CS 791 Multisensory Computing 15 September 2002

CS 791 Multisensory Computing 15 September 2002
5. Music Theory CS 791 Multisensory Computing 15 September 2002

Color in Culture U.S. Raises Terror Alert Level By John Solomon
Associated Press Writer Tuesday, September 10, 2002; 1:45 PM WASHINGTON –– The Bush administration raised the nation's terror alert warning to its second highest level Tuesday – code orange – signaling a "high risk" of attack ahead of the Sept. 11 anniversary.

Today’s Outline Music Theory Composition Theory
NSF Sonification Report

Music Theory

Reference Music Theory MiBAC Music Software P.O. Box 468
Northfield MN 55057

Pitch how high or low a note sounds the frequency of a note

Musical Alphabet letters A, B, C, D, E, F, G
correspond to white keys on piano A above middle C has frequency 440 cycles per second

Keyboard White Keys piano keyboard has 88 keys
white keys correspond to musical alphabet A to G black keys correspond to “sharps” and “flats” C is always the white key immediatelyto the left of a two black key group

Music Staff The music staff consists of five lines and four spaces.
Each letter of the musical alphabet A to G corresponds to a specific line or space. The plural of staff is staves. Staves are often connected by a brace or bracket and barlines.

Lines and Spaces Notes can be drawn on any of the staff's five lines or within any of the four spaces. A note on a line is centered on the line. A note in a space is contained within the space between the lines.

Ledger Lines Ledger lines are short horizontal lines placed above or below the musical staff that extend the range of the staff. Ledger lines maintain the spacing of the staff lines and extend slightly beyond each note head.

Pitch Order There is an exact correlation in pitch order between playing consecutive white keys on the piano, writing notes on the musical staff, and the letters of the musical alphabet.

Whole and Half steps The half step is the smallest unit of pitch used in Western music. On the piano, a half step is the musical interval from any one key to its closest neighbor, either black or white. Half steps occur naturally between the two white key pairs E-F and B-C. Two consecutive half steps are called a whole step.

Accidentals Accidentals are symbols that alter the pitch of a note.
Accidentals are placed immediately to the left of the note they affect.

Keyboard Black Keys The black keys on the piano are used to play sharp or flat notes. The key immediately to the right of any white key is called "that white key name" sharp. The key immediately to the left of any white key is called "that white key name" flat. It is possible to have a white key called sharp or flat. For example, the note B could be called C flat and the note C could be called B sharp.

Enharmonic Notes Enharmonic notes are two notes that have the same pitch but are written or spelled differently. For example, A sharp and B flat are enharmonic equivalents because they are played using the same black key on the piano. Starting with A, one half step higher is A sharp. Starting with B, one half step lower is B flat.

Enharmonic Keyboard The piano is an enharmonic keyboard. Each key of the piano can represent several notes.

Clefs A clef symbol is placed at the beginning of each staff to fix the location of a specific pitch.

Treble Clef Names The treble clef is also called the G clef because the clef symbol curls around the line that represents the G above middle C. The names of the treble clef lines can be remembered by the saying "Every Good Boy Does Fine." The spaces spell "F A C E."

Bass Clef Names The bass clef is also called the F clef because the clef symbol locates the line that represents the F below middle C. The names of the bass clef lines can be remembered by the saying "Good Boys Don't Fight At all." The spaces by "All Cows Eat Grass" or "All Cars Eat Gas."

Alto Clef Names The alto clef is also called the C clef because the clef symbol locates the line that represents middle C. The alto clef is used less often than the treble or bass clefs.

What Is a Fifth?

What Is a Fifth? A fifth is the interval between two notes whose letter names are five alphabet letters, or five lines and spaces, apart. The note G is a fifth above C and the note F is a fifth below C.

Circle Diagram In the circle of fifths diagram, the ascending circle of fifths moves clockwise, while the descending circle of fifths moves counter-clockwise. If you start at any point on the circle and go through 12 consecutive fifths, you'll end up at the note you started from and will use all 12 chromatic pitches in the process. The order that sharps and flats occur in the key signature and the names of the major and minor keys, in order of the increasing number of sharps or flats used in the key signature, are based on the circle of fifths.

Ascending/Descending Fifths
C to G is an ascending fifth in the circle of fifths. It can be written as an ascending fifth, or its complement, a descending fourth. Similarly, F to C is a descending fifth in the circle of fifths. It can be written as either a descending fifth, or its complement, an ascending fourth.

Major Sharp Key Names Major sharp key names follow the ascending circle of fifths beginning with C and continuing to C sharp. The key of C major has no sharps, the key of G major has one sharp, the key of D major has two sharps, etc.

Major Flat Key Names Major flat key names follow the descending circle of fifths beginning with C and continuing to C flat. The key of C major has no flats, the key of F major has one flat, the key of B flat major has two flats, etc.

Minor Sharp Key Names Minor sharp key names follow the ascending circle of fifths beginning with A and continuing to A sharp. The key of A minor has no sharps, the key of E minor has one sharp, the key of B minor has two sharps, etc.

Minor Flat Key Names Minor flat key names follow the descending circle of fifths beginning with A and continuing to A flat. The key of A minor has no flats, the key of D minor has one flat, the key of G minor has two flats, etc.

Order of Sharps The order of sharps in the key signature follow the ascending circle of fifths beginning with F sharp and continuing to B sharp.

