rests and held notes, felt even when nothing sounds. Tempo is only how quickly they arrive. That is why a ritardando changes the tempo while the meter, and the beat you count, stay the same, and why a fermata, which holds a note as long as taste dictates, interrupts the count without changing the meter.

In 2/4, 3/4 or 4/4 each beat is a plain, undotted note that splits into two equal halves, so counting one-and fits. Because the beat is a single note value, the time signature can name it directly: the lower number is the note that gets the beat and the upper number is how many such beats fill a bar.

In compound meter the beat is a dotted note that splits into three, so a bar of 6/8 holds six eighths but only two beats when the tempo moves. Some older books use the word compound differently, for any bar built from smaller groups, which makes 4/4 compound too, so check a writer's definition before applying it.

When the top number is 6, 9 or 12, the meter is usually compound: divide the top number by three to get the beats, and gather three of the lower note value into each dotted beat. Other top numbers normally count beats directly. Six eighths can fill a bar of 6/8 or of 3/4, and only the grouping tells you which.

Duple, triple and quadruple count beats per bar, and they say nothing about how each beat divides: a compound bar of two dotted beats is just as duple as a simple bar of two plain beats. In quadruple meter beat three carries a secondary accent, lighter than beat one, which is why some writers hear four as two pairs of beats.

Bars of five or seven beats cannot split into equal halves, so they are felt as unequal groups of twos and threes, and one piece can change the order of the groups from bar to bar. When the meter itself changes, a new time signature appears at that point, and it holds until another one replaces it.

A piece may open with an incomplete bar of upbeat notes leading into the first strong beat. When you number bars, start with the first complete bar as bar one, never the partial bar. The last bar of a piece that opens this way is often short as well.

Accent works above the barline too: of two successive bars, the first is felt slightly heavier, just as beat one outweighs beat two. Pairs of bars then group into phrases, and the typical phrase in this music is four bars long, with two-bar units sometimes called sections.

Syncopation is defined against the meter: a note starts on a weak beat or a weak part of a beat and is held through, or followed by silence on, the strong position after it, so the expected accent moves. Because the meter decides which positions are strong, the same rhythm can be syncopated in one time signature and plain in another.

A hemiola regroups the same even pulses: six beats heard as two groups of three are followed by six heard as three groups of two, so two bars of triple time briefly feel like three bars of duple. Nothing speeds up or slows down; only the accents move. The device appears in Western music from at least the sixteenth century.

A polyrhythm sounds two or more even pulses at once that share a cycle without one dividing the other, such as three evenly spaced notes against two in the same span. It differs from syncopation, which displaces accents inside a single pulse. Listeners usually hear a polyrhythm as one combined pattern rather than two separate streams.

Two notations can add up to the same length and still differ in correctness. In 6/8 a note lasting a beat and a third should be a dotted quarter tied to an eighth, not a single half note, because the half note hides where the second beat starts. Write rhythms so the reader can see each beat, even when it costs an extra tie.

In jazz, swing divides each beat into a long note followed by a short one instead of two equal halves, and players differ measurably in how uneven they make the pair. Because eighth notes on the page are equal by definition, the uneven reading comes from the style of the music, not from the note values themselves.

A metronome mark such as M.M. 72 fixes the rate exactly: 72 beats a minute. Italian terms are looser and carry mood as well as speed; allegro literally means happy, and andantino is now usually taken a little faster than andante, though its ending suggests slower. Treat a tempo word as a range rather than a number.

Because the pattern is fixed, there is really one major scale, written from twelve different starting pitches. Split it in the middle and you get two identical four-note groups, each whole–whole–half, joined by a whole step. The upper group of one sharp key becomes the lower group of the next sharp key, which is how the keys link up.

The names describe relations to the tonic. The dominant lies a fifth above it and the subdominant a fifth below, which is what “sub-” means here, not “the note under the dominant.” The mediant and submediant sit midway to each. Degree seven changes its name with its distance below the tonic, because only the closer version pulls up into it.

A key signature gathers the sharps or flats a key needs at the start of each staff, so they need not be written before every note. Each sign sits in a fixed spot; in the treble clef the first sharp goes on the top line, not the bottom space. One signature always names two keys, a major and its relative minor.

Each new sharp in the series is the seventh degree of the key it creates, and each new flat is that key's fourth degree. That is why the series moves in fifths: the next sharp key starts on the fifth degree of the last one, and the next flat key starts on its fourth. Flats come in exactly the reverse order of sharps.

Moving up a fifth adds one sharp and moving down a fifth adds one flat, so keys side by side on the circle share all but one note. That is why the keys a fifth above and below the tonic, together with the relative minors, count as its nearest relatives when music changes key.

Both shortcuts come from how signatures grow. Each added sharp is the seventh degree of its new key, so the tonic lies a half step above the last sharp; each added flat is the fourth degree, so the flat before it names the tonic. Both give the major key, and the same signature also serves its relative minor, so check the final chord before you decide.