Order of Flats The order of flats in the key signature follow the descending circle of fifths beginning with B flat and continuing to F flat.

Key Signatures

A key signature consists of a series of sharps or flats written immediately to the right of the clef. A key signature can represent either a major key or a minor key. The actual key, major or minor, must be determined by studying the notes and chords used in the music. When a sharp or flat is used in a key signature, all notes of that name appearing in the music are automatically sharped or flatted. For example, in E major every F, C, G, and D is sharped.

The rules for determining major sharp keys are:
* The key of C major has no sharps or flats. * For key signatures having one to seven sharps, the name of the major key is one half step higher than the last sharp (the sharp furthest to the right).

The rules for determining major flat keys are:
* The key of C major has no sharps or flats. * The key of F major has one flat. * For key signatures having two to seven flats, the name of the major key is the name of the next to the last flat (the flat 2nd from the right).

Each key signature can specify either a major key or a minor key
Each key signature can specify either a major key or a minor key. The name of the minor key is found by first finding the name of the major key and then counting backwards three scale notes. Sharps and flats present in the key signature affect the key name.

Relative keys are major and minor keys that share the same key signature. For example, E minor is the relative minor of G major and A flat major is the relative major of F minor.

Parallel major and parallel minor are major and minor keys that share the same name, but use different key signatures. For example, B minor is the parallel minor of B major, and B major is the parallel major of B minor.

An accidental is a sharp or flat used in the music that is not part of the key signature. When an accidental is used, it affects all notes of that pitch in that measure. The accidental is automatically canceled when you move to the next measure.

A scale consists of a series of pitches arranged in ascending order, spanning an octave.
The most commonly used scales are major and minor. Many other types of scales are used including Modes and Jazz Scales.

Major Scale The major scale consists of eight consecutive notes of the musical alphabet forming a definite pattern of whole steps and half steps. Note that sharps had to be used to make the E major scale conform to this pattern.

Natural Minor Scale The natural minor scale consists of eight consecutive notes of the musical alphabet forming this pattern of whole and half steps:

Harmonic Minor Scale The harmonic minor scale is based on the natural minor scale, with the seventh note of the scale raised one half step. The pattern of whole and half steps is: Raising the seventh note creates an interval of three half steps between the sixth and seventh notes, and a half step between the seventh and eighth notes.

Melodic Minor Scale The melodic minor scale is based on the natural minor scale, with the sixth and seventh notes of the scale raised one half step. The pattern of whole and half steps is: The melodic minor scale is used for ascending melodic motion, but reverts to the natural minor form in descending melodic motion.

Relative Major/Minor Scales
Relative major and minor scales share the same key signature, but begin on different notes. G major and E minor are relative major and minor scales.

Parallel Major/Minor Scales
Parallel major and minor scales start on the same note, but use different key signatures. G major and G minor are parallel major and minor scales.

What Is a Mode? Modes were used to organize the melodic and harmonic elements of music in the Middle Ages and Renaissance periods. You can think of modes as scales which use the white keys of the piano. The Ionian mode (same as the major scale) uses the white keys from C to C. The six remaining modes also use the white keys but start on different notes. For example the Dorian mode uses the white keys from D to D. During the 17th to the late 19th Century, the modes were not commonly used, being replaced by the major and minor scales. Modes are often heard in music today.

Ionian Ionian mode starts on the first scale degree of a major scale and ascends an octave. The pattern of whole and half steps is:

Dorian Dorian mode starts on the second scale degree of a major scale and ascends an octave. The pattern of whole and half steps is: Dorian mode is the same as a natural minor scale with a raised sixth note.

Phrygian Phrygian mode starts on the third scale degree of a major scale and ascends an octave. The pattern of whole and half steps is: The Phrygian mode is the same as a natural minor scale with a lowered second note.

Lydian Lydian mode starts on the fourth scale degree of a major scale and ascends an octave. The pattern of whole and half steps is: The Lydian mode is the same as a major scale with a raised fourth note.

Mixolydian Mixolydian mode starts on the fifth scale degree of a major scale and ascends an octave. The pattern of whole and half steps is: The Mixolydian mode is the same as a major scale with a lowered seventh note.

Aeolian Aeolian mode starts on the sixth scale degree of a major scale and ascends an octave. The pattern of whole and half steps is: The Aeolian mode is the same as a natural minor scale.

Locrian Locrian mode starts on the seventh scale degree of a major scale and ascends an octave. The pattern of whole and half steps is: The Locrian mode is the same as a natural minor scale with lowered second and fifth notes.

Transposed Modes It is easy to think of modes using the white keys of the piano, but they can be transposed to any of the 12 chromatic pitches.

Table of Modes

Modes - Relation to Major
The Ionian, Lydian, and Mixolydian modes are closely related to the major scale. Modal scales can begin on any of the 12 chromatic pitches, provided they follow the pattern of whole and half steps for that mode.

Modes - Relation to Minor
The Aeolian, Dorian, Phrygian and Locrian modes are closely related to the Natural minor scale. Modal scales can begin on any of the 12 chromatic pitches, provided they follow the pattern of whole and half steps for that mode

What Is a Jazz Scale? Jazz scales are used by improvisers to convey complex harmonies common in Jazz. The names of the jazz scales imply that they are based on the modes, with certain scale degrees altered. If you know the modes you can learn the jazz scales. The jazz scales are based on the ascending melodic minor scale. Just as the modes were based on the major scale starting on different scale degrees, the jazz scales are based on the melodic minor scale, starting on different scale degrees.

Dorian Flat 2 The Dorian Flat 2 scale starts on the second scale degree of a melodic minor scale and ascends an octave. The pattern of whole and half steps is:

Lydian Sharp 5 The Lydian Sharp 5 scale starts on the third scale degree of a melodic minor scale and ascends an octave. The pattern of whole and half steps is:

Mixolydian Sharp 4 The Mixolydian Sharp 4 scale starts on the fourth scale degree of a melodic minor scale and ascends an octave. The pattern of whole and half steps is:

Mixolydian Flat 6 The Mixolydian Flat 6 scale starts on the fifth scale degree of a melodic minor scale and ascends an octave. The pattern of whole and half steps is:

Minor Flat 5 The minor Flat 5 scale starts on the sixth scale degree of a melodic minor scale and ascends an octave. The pattern of whole and half steps is:

Locrian Flat 4 The Locrian Flat 4 scale starts on the seventh scale degree of a melodic minor scale and ascends an octave. The pattern of whole and half steps is: This scale is sometimes called the Super Locrian or Diminished Whole Tone scale.

Table of Jazz Scales

What Is a Scale Degree?

What Is a Scale Degree? Each note of the scale, or scale degree, has a conventional name. The most important scale degree is the tonic, the second most important is the dominant. The names of the other scale degrees reflect their relationship to the tonic or dominant.

Tonic The tonic is the first (or eighth) note of the scale, and is often described as the note that feels most "at rest."

Supertonic The supertonic is the second note of the scale. The prefix "super" (above) indicates the note above the tonic.

Mediant The mediant is the third note of the scale. The term mediant (median or middle) indicates the note midway between the tonic and dominant.

Subdominant The subdominant is the fourth note of the scale. The prefix "sub" (below) indicates the dominant (fifth) below the tonic.

Dominant The dominant is the fifth note of the scale. Its name reflects its importance.

Submediant The submediant is the sixth note of the scale. The term submediant (below - median, middle) indicates the note midway between the tonic and subdominant.

Subtonic The subtonic is the seventh note of the natural minor Scale. The subtonic is a whole step lower than the tonic. The prefix "sub" (below) indicates the note below the tonic.

Leading Tone The leading tone is the seventh note of the major, harmonic, and melodic minor scales. The leading tone is a half step lower than the tonic. Its name indicates that it is used melodically to lead into the tonic.

What Is an Interval?

What Is an Interval? An interval is the distance in pitch between two notes. There are two parts to an interval name, quality and size.

Size Interval size is measured by counting the number of lines and spaces (or alphabet letters) between two notes, including both notes. For example, the size of the interval between F-C is a fifth

Quality The quality of an interval is determined by the number of half steps contained in the interval. Intervals with the same size can have different qualities. For example, the intervals between C-E and E-G are both thirds, but there are four half steps between C-E, versus three half steps between E-G. The third containing four half steps is called a major third. The third containing three half steps is called a minor third.

Terminology The terms perfect, major, minor, diminished, and augmented are used to describe the quality of an interval. Perfect is used with unisons, fourths, fifths, and octaves. Major and minor is used with seconds, thirds, sixths and sevenths. Diminished and augmented are used with all intervals. Perfect intervals are labeled with an upper case "P." Major intervals are labeled with an upper case "M." Minor intervals are labeled with a lower case "m." Diminished intervals are labeled "d", "dim." or "deg. or " o." Augmented intervals are labeled "A", "Aug." or "+." Examples: P1, P4, m2, m6, M3, M7, d3, deg.5, dim. 5, A6, Aug. 6, +6.

Identification 1 To identify the size and quality of an interval using a major scale for reference, assume the bottom note of the interval is the tonic of a major scale. 1. If the upper note of the interval belongs to that major scale, then unisons, 4ths, 5ths and 8ves will be perfect, and 2nds, 3rds, 6ths, and 7ths will be major. 2. If the upper note of the interval does not belong to that major scale, determine by how many half steps it differs from that scale degree of the major scale. Based on the half step differential, determine the quality.

Identification 2 To identify the size and quality of an interval without a key reference to a major scale, do the following: 1. Find the interval size by counting the lines and spaces between the two notes (including both notes). 2. Find the interval quality by determining the number of half steps between the two notes and then use the table of interval sizes to determine the quality.

Perfect Intervals Perfect intervals are the unison, fourth, fifth, and octave. Perfect intervals are formed in the major scale when the lower note is the tonic. Perfect unison (P1) has 0 half steps Perfect fourth (P4) has 5 half steps Perfect fifth (P5) has 7 half steps Perfect octave (P8) has 12 half steps

Major Intervals Major intervals are the second, third, sixth, and seventh. Major intervals are formed in the major scale when the lower note is the tonic. Major second (M2) has 2 half steps Major third (M3) has 4 half steps Major sixth (M6) has 9 half steps Major seventh (M7) has 11 half steps

Minor Intervals Minor Intervals are the second, third, sixth, and seventh. minor intervals are formed in the major scale when the upper note is the tonic. Minor second (m2) has 1 half steps Minor third (m3) has 3 half steps Minor sixth (m6) has 8 half steps Minor seventh (m7) has 10 half steps

Harmonic/Melodic Intervals
Intervals can appear as harmonic or melodic intervals. In harmonic intervals the notes are played simultaneously. In melodic intervals the notes are played separately. Melodic intervals can appear as ascending or descending intervals.