Only three pairs of major keys are regularly written under both names: the keys of five, six and seven sharps against those of seven, six and five flats. Past them, one spelling would need double sharps or double flats in the signature, which is hard to read, so music settles on the other name. Keys past seven sharps or flats are called theoretical: their signatures are not written, though a passage can travel through one.

In movable do the syllable do is always the tonic, so the syllables track scale degrees in any key; in fixed do, long used in France and Italy, do is always C. Movable-do teachers also split over minor: some call its tonic la, while others keep do as the tonic and change the syllables for the lowered third and sixth.

Natural minor has half steps between degrees two and three and between five and six, and a whole step from seven up to the tonic. That last whole step means it has no leading tone, which is why older books call it the primitive form of minor and treat it as too weak for harmony without a raised seventh.

Raising degree seven puts it a half step under the tonic, which also makes the chord on the dominant major. The cost is a gap of three half steps between degrees six and seven, a leap that is awkward to sing. Even so, harmonic minor is the form in near-universal use.

Raising degree six as well as seven closes the three-half-step gap when a line climbs to the tonic. Coming down, the seventh is no longer leading anywhere, so both degrees return to natural minor, which also keeps the scale from sounding like the tonic major. The form serves melodies; chords in minor usually come from harmonic minor.

To find the relative minor, count up to degree six of the major scale; to go the other way, count up to degree three of the minor scale. The two keys use the same notes and differ only in which one sounds like home. Some older writers used relative and parallel as synonyms, exactly the confusion to avoid.

A parallel minor has three more flats or three fewer sharps than its major: lower degrees three, six and seven of the major scale and you have its signature. Some books call it the tonic minor, because the two keys share a tonic.

Putting the raised seventh in the signature would give minor keys irregular signatures, so it is always written as an accidental. It is also not raised everywhere: composers raise it mainly where the music moves to the tonic, so a minor passage can show the sign in some bars and not in others.

Play the white keys from C to C and you have the major scale. Start the same seven notes on any of the other six white keys and you get the other six modes. The pitches never change; moving the starting note moves the two half steps to new positions in the scale, and that new pattern is what gives each mode its sound.

Ionian is simply the major scale. Dorian reads like natural minor until degree six, which lies a whole step above five, so the half step falls between six and seven instead. Phrygian is minor whose very first step is a half step. Both Dorian and Phrygian keep a whole step from seven up to the tonic.

Lydian matches the major scale except that its half step falls between degrees four and five, because the fourth is raised. Mixolydian matches major except for a whole step from seven to the tonic. That missing leading tone made Mixolydian rare once harmony came to rely on a major chord on the dominant.

Aeolian has the same steps as natural minor, including the whole step from seven up to the tonic. Locrian builds a diminished triad on its own tonic, a chord that harmony books class as restless rather than final, so it cannot settle the way a tonic should. In one listening study, it and Phrygian were the only modes liked significantly less.

Compare each mode with the major or natural minor scale it most resembles and look for the degree that differs: the fourth in Lydian, the seventh in Mixolydian, the sixth in Dorian, the second in Phrygian. Locrian is the outlier, differing from natural minor at two degrees, the second and the fifth.

Tonal harmony leans on a seventh degree only a half step under the tonic, which makes the dominant chord major. Most modes lack that half step, and as harmony developed, singers and composers tended to raise the seventh, wearing modes such as Mixolydian away. Modal writing keeps its color by leaving that degree unraised.

Count letters, including both ends, to get the number: E-flat up to B is still a fifth, because the flat changes the size, not the letters. Then measure the size to get the quality. Starting from the keyboard instead is how a diminished fourth, which sounds like a major third, ends up labeled as one.

Use the major scale of the lower note as a ruler: if the upper note belongs to it, the interval is either perfect (unison, fourth, fifth, octave) or major (second, third, sixth, seventh). A perfect interval never becomes minor; make it a half step smaller and it is diminished.

Change the size without changing the letters. Widen a major or perfect interval by a half step and it becomes augmented; narrow a minor or perfect one by a half step and it becomes diminished. So seconds, thirds, sixths and sevenths run diminished, minor, major, augmented, while the others run diminished, perfect, augmented.

Half-step counts confirm a quality but cannot name an interval alone, because different numbers share a size: five half steps is a perfect fourth or an augmented third, and every size has more than one spelling. Fix the number from the letters first, then let the count choose the quality.

Inverting an interval moves its lower note up an octave, so the two notes keep their letters while the interval's size and quality flip. Perfect intervals stay perfect, which gives you a quick check on your work. Reduce a ninth or tenth to its simple form before you invert it.

A ninth is an octave plus a second and a tenth an octave plus a third, and harmony usually treats them as their simple forms. Two octaves make a fifteenth, not a sixteenth, because each octave you add brings seven more letters, and the shared note is counted once.

Counterpoint books sort intervals by how you may use them: unisons, fifths and octaves are perfect consonances, thirds and sixths imperfect ones, and the rest are dissonances. The fourth shows that this is a stylistic rule, not physics: two-voice counterpoint treats it as dissonant, while one nineteenth-century theorist filed fourths in a mixed category.

An augmented fourth and a diminished fifth are the same size on a keyboard but different intervals: the fourth spans four letters and the fifth spans five. Respelling either note of any interval gives a new name for the same sound, so the spelling records which interval the music actually means.

A major triad stacks a minor third on a major third, and a minor triad reverses them. Two minor thirds make a diminished triad and two major thirds an augmented one. Only major and minor have a perfect fifth from root to top, which is why older books call them the independent triads, the ones able to end a piece.

Arrange the notes in thirds to find the root: it is the bottom of that stack, wherever it actually sounds. If the third of a chord is its lowest note, the chord keeps its root's name and is simply in first inversion; the bass note does not become the chord's name. A chord is inverted whenever a member other than the root is in the bass.

The figures name intervals above the bass. With the third in the bass the root lies a sixth above it, hence 6; with the fifth in the bass the root is a fourth up and the third a sixth up, hence 6/4. Strict counterpoint books advise using diminished and augmented triads mainly in first inversion.

Spacing looks only at the three upper voices: if they fit within an octave the chord is in close position, and if they spread wider it is in open position. Neither changes the chord's notes or which one is in the bass, so the root, quality and inversion stay exactly the same.

Four voices on a three-note chord means one note appears twice, and the choice is not free. The leading tone is the standard exception, even when the triad is built on it: doubling it often leads to a faulty progression. When the third is doubled instead, it is usually to get a smoother line.

Stack thirds on each degree using only the notes of the key, and the half steps decide each quality. A major key yields three major triads, three minor and one diminished, the diminished one on the leading tone. In harmonic minor, recheck every triad that contains the raised seventh: the ones on III, V and vii all change quality from their natural-minor forms.

A lead-sheet symbol names a chord by its own root and type, so it means the same chord in any key, and the player chooses the voicing and inversion. A Roman numeral names the root as a degree of the key, so the same chord gets a different numeral when the key around it changes.

A seventh chord is named by its triad plus the seventh above its root. A major triad takes a major or a minor seventh, a minor triad a minor seventh, and a diminished triad a minor or a diminished seventh. A major key uses four of the five; the diminished triad with a diminished seventh comes from harmonic minor.

Built on degree five, it adds a minor seventh to a major triad, so in any major key it uses degrees five, seven, two and four, and its third and seventh lie a tritone apart. Like every seventh chord it is dependent, asking for a following chord, and it normally resolves to the tonic in the authentic close. It is also the chord most often used to move into a new key.

Both start from a diminished triad and differ only in the seventh. On the leading tone of harmonic minor that seventh is diminished, so the chord stacks three minor thirds; on the leading tone of major it is minor, and the same shape also sits on degree two of minor. Count the thirds: three minor thirds means fully diminished, while a major third on top means half-diminished.

Each figure is shorthand for the full stack of intervals above the bass, with the obvious ones left out. With the third in the bass you see 6/5, with the fifth 4/3, and with the seventh 4/2 or just 2. The full stacks would be 6/5/3, 6/4/3 and 6/4/2.

Every seventh chord is dependent: it needs another chord after it, and its usual move is to the chord whose root lies a fifth below. When the seventh is held over from the previous chord as a suspension, it is a temporary stand-in for the chord tone a step below, so it moves down one step to that tone.

In major, I and IV carry major sevenths, V the dominant seventh, ii, iii and vi minor sevenths, and vii a diminished triad with a minor seventh. Harmonic minor adds three qualities that major lacks: a minor triad with a major seventh on i, an augmented triad with a major seventh on III, and the fully diminished seventh on vii.

Thoroughbass figures count intervals up from the written bass, not from a chord's root, and they say nothing about octave or spacing. A 6 with a bass note tells you a sixth above it belongs to the chord; how many voices to use and where to place them was left to the accompanist.

Realizing a figured bass means turning the line and its numbers into full chords at the keyboard, historically improvised during performance. Modern editions of such music often print a realization in full and drop the figures, but those chords are an editor's choice, not part of what the composer wrote.

Figured basses carry sharps and flats among their numbers, because a figure counts letter steps above the bass and cannot by itself say whether that note is raised or lowered from the key. When the music needs a pitch outside the key signature, the figure has to carry the accidental.

The two labels answer different questions and are often written together: the figures over the bass describe the intervals sounding above it, while the Roman numeral beneath names the chord's root as a degree of the key. A 6 alone tells you a first inversion; only the numeral tells you which chord of the key it is.

In seventeenth- and eighteenth-century music, one chord-playing instrument, often a harpsichord or organ, read the figured bass and supplied the harmony, while a low melody instrument could double the bass line. The notation assumed a player who knew harmony well enough to supply simple supporting chords with no written-out part.