Altered Perfect Intervals
When a perfect interval is made one half step larger it becomes augmented. When a perfect interval is made one half step smaller it becomes diminished. Notice how you can shrink or expand the interval from either the top or bottom note.

Altered Major/Minor Intervals
A major interval one half step larger becomes augmented. A major interval one half step smaller becomes minor. A minor interval one half step larger becomes major. A minor interval one half step smaller becomes diminished.

Altered Diminished-Augmented Intervals
An augmented interval one half step larger becomes doubly augmented. A diminished interval one half step smaller becomes doubly diminished.

Table of Intervals

Note Values

Time Signatures Time signatures are used to indicate how the musical rhythm and meter is organized. The rhythm and meter of a piece of music are independent of the tempo. Whether the piece is played fast or slow, the rhythm and meter stay the same. The upper number in the time signature indicates the number of beats in a measure. The lower number indicates which note value receives one beat.

Note Symbols This table shows the music symbols and names of the most commonly used notes.

Rest Symbols This table shows the music symbols and names of the most commonly used rests. Rests are used to indicate silence.

Dotted Notes A dot following a note or rest increases its duration by half the original value.

Note Value Tree Each of these notes is half as long as the note above it.

Rest Value Tree Each of these rests is half as long as the rest above it.

Beat Unit Examples This table illustrates how beat units (the lower number of the time signature) affect the number of beats a note and rest receives.

Music Theory Chord Elements

Thirds The interval of a third is formed by two notes that are three lines and spaces apart, or three alphabet letters apart, counting both the beginning note and ending note.

Major Third A major third contains four half steps.

Minor Third A minor third contains three half steps.

Chord Three or more notes form a chord. Two notes form an interval.

Triad Definition A triads is a three note chord built with two thirds, one stacked on top of the other. Four types of triads can be built using major and minor thirds. Note: The notes of the triad appear on three consecutive lines or three consecutive spaces.

Root Position A triad is in root position when the notes of the chord are as close together as possible. In root position all notes of the triad will fall on three consecutive lines or three consecutive spaces.

Root Third Fifth The individual notes of a triad are termed root, third, and fifth. The root is the lowest note of a triad in root position. The third is the middle note of a triad in root position. The fifth is the highest note of a triad in root position. The third and fifth get their names from their interval distance from the root.

Inversions 1 When the notes of a triad are rearranged, you get an inversion of that triad.

Inversions 2 There are three Triad inversions: * Root Position
* First Inversion * Second Inversion

Inversions 3 * In root position the root is the lowest note.
* In first inversion te third is the lowest note. * In second inversion the fifth is the lowest note

Block Style When the notes of the chord are written or played simultaneously it's called block style or chord style.

Broken Style When the notes of a chord are written or played one at a time it's called broken style or arpeggio style.

Arpeggio A chord written or played in a broken style is called an arpeggio.

Chord Elements Example - Naming
The first step in understanding triads and seventh chords is learning to identify major and minor thirds. Question: Is this a major or minor third?

1. Count the half steps 2. Answer: It's a major third because the interval spans four half steps.

The notes in a triad are termed the root, third and fifth. Recognizing which note is the root, third or fifth is essential to understanding chord inversions. Question: Name the highlighted note. Root, third, fifth, or seventh.

Chord Elements - Naming
1. Rearrange the notes of the chord to put it in root position. Answer: It's the third.

Chord Elements Example - Writing and Playing
The first step in understanding triads and seventh chords is learning to identify major and minor thirds. Question: Write the note a minor third below Db.

1. Count down three half steps A minor third has three half steps. Going backwards throught the chromatic scale we get: Db -> C -> B -> Bb. 2. Answer: It's Bb.

The notes in a triad are termed the root, third and fifth. Recognizing which note is the root, third or fifth is essential to understanding chord inversions. Question: This is the third of a major chord. Write the chord in first inversion.

A major triad is built from two stacked thirds. 1. Find the Major third below G. It's Eb because there are four half steps in a major third.

2. Find the Minor third above G. The upper third is a minor third.

3. Build the triad. The root position Major triad now looks like this.

4. Write the chord in first inversion. A first inversion chord has the third as the lowest note. 5. Answer

Triad A triad is a three note chord built with two thirds, one stacked on top of the other. Four types of triads can be built using major and minor thirds

Note: The notes of the triad appear on three consecutive lines or three consecutive spaces.

The following chord is also a triad because its notes can be rearranged to fall on three consecutive lines.

Triad Identification To fully identify a triad you need to determine three things: * Root * Quality * Inversion The Root of the triad is a letter of the musical alphabet. The Quality of a triad can be major, minor, diminished, or augmented. The Inversion of a triad can be root position, first inversion, or second inversion.

Triad Rood The root of a triad is the name of the bottom note when the triad is in root position.

Triad Qualities There are four triad qualities: * major * minor
* diminished * augmented The qualities are determined by type and stacking order of the major and minor thirds in the chord.

Major Triad The major triad has a major third on the bottom and a minor third on top.

Minor Triad The minor triad has a minor third on the bottom and a major third on top.

Diminished Triad The diminished triad has a minor third on both the bottom and top.

Augmented Triad The augmented triad has a major third on both the bottom and top.

Triad Symbols A common convention uses: upper case for major chords
lower case for minor chords º for diminished chords + for augmented chords Diminihed chords are written in lower case followed by the º Augmented chords are written in upper case followed by the + Other symbols you may see are shown at right.

Triad Inversions Triads can appear in three inversions:
* root position * first inversion * second inversion

Triad Inversions (2) The inversion is determined by whether the root, third, or fifth is the lowest note of the chord. * In root position the root is the lowest note. * In first inversion the third is the lowest note. * In second inversion the fifth is the lowest note.

Inversion Symbols The symbols used to identify inversions are based on unique interval structures between the chord notes for that inversion. * A chord name with no suffix refers to root position. * A chord name followed by a 6 refers to first inversion. * A chord name followed by 64 (often written vertically) refers to second inversion.

Closed and Open Spacing
When the notes of a chord appear as close together as possible, the chord is in a closed spacing. Closed spacing is sometimes called closed voicing or closed position.

Closed and Open Spacing (2)
When the notes of a chord are more spread out than closed spacing, the chord is in open spacing. Open spacing is sometimes called open voicing or open position.

Closed and Open Spacing
The three chords in measure one are C Major triads in root position, first inversion, and second inversion in closed spacing. The chords in measure two are also C Major triads in root position, first inversion, and second inversion in open spacing.

Triads Example - Naming
To fully identify a triad you need to determine three things: * Root * Quality * Inversion

Question: Name this chord.

1. Rearrange the notes of the chord to match a root position triad.

2. Root (It's Eb because that's the bottom note when the triad is in root position)

3. Quality (It's a Major triad because there's a Major third on the bottom and a Minor third on the top)

4. Inversion (It's a second inversion triad because the fifth is the lowest note)

Answer: E flat major second inversion

Triads Example - Writing and Playing

Question: Write (or Play) an F minor triad in first inversion.
1. Root (it's F - the directions said so) 2. Quality (a minor triad has a minor third on the bottom and a major third on the top)

3. Inversion (a first inversion triad has the third in the bass)

4. Answer:

Seventh Chords If you add another third on top of a triad you get a seventh chord. The interval of a seventh is formed between the root and the bass.

The names of the chord notes are similar to triads - root, third, fifth, and seventh.

Seventh Chord Qualities
There are nine seventh chord qualities. Eight of them are formed from the combination of the four triad qualities combined with a major or minor seventh. The ninth quality is the fully diminished seven chord that is formed from a diminished triad and a the interval of a diminished seventh.

The ninth quality is the fully diminished seven chord that is formed from a diminished triad and a the interval of a diminished seventh.

Seven or Seventh? It can be confusing at first whether to call a chord a "seventh" chord or a "seven" chord. We use the term seventh to refer to an interval (two notes), or to a class of chords as in "seventh chords are more common in the Romantic period than in the Classical period." The term seven refers to a specific chord as in "that's a G seven chord."

Seventh Chord Names The general form for a seventh chord name is
<ROOT PITCH><TRIAD QUALITY> <SEVENTH QUALITY> An example would be an Eb Major Minor 7 chord. The first term (Eb) refers to the root of the chord. The second term (Major) refers to the quality of the triad that forms the lower three notes of the seventh chord. The third term (Minor) refers to the quality of the interval of the seventh formed between the root and the seventh. You can abbreviate the names by using upper case M for major and lower case m for minor.

Major Major Seven (M7) Long name: F Major Major 7
Short name: FM7, FMaj7, F Major 7

Major Minor Seven (7) Long name: F Major Minor 7 Short name: F7
Other names: Dominant 7

Minor Major 7 (mM7) Long name: F Minor Major 7 Short name: FmM7

Minor Minor 7 (mm7) Long name: F Minor Minor 7
Short name: Fm7, Fmin7, F minor 7

Diminished Major 7 (dM7)*
Long name: F Diminished Major 7 Short name: FdM7 *Rare, not used in MUSIC LESSONS II

Diminished Minor Seven (Half Diminished) (f7)
Long name: F Diminished Minor 7 Short name: Fø7, Fm7b5

Augumented Major Seven (+M7)
Long name: F Augmented Major 7 Short name: F+M7, FM7#5

Augmented Minor Seven (+m7)
Long name: F Augmented Minor 7 Short name: F+7, F7#5

Diminished Seven (o7) Long name: F Diminished 7 Short name: F°7, Fdim7

Five Common Seventh Chords
Five seventh chords are commonly used: MM7 (Major Major 7) 7 (Major Minor 7) m7 (Minor Minor 7) ø7 (Diminished Minor 7) °7 (Diminished Diminished 7)

Seventh Chord Inversions
A seventh chord can appear in four inversions depending on whether the root, third, fifth, or seventh is the lowest note. In the following example, the CM7 chord appears in four different inversions.

Seventh Chord Inversion Symbols
The symbols used to identify seventh chord inversions are based on the interval structure.

Dominant Seven Chord In scale degree terms the fifth note of the scale is the dominant. The seventh chord that is built on the fifth note of the scale is called the dominant seven chord. The dominant seven chord is the most commonly used seventh chord. The tonic and dominant triads plus the dominant seven chord are the by far the most used chords in western music.