Read the numeral's size before you play it: in a major key ii is minor, and vii with its small circle is diminished. A capital numeral without a mark means a major chord in any key. Older books mark an augmented triad with an accent mark beside a capital numeral rather than a plus sign, so expect both.

An inversion is shown by attaching figured-bass numbers to the Roman numeral, the same figures you would write over the bass. The numeral still names the root, so a dominant chord with its third in the bass is still V; only the figures beside it change to describe what sounds above the bass.

Harmonic minor's raised seventh makes the chord on V major and the chord on vii diminished, the same qualities they have in major. Read the accidental in the score: where the seventh is left unraised, the chord on the fifth degree is minor instead, and the label changes to v.

A key signature names two keys, a major and its relative minor, so it cannot settle an analysis by itself. Look for the tonic the music keeps returning to and closes on; in a harmonized piece the final chord is usually decisive, and in minor the raised seventh shows up as an accidental.

Before naming a chord, sort its notes: chord tones are often connected by passing and neighbor tones that do not belong to the harmony. A note that moves on by step tends to be one of these, while a note that forms a consonant leap with another tends to belong to the chord.

Harmonic rhythm is how often the chords change, not how fast the notes move: a progression might change chord once, twice or four times a bar. That rate can stay as regular as a pulse, follow a pattern of its own, or speed up and slow down, and even a melody played alone can show it through the chords it implies.

A chart tells an accompanist which chord to play and leaves voicing, inversion and rhythm open. An analysis asks what each chord does in the key, which depends on the key and on the chords around it. The same chart symbol can carry different numerals in two passages if the key has changed between them.

The tonic chord is the point of rest. Dominant harmony, built on degree five, pulls back toward it, and predominant chords such as ii and IV prepare the dominant. Grouping chords by job lets one stand in for another, so ii and IV can each lead into V because both do the preparing.

Common-practice harmony is directional: some chord moves occur far more often in one direction than in the other, and that imbalance is part of what listeners learn to expect. A progression that runs from the dominant back to a predominant works against that flow, which is why it can sound backward.

Root motion down a fifth, or up a fourth, which lands on the same chord, is the prototype of tonal progression, and V to I is its strongest case. Older harmony books build on the same motion, treating a seventh chord's natural resolution as a move to the chord whose root lies a fifth below.

In a deceptive progression the dominant goes somewhere other than the tonic, most often to vi. The chord on vi shares two of the tonic chord’s three notes but gives no definite close, so composers use the move for variety inside a phrase and never to end a piece.

A harmonic sequence repeats a short progression at successively higher or lower pitch levels, usually driven by a regular pattern in the bass. Melodies can be sequenced the same way, by repeating a figure a step higher or lower with its rhythm and direction kept.

A pedal point holds one note, most often the tonic or the dominant, while the harmonies above it change. It belongs to some of those chords and clashes with others, and you analyze the clashes against the pedal rather than as new chords. The name comes from the organ, where a foot can hold the low note.

Whether a progression counts as strong or weak is a property of a style, not of chords in general. Corpus research finds the descending-fifth progression central to tonal harmony in contrast to other Western styles, so judge a progression by the repertoire it comes from.

The weight of the close comes from the keynote. When the final tonic chord has the keynote both on top and in the bass, the cadence sounds final. Put the third or fifth of that chord on top and the same dominant-to-tonic motion becomes a lighter, less conclusive ending, so the soprano note decides the label.

The chords still go from dominant to tonic, but the top voice ends on the third or fifth of the tonic chord instead of the keynote. Without the keynote in that exposed position the close loses part of its finality, which is why a phrase ending this way can still be answered by a later, conclusive cadence.

A half cadence ends a phrase on the dominant chord, so the phrase pauses without closing. One older definition asks for the tonic just before it, while others class a cadence by the chord it rests on, with the dominant the usual choice for an open ending. Because it gives no definite close in the tonic key, it punctuates the middle of a piece rather than ending it.

In a minor key, the iv chord in first inversion has the sixth degree in its bass. Minor lowers that degree, so it sits only a half step above the dominant, and the bass sinks a half step onto the root of V. The phrase then rests on V, so like any half cadence it pauses without closing and leaves the real close in the tonic for later.

The plagal cadence moves from the subdominant to the tonic, IV to I, and is also called the church or amen cadence. It often follows an authentic cadence that has already closed the music, as an added after-cadence, which is why it tends to confirm an ending rather than create one.

In a deceptive cadence the dominant moves somewhere other than the tonic, most often to vi. The tonic and vi share two tones, so the arrival sounds close to the expected resolution while withholding it, and the music goes on toward the authentic close it has delayed. Like a half cadence, it is not used to end a piece.

A tonic chord with its fifth in the bass, placed just before the dominant at a cadence, acts as a dominant decorated by a six-four suspension. In the major-key passages of Beethoven's string quartets this suspended chord moves on to V or V7 almost 80 percent of the time, so label it as part of the dominant, not as a tonic.