Seventh Chords Example - Naming
To fully identify a seventh chord you need to determine three things: * Root * Quality * Inversion

Question: Name this seventh chord.

1. Rearrange the notes to match a root position seventh chord.

2. Root (It's A, because that's the bottom note when the seventh chord is in root position )

3. Quality (Its a Major Minor 7 chord because the lower three notes form a Major triad, and the upper note forms the interval of a seventh with the root)

4. Inversion (It's a third inversion chord because the seventh is the lowest note)

Answer: A7 third inversion

Seventh Chords Examples - Writing and Playing

Question: Write (or Play) a D half diminished seven chord in first inversion.
1. Root (it's D - the directions said so) 2. Quality (a half diminished seven chord has a diminished triad and a minor 7)

3. Inversion (a first inversion seventh chord has the third in the bass)

4. Answer: There are several correct answers to this question. Any chord that uses the notes D F Ab and C and has the F as the lowest note is correct.

Roman Numerals

Roman Numerals Roman Numerals identify a chord in a musical context.
They fully identify the Root, Quality, and Inversion of a chord with respect to a given key.

Number the notes of the G Major scale as shown.
Using notes of the G Major scale, build triads on every scale degree.

Major chords appear on scale degrees 1, 4, and 5
Major chords appear on scale degrees 1, 4, and 5. Minor chords appear on scale degrees 2, 3, and 6. A Diminished chord appears on scale degree 7. This pattern of Major, Minor, and Diminished triads holds true for every Major scale.

Roman Numeral Triad Names - Root
The naming conventions for triads also apply to Roman Numerals. Root * The scale degree expressed as a Roman Numeral, e.g.: I, ii, iii, iv V

Roman Numeal Triad Names - Quality
Major is upper case, e.g.: I IV V Minor is lower case, e.g.: ii iii vi Diminished is lower case with added º, e.g.: vii° Augmented is upper case with added +, e.g.: III+

Roman Numeral Triad Names - Inversion
Triad root position has no suffix Triad first inversion is 6 Triad second inversion is 64 Seventh chord third inversion is 42

Roman Numeral Seventh Chord Names - Root
The naming conventions for seventh chords also apply to Roman Numerals. Root * The scale degree expressed as a Roman Numeral, e.g.: I, ii, iii, iv V

Roman Numberal Seventh Chord Names - Quality
M7 is a Major Major 7 chord, e.g.: IM7 IVM7 7 is a Major Minor 7 chord, e.g.: V7 m7 is a Minor Minor 7 chord, e.g.: ii7 iii7 vi7 ø7 is a Diminished Minor 7 chord, e.g.: iiø7 °7 is a fully Diminished 7 chord, e.g.: vii°7 mM7 is a Minor Major 7 chord, e.g.: imM7 +M7 is a Augmented Major 7 chord, e.g.: III+M7 +7 is a Augmented Minor 7 chord, e.g.: III+7

M7 is a Major Major 7 chord, e.g.: IM7 IVM7
7 is a Major Minor 7 chord, e.g.: V7 m7 is a Minor Minor 7 chord, e.g.: ii7 iii7 vi7 ø7 is a Diminished Minor 7 chord, e.g.: iiø7 °7 is a fully Diminished 7 chord, e.g.: vii°7 mM7 is a Minor Major 7 chord, e.g.: imM7 +M7 is a Augmented Major 7 chord, e.g.: III+M7 +7 is a Augmented Minor 7 chord, e.g.: III+7

Roman Numeral Seventh Chord Names - Inversion
Seventh chord root position is 7 Seventh chord first inversion is 65 Seventh chord second inversion is 43 Seventh chord third inversion is 42

Diatonic Chords We'll use the term diatonic to refer to a chord where all the notes of the chord occur within a given scale or key. For example, the d Minor chord is a diatonic chord in the key of C because its notes ( D F A ) occur in the C Major scale. The D Major chord ( D F# A ) is not a diatonic chord in the key of C because the F# does not occur in the scale of C Major. For Minor keys, we'll call a chord diatonic if its notes belong to any one of the three Minor scale types (natural, harmonic, or melodic) for that key.

Major Scale Diatonic Triads
This example is in C Major, but the pattern of Major and Minor chords is true for every natural Minor scale. * Major: I IV V * Minor: ii iii vi * Dim: vii * The I, IV, and V chords are Major. * The ii, iii, and vi chords are Minor. * The vii chord is Diminished.

Natural Minor Scale Diatonic Triads
* Minor: i iv v * Major: III VI VII * Dim: ii * The i, iv, and v chords are Minor. * The III, VI, and VII chords are Major. * The ii chord is Diminished

Harmonic Minor Scale Diatonic Triads
Minor: i iv Major: V VI Dim: iiº viiº Aug: III+ The i and iv chords are Minor. The V and VI chords are Major. The ii and vii chords are Diminished. The III chord is Augmented.

Melodic Minor Scale Diatonic Triads
* Minor: i ii vi * Major: IV V * Dim: vi° vii° * Aug: III+ The i, ii, and vi chords are Minor. The IV and V chords are Major. The vii chords is Diminished. The III chord is Augmented.

Major Scale Diatonic Sevenths
MM7: I IV 7: V mm7: ii iii vi Ø7: vii º7: mM7: +M7: The I and IV chords are Major Major sevenths. The V chord is a Major Minor seventh. The ii, iii, and vi chords are Minor Minor sevenths The vii chord is a Half Diminished seventh.