Four-part writing names its voices soprano, alto, tenor and bass. A triad has only three tones, so one of them must be doubled, and any of the three may be. Strict exercises also keep every part within the compass of its voice, and close position puts the three upper voices within an octave of one another.

Motion types compare the direction of two voices. In contrary motion one voice rises as the other falls; in parallel motion they move together and keep the same interval, as in a chain of thirds or sixths. Common-practice voice leading welcomes parallel thirds and sixths, avoids parallel perfect intervals, and favors contrary motion to keep two lines audibly independent.

Two voices moving in parallel fifths, octaves or unisons stop sounding like separate lines, which is why common-practice style avoids them. One study built on standard voice-leading rules lists that avoidance, with a preference for contrary motion, as the two rules that let listeners hear independent voices. Chains of parallel thirds and sixths raise no such problem.

One strict counterpoint method treats hidden, or covered, fifths and octaves as faults, with one exception it keeps from two parts up to four: they are allowed in the progressions I to V and V to I. In two-part writing it also avoids both parts leaping in contrary motion into a fifth or an octave.

Crossing happens when a lower voice moves above a higher one. Simple counterpoint keeps every part in the same relative position, and the first exercises forbid crossing outright; later exercises allow an occasional crossing, as long as the parts return to their normal order right away.

Minimal voice leading in common-practice style rests on two preferences: keep any note the two chords share in the same voice, and move the other voices by small steps rather than leaps. Dissonances and leading tones add a third, stepwise resolution. The preferences can pull against each other, and one study wrote its example progressions to satisfy as many of them as possible.

Keep the upper parts within an octave of each other; strict exercises tolerate a tenth only for a chord or two. A doubling matters for where the voices go next: if the two voices holding the doubled tone move to the same new note, they form parallel octaves or unisons. A tone that must resolve by step is the risky one to double, since both copies are pulled to the same place.

The same four-part harmony can be laid out two ways. In close position the three upper voices are written close together, with the soprano and tenor never more than an octave apart; in open position they are spread wider. The test looks only at the three upper voices, so measure the soprano-to-tenor span rather than the distance to the bass.

The cantus firmus is the given melody that counterpoint is written against, with new parts added above or below it; every other part is the counterpoint. Exercises begin and end on tonic harmony, and in simple counterpoint the parts keep their positions relative to one another, so the cantus is the fixed line every interval is measured from.

First species sets one counterpoint note against each cantus note. It may open on a unison, fifth or octave and close on a unison or octave; in between, strict style prefers imperfect consonances, thirds and sixths, and uses perfect intervals sparingly and never two in a row. No more than three thirds or sixths should run in succession.

Second species writes two notes against each cantus note. The first beat takes a consonance, while the weak half may hold a passing tone or an embellishment that clashes with the cantus. These exercises forbid repeating a note, and they treat fifths or octaves on consecutive strong beats as faulty even with a note between them.

Third species sets four notes against each cantus note, usually entering on the second quarter, and at least one of the first three quarters should move by step. A passing tone may skip a third past its goal and then come back to it, and a neighbor figure can be treated the same way, a shape that works best when the main note is the leading tone.

Fourth species ties the second half of each measure into the next. When the tied note clashes with the new cantus note it forms a suspension: prepared as a consonance, held into a dissonance on the strong beat, then resolved down a step to an imperfect consonance. Strict style allows an upward resolution, a retardation, only when the leading tone prepares it.

Florid counterpoint mixes the second, third and fourth species and adds pairs of eighth notes on weak quarters. No single species should run more than about a measure and a half in one part. A suspension may resolve ornamentally, with notes inserted before the resolution, provided the resolution itself lands where it normally would.

Strict counterpoint treats leaps as events in a mostly stepwise line. It avoids melodic sevenths, avoids two similar skips in a row in one direction (a pair of minor thirds excepted), and never covers more than an octave in two skips one way. After two skips of a fourth the line returns one step, and some authorities also avoid the augmented fourth as a melodic interval.

A passing tone is approached by step and left by step in the same direction, so it fills the gap between two notes a third apart. Because it keeps going, it never turns back, which separates it from a neighbor tone. A chord tone can also pass between two other tones of the same chord; that middle note is a harmonic passing tone.

A neighbor tone steps away from a note and returns to the same note, which is what distinguishes it from a passing tone. One strict counterpoint method first allows an upper neighbor a half or whole step above but a lower neighbor only a half step below; later it allows a whole-step lower neighbor, best when it is the ninth of the implied chord.

A suspension has three stages: a consonant preparation, the same note held into a new chord where it clashes on the strong beat, and a resolution down a step to the chord tone. Describe it by the interval the held note makes above the bass and the one it falls to, such as a fourth falling to a third or a seventh to a sixth. If the held tone rises instead, it is a retardation.

An anticipation sounds a tone of the next chord early, before the rest of that chord arrives. Against the current harmony it is a nonchord tone, but it needs no resolution of its own: when the harmony changes, the note simply becomes a chord tone.