Natural Minor Scale Diatonic Sevenths
MM7: III VI Mm7: VII mm7: i iv v ø7: ii º7: mM7: +M7: The III and VI chords are Major Major sevenths. The VII chord is a Major Minor seventh. The i, iv, and v chords are Minor Minor sevenths. The ii chord is a Half Diminished seventh.

Harmonic Minor Scale Diatonic Sevenths
MM7: VI Mm7: V mm7: iv ø 7: ii vii º7: mM7: i +M7: III The VI chord is a Major Major sevenths. The V chord is a Major Minor seventh. The iv chord is a Minor Minor seventh. The ii and vii chords are Half Diminished sevenths. The i chord is a Minor Major seventh. The III chord is an Augmented Major seventh.

Melodic Minor Scale Diatonic Sevenths
* MM7: * Mm7: IV V * mm7: ii * ø 7: vi * º7: vii * mM7: III * +M7: i The IV and V chords are Major Minor sevenths. The ii chord is a Minor Minor seventh. The vi chord is a Half Diminished seventh. The vii chord is a Fully Diminished seventh. The i chord is a Minor Major seventh. The III chord is an Augmented Major seventh.

The Roman Numeral identifies the chord's function within the key
The Roman Numeral identifies the chord's function within the key. It is possible for the same chord to have different Roman Numeral Names. If you see this chord, you can name it immediately as F major. To assign a Roman Numeral name to it you have to know what key it's being used in. This F chord could have the following Roman Numeral names.

Roman Numeral Example - Naming
Question: Name this chord in the key of D Major.

1. Key (It's D Major - the directions said so)
2. Root (it's E)

3. Quality (It's Minor Minor 7)

4. Inversion (It's 65, because that's the symbol for a first inversion seventh chord)

5. Roman Numeral Root (its ii becuase E is the second note in the scale of D Major)
6. Answer: ii65

Roman Numeral Example - Writing and Playing
Question: Write (or Play) a iiø43 chord in the key of G Minor. 1. Key (It's g Minor - the directions said so) 2. Root Scale Degree (It's A because A is the second (ii) note of the G Minor scale)

3. Quality (It's half Diminished 7 because of the ø)

4. Inversion (It's a second inversion seventh chord because of the 43)

5. Answer:

Secondary Dominants

Secondary Dominants A Dominant chord is built on the fifth note of the scale. It's a major triad or a Major Minor seven chord in all major and minor keys. Strictly speaking the dominant chord of a natural minor scale is minor, but in practice the major form of the chord is almost always used.

Dominant to Tonic The most common chord progression in western European music of the last 400 years is the V chord moving to the I chord (Dominant to Tonic). The V to I chord progression has ended thousands of compositions.

Circle of Fifth Root Motion
The roots of the Dominant (V chord) and Tonic (I chord) are a fifth apart. The root motion can be descending or ascending.A sequence of chords whose roots are related by descending fiths (or it's inversion, the ascending fourth) are traversing the "Circle of Fifths."

Diatonic Chords vs. Secondary Dominants
Here's a common ii-V chord progression in the key of C.

Here's a very similar progression, this time using the D Major chord instead of the D Minor chord. This time we cannot call the D chord a ii chord because the F# does not occur in the key of C. Its correct name is the V/V (five of five) chord. In this example it's in first inversion so it's labelled as the V6/V chord.

Important point: All secondary dominants will have a note that does not belong to the main key.

Secondary Dominant Usage
You can use the V-I relationship at any time. Stated another way, any chord can be preceded by its five chord. When the "V-I" relationship is used between chords other than the V - I chords the first chord is called the secondary dominant. The second chord could then be thought of as the secondary tonic. It's as if you had a miniature V-I chord progression in a different key between those two chords.

Here's a simple progression of four chords that goes I vi V I.

Here's the same chord progression with the second and third chords preceded by secondary dominants.

Secondary Dominant Example - Naming
Question: Name this chord in the key of G.

The first clue that it's a secondary dominant is the G#
The first clue that it's a secondary dominant is the G#. G# does not naturally occur in the key of G. 1. Find the key where the above chord would be the V or V7 chord. (It's either A Major or A Minor).

2. Find the "target" for this secondary dominant
2. Find the "target" for this secondary dominant. (It's A because A would be the "secondary tonic"). 3. Find the scale degree for the target note. (It's ii).

4. Answer: It's the V65/ii in the key of G.

Secondary Dominant Example - Writing and Playing
Question: Write the V6/vi chord in the key of F. 1. Find the target note. (It's D because that's note vi in the scale of F).

2. Find the V chord in the key of D. (It's A Major).

3. Answer: Write the A chord in first inversion form (V6).

Neapolitan Chords The Neapolitan sixth chord is a first inversion Major chord built on the flat supertonic. The sixth refers to the standard inversion symbol for first inversion. The flat supertonic is the second note of the scale lowered by one half step. For example in the key of C Major, the flat supertonic note would be Db. The N6 chord in the key of C is the first inversion of the Db Major chord.

Neapolitan Usage The Neapolitan sixth chord sometimes substitutes for the IV chord.

Augmented Sixth Chords
Augmented sixth chords are built on the lowered submediant scale degree (flat 6) and get their name from the interval of the augmented sixth that appears between the bottom and the top note of the chord. The different types of augmented sixth chords fill in the middle notes differently.