The appoggiatura, literally a leaning note, delays a melody tone: the ornamental note sounds first and takes its time from the note it decorates, usually half of that note's value, or two-thirds when the note is dotted. Because it occupies time that belonged to the main note, it falls where that note was due and then gives way to it.

A pedal point is a tone sustained while the harmony changes around it, belonging to some of those chords and clashing with others; the tonic and dominant are the usual choices. A retardation is the upward counterpart of a suspension: the delaying tone sits a step below the chord tone and rises to it, and strict counterpoint uses it only when the leading tone prepares it.

Classify a nonchord tone by its path. Step in and step on in the same direction is a passing tone; step away and back is a neighbor; a tone held over from the previous chord and resolved down by step is a suspension, or a retardation if it rises; a chord tone sounded before the rest of its chord is an anticipation. Sound alone will not tell them apart.

Scale degree 7 lies a half step below the tonic, and tonal practice expects it to resolve by step up to it; the pull depends on that half step. Minor keys get it by raising degree 7 with an accidental, and the descending form of melodic minor lowers it again, because a falling line is not heading for the tonic.

Adding a seventh to a triad makes the chord dependent: restless, and in need of a following chord. The seventh is the dissonant member, so voice-leading practice expects it to resolve by step instead of leaping away. The most common case is the dominant seventh, whose natural resolution is to the tonic, a fifth below its root.

The dominant seventh holds a tritone between its third and its seventh. Unstable intervals such as the tritone create tension and seek a more stable one, such as a third: the chord's third can rise a half step to the tonic while the seventh falls a step to the tonic chord's third. That tritone is part of why the dominant seventh sounds tense.

In tonal harmony, dissonance gives direction. A chord containing a dissonant interval is restless and calls for a following chord, while a chord without one can end a piece. Unstable intervals such as seconds, sevenths and the tritone create tension that seeks a more stable interval, so the dissonance points to where the music goes next.

A secondary dominant is the dominant of a chord other than the tonic, written V/V or V/vi. It brings in that chord's own leading tone, so the target briefly sounds like a tonic while the key stays the same. In a standard I-vi-ii-V progression, vi and ii can each be preceded by its own dominant, V/vi and V/ii.

An applied chord can use a leading-tone chord instead of a dominant: a diminished chord built on the target's own leading tone. Analysts write it with the same slash, as in viio7/V, the leading-tone seventh chord of V. It moves to the chord it points at, just as the home key's leading-tone chord moves most often to I.

A chromatic note does not by itself change the key; it may or may not lead to a modulation. A secondary dominant tonicizes its target only for a moment, and the music carries on in the home key. A modulation is confirmed by a cadence in the new key, so look for that cadence before calling a key change.

To spell an applied dominant, build the dominant seventh of the target as if it were a tonic. The dominant seventh of D is A, C-sharp, E and G, so in C major the chord aimed at ii brings in C-sharp. Keep that accidental as written: the raised note is the borrowed leading tone and needs to rise to its target.

An applied chord normally goes to the chord it points at. In the major-key passages of Beethoven's string quartets, V7/V and V7/IV each most often continue to V and IV respectively. Another continuation is possible, but it is heard against that expectation, the way a deceptive cadence is heard against the tonic it withholds.

Applied dominants can follow one another, each the dominant of the next chord, so their roots fall by fifths until the home dominant arrives. A gentler version slots them into the familiar I-vi-ii-V progression, putting V/vi before vi and V/ii before ii, so each target is tonicized for a moment on the way to the cadence.

The parallel minor shares a major key's tonic but lowers scale degrees 3, 6 and 7. Composers can borrow from it without leaving the key, inflecting a note to its lowered form so that a phrase shifts from major color to minor and back. The shared tonic is what separates mixture from a modulation.

The Neapolitan is a major triad on the lowered second degree, a chromatic chord with tones from outside the key. It normally appears in first inversion as a predominant and moves to the dominant. In listening experiments it is accepted where a subdominant would stand, but placed where the tonic is expected it registers as a broken ending.

Augmented sixth chords are predominants named for the interval between two of their tones, and they normally resolve to the dominant. The Italian, French and German types share that interval and differ in their other tones. The augmented sixth sounds like a minor seventh, so respelling the chord can redirect it, a route to distant keys.

A fully diminished seventh chord adds a diminished seventh above the root of a diminished triad. Its adjacent tones all lie the same distance apart, so respelling it enharmonically can give it a different root. Read its function from where it goes, not from its sound alone.

Mediant relations link keys or chords a third apart, such as a major key and the major key a major third above or below it. From Beethoven on, a second theme in a mediant key often replaced the expected dominant key, and one writer judged the change more stimulating than the tonic-dominant contrast it largely displaced. Two major triads a major third apart share exactly one tone.

In minor keys the tonic chord can appear with a major third: the third is raised while the keynote stays the same, so the chord changes mode without changing key. In Beethoven's string quartets major tonic chords turn up often inside minor-key passages, and the dominant there leads to either the minor or the major tonic.