Italian Augmented Sixth (It+6)
The Italian Augmented Sixth chord is the only augmented sixth chord with three notes. The others have four. The middle note is a major third above the root.

French Augmented Sicth (Fr+6)
The middle two notes of the French Augmented Sixth chord are a major third and an augmented fourth above the root.

German Augmented Sixth (Gr+6)
The middle two notes of the German Augmented Sixth chord are a major third and a perfect fifth above the root. It sounds the same as a Major Minor 7 chord built on the flat six scale degree.

Doubly Augmented Sixth (DA+6)
The middle two notes of the Doubly Augmented Sixth chord are a major third and an augmented fourth above the root. It gets its name from the doubly augmented interval of the fourth between Ab and D# in this example. It also sounds like a Major Minor 7 chord built on the flat six scale degree.

Augmented Sixth Usage Augmented sixth chords typically precede the V chord. Notice how the bottom and top note of the Augmented Sixth chord expand outward by half steps to the root of the V chord.

Neapolitan Aug. Sixth Example - Naming
Question: Name this chord in the key of F.

1. Notice the augmented sixth interval between the bottom and top notes. (It's some type of Augmented sixth.) 2. Identify the type of Augmented Sixth. (It's a French Augmented Sixth chord because the middle two notes have the intervals of a major third and augmented fourth above the root.)

3. Answer: Fr+6

Neapolitan Aug. Sixth Example - Writing
Question: Write an N6 chord in the key of A minor. 1. Find the flat supertonic scale degree. (It's Bb)

2. Construct a Bb major first inversion chord
2. Construct a Bb major first inversion chord. (It's got the third, D, in the bass)

3. Answer:

Music Composition

Reference A Practical Guide to Musical Composition by Alan Belkin, University of Montreal, Canada

Beethoven’s 3rd Symphony (Eroica) 1st Movement

Beethoven’s 5th Symphony 1st Movement

Beethoven’s 5th Symphony 3rd Movement

Beethoven’s 5th Symphony 4th Movement

Beethoven’s 6th Symphony (Pastoral) 1st Movement

Beethoven’s 7th Symphony 1st Movement

Beethoven Piano Sonato #1

Beethoven Piano Sonata #3

Bartok 1st Concerto

Chopin Nocture Opus 32

Dukas l’Apprenti Sorcier

Mozart’s 40th Symphony 1st Movement

Mozart 41st Symphony (Jupiter) 1st Movement

Mozart 41st Symphony (Jupiter) 4th Movement

Ravel Rapsodie Espagnol 1st movement

Ravel Rapsodie Espagnol 2nd movement

Ravel Rapsodie Espagnol 3rd movement

Ravel Rapsodie Espagnol 4th movement

Ravel Bolero

Basics (1) Since music is heard consecutively in time, our examination of the structure of a musical composition will be mainly organized chronologically. We will follow the same path as a listener, examining the structural requirements for beginning, for continuing and developing, and for bringing the work to a satisfactory close.

Basics (2) This mode of presentation deliberately avoids concentrating on conventional "forms", since these principles seem basic to any satisfactory musical construction, always of course within the limits set forth in the introduction.

Foreground vs. Background
All other things being equal, the ear follows as foreground: complexity novelty loudness or timbral richness

Complexity usually the element with the greatest level of activity attracts the most attention, e.g. in a texture consisting of simultaneous held notes and moving lines, the moving lines take precedence.

Complexity Example Beethoven, 6th Symphony, 1st movement, m.115 ff: Here the violin line emerges over sustained pedal tones in the other instruments, due to its greater complexity of pitch, rhythm, and articulation.

Novelty novelty: when presented with familiar and new material at the same time, the new material demands more attention.

Novelty example Ravel, Rapsodie espagnole, "Prélude à la nuit", m. 28: When the new melody arrives at m. 28, it stands out because of its novelty, compared to the four note ostinato that has been playing since the beginning of the piece.

Loudness or Timbrel Richness
loudness or timbral richness: if playing lines of equal complexity in the same register, a trumpet will demand more attention than a flute.

Loudness example Bartok, Concerto for Orchestra, 2nd movement, m. 90: despite a very active accompaniment by the strings in the same register, the main line, played by 2 trumpets, has no trouble emerging clearly.

Unity vs. Variety The temporal nature of music does not permit perception of the whole except in retrospect; or, perhaps more accurately, as an experience spread out over time. Music depends on a web of memories and associations that gets richer as the piece progresses.

Unity Unity is thereforerequired on (at least) two levels:
local flow - the convincing connection of one event to the next -and long range association and overall balance.

Successions of musical ideas can be thought of on a continuum of various degrees of continuity, ranging from the smoothest flow to the most abrupt change. Unity and variety thus emerge not as separate, but rather as different degrees of same thing. If the flow of the piece provides little novelty, the music becomes boring; if there are too many fits and starts, the discontinuities eventually break up the work's coherence.

The composer's first and most fundamental problem is therefore to ensure that the overall flow is not broken from the beginning to the end of the piece. However the degree of novelty must be varied at different points.

The key to controlling this balance between emphasizing common elements and introducing novelty lies in the interaction between the perceptual levels described above.

If the foreground elements are new, the effect will be one of contrast
If the foreground elements are new, the effect will be one of contrast. If the changing elements