The keys closest to a major tonic are its dominant, its subdominant, its relative minor, and the relative minors of the dominant and subdominant, five in all. Each differs from the home key by at most one sharp or flat, and a large majority of modulations go to one of them. In Roman numerals they are the keys of V, IV, vi, iii and ii.

A pivot-chord modulation uses a chord whose tones belong to both keys, so the music enters it in the old key and leaves it in the new one. A triad that is vi in one key, for instance, is ii in the key a fifth higher. Of all chords, the dominant seventh is the one most often used in modulating.

A direct modulation changes key without a chord that belongs to both keys; the new key simply begins. It can come right after a pause, as in a Haydn passage whose sudden key change was almost revolutionary in its day, and Haydn used abrupt shifts of this kind as his richest source of harmonic color.

A sequence repeats a progression or melodic pattern at successive pitch levels. Because each repetition starts in a new place, a sequence can carry the music into another key; in one of Bach's inventions a long sequential passage moves through the subdominant key on its way to the closing cadence in the home key.

Enharmonic modulation respells a chord using notes that sound the same but are written differently, such as D-sharp and E-flat. On a keyboard the chord is unchanged, but its new spelling belongs to another key, so it can resolve somewhere unexpected. Respelling an augmented sixth chord can carry the music to a key a half step away.

One chromatic note does not settle the question; it may or may not lead to a new key. A modulation shows itself when a cadence arrives in the new key, as when a phrase raises the fourth scale degree and then closes in the dominant key. Without that cadence, treat the accidental as a passing tonicization.

A phrase is the smallest unit that expresses a complete musical idea, and a cadence marks its end. Most phrases last four measures, but that is only the usual case: a phrase can run on to five or six measures when no ending arrives sooner. Locate the cadence, and the next phrase begins right after it.

A short idea is often stated and then immediately repeated: in many four-measure phrases a two-measure motive does not sound complete until it comes back, so the repetition is part of the thought. Older books use the word sentence loosely, for a phrase or for a whole eight-measure period, so check which unit a text means.

A period joins two phrases, an antecedent and a consequent, usually eight measures in all. The first ends with a semicadence, which sounds like a question; the second answers with a perfect cadence. If the second phrase repeated the first with the same light ending, it would be a repetition, not a period: the stronger cadence makes the answer.

The consequent can follow the antecedent closely, matching it figure for figure until its cadence changes, or it can differ almost completely, even in rhythm, keeping only the same length, accompaniment and character. Either way it balances the first phrase and supplies the conclusive cadence the antecedent held back.

A phrase can be stretched from within by repeating and varying its figures while holding back the cadence that is due. Because no cadence intervenes, the added measures belong to the same phrase rather than starting a new one, and four measures can grow to ten or even sixteen. Repeating the final cadence is a simpler way to extend a phrase.

In an elision, or overlap, one measure does double duty: it completes the cadence of one phrase and is also the first measure of the next. Counting reveals it, because the next phrase has its full four measures only if the cadence measure is counted twice. True elisions are rarer than cadences merely disguised by continuing motion.

Binary form has two parts, each often repeated. In the classic pattern the first part moves from the home key to a related key, usually the dominant, and the second part starts there and works back to a final cadence at home. The tonal journey, out and back, is what defines the two halves, more than any change of theme.

A rounded binary keeps the two-part layout, but the second part, after working back to the home key, brings back the opening's main sentence before the end. Haydn and Mozart often did this. That return of the beginning is the same principle a three-part form makes its central idea.

Ternary form states an idea, departs to contrasting material, and returns to the opening. The return is what a two-part form lacks: it confirms the leading idea by bringing it back. The first part usually ends with a firm cadence, so the middle section sits between two complete statements of the main idea.

A minuet and trio joins two complete song forms, each usually in two or three parts, and repeats the first after the second, marked da capo. The middle one is called the trio from an older habit of writing it for only three instruments. The whole becomes a large three-part form: minuet, trio, minuet again.

A theme and variations presents a complete tune, often in period form, then repeats it in altered versions. Early variation sets mostly kept the key and harmony and dressed the melody in figuration and faster notes; some later sets modulate freely and give each variation a strongly individual character.

A strophic song sings every verse to the same tune, as early ballads did. A through-composed song gives each verse different music, so the setting can follow what happens in the text, as in the art ballads that grew out of the simpler strophic ballad.

A rondo brings its principal theme back after each contrasting digression, almost always in the same form rather than varied. That periodic return gives the form its circular shape. It is described as the oldest of the larger forms in melody-with-accompaniment style and as one of the direct ancestors of the sonata.

The five-part rondo alternates the principal theme with two different episodes, and the second usually contrasts more strongly than the first. The seven-part rondo avoids too much variety by making its third episode a return of the first, so the whole groups into a statement, a contrasting middle and a recapitulation.

The exposition presents two main themes in two keys, linked by a modulating bridge passage and rounded off by a closing theme. Haydn and Mozart paired tonic with dominant, or major with relative minor; from Beethoven on, mediant keys became common. The exposition normally ends with a firm cadence and was traditionally repeated.

The development works over material from the exposition, breaking it into figures and motives, recombining them and moving through many keys where the exposition held to two. It may even introduce a new theme. It ends with a retransition that leads back toward the home key for the recapitulation.

The recapitulation restates the exposition's themes, but both now stand in the home key. That forces one real change: the bridge passage, which originally modulated, has to be rewritten to connect two themes in the same key. A coda then brings the movement to a firmer close.

A sonata-rondo is a hybrid: it keeps the rondo's returning principal theme but takes on features of sonata form. The seven-part rondo already comes close, since its opening section works like an exposition and its last section restates it like a recapitulation. Beethoven's sonata finales titled rondo are, with few exceptions, of this type.

A classical sonata, string quartet or symphony usually has four movements: a fast first movement in sonata form, a slow movement, a minuet or scherzo with trio, and a fast finale that may be a rondo, another sonata form or a set of variations. The movements sit in closely related keys and contrast in rhythm.

In one model of improvisation, a twelve-bar blues progression is a referent: a known structure that guides what the player invents. Each full pass through the twelve bars is a chorus, and a solo is a string of choruses, each with its own development of a motive while the progression underneath stays the same.

A loop repeats a short chord pattern again and again. In a large multi-genre corpus of chord annotations, the most frequent four-chord strings are just two chords a fifth apart, alternating, so a four-chord pattern can hold only two harmonies. Longer standard patterns, such as I-vi-ii-V, recur across many songs.

Song analysis divides popular songs into sections such as intro, verse, pre-chorus, chorus, bridge and outro. One analysis describes a hit song as strophic, with four verses each followed by a chorus and the whole framed by an intro and outro. Strophic means each verse is sung to the same tune, so the verse music returns each time with new words.

A chord symbol names a root and a chord type: A7 is read as A dominant seventh and stands for A, C-sharp, E and G. The symbol says which notes, not how to arrange them, so players choose the voicing, and in jazz they commonly add extensions or substitute other chords.

Music without a key can still suggest a center. In Debussy's melodies, one study notes, a note that is emphasized and held can take on a temporary tonic quality, and composers such as Debussy divide the octave into six equal whole steps. Atonal music goes further and tends to avoid any pitch center at all.

Schoenberg's twelve-tone technique, devised around 1920, builds a piece from a row of tones and aims to treat all twelve tones of the octave as equals, so that none becomes a tonic. In one series of experiments, after hearing a twelve-tone row, trained musicians expected the next tone to be one that had not yet been heard.

Besides its original form, a twelve-tone row can be presented reversed, turned upside down, or both. The system is strict on paper, yet one brief report argues that listeners barely perceive these row relationships, the gap a theorist had in mind in calling serial music cognitively opaque.

The orchestra groups its instruments into four classes: strings, woodwinds, brass and percussion. The grouping follows how the tone is produced, which is why one stringed instrument is classed apart from the bowed strings. Ensembles differ the same way: an orchestra draws its main body of tone from the strings, while a band uses only wind and percussion.

A transposing instrument's written note and its sounding note differ by a fixed interval. A clarinet in B-flat sounds a whole step lower than written, so a written C scale comes out as B-flat. The score names each transposing instrument's key, which tells you the interval needed to work out the real sounds.

The rule is in the name: an instrument in a given key sounds that note when C is written. A clarinet in B-flat therefore sounds a whole step lower than written and a clarinet in A a minor third lower, and the score names each one's key so the reader knows which interval applies.

Move every note by the instrument's interval and move the key signature with it. For a B-flat clarinet, music meant to sound in five flats is written in three flats, a whole step higher; for a clarinet in A, six sharps of sound come from three sharps on the page. Older orchestral scores wrote horn and trumpet parts with no key signature and added every accidental by hand.

An instrument has a practical orchestral range and a wider range a soloist may reach, and a reference may list only the practical one. Within it, register changes color: Rimsky-Korsakov heard the flute's low register as dull and cold and its very high one as brilliant, and the low notes of oboes and bassoons as thick and rough.

A full orchestral score gives each part its own staff, from sixteen to twenty-four of them, in a customary order: woodwinds at the top, then brass, timpani and percussion, harp, and the strings at the bottom. Transposing parts are labeled with their key, so reading a score at the piano means transposing those parts as you go.

Dynamic marks run from ppp, as softly as possible, to fff, as loudly as possible, but every mark is relative: it shows that one passage is louder than another, never exactly how loud. Accents work the same way, so sf inside a soft passage asks for a much milder accent than sf inside a loud one. Read each mark against its surroundings.

Tempo and character are traditionally marked in Italian, which performers everywhere read. Like dynamics, tempo words are relative rather than exact. Most compound markings decode from their parts: andante con moto is a little faster than andante, and lento assai means very slowly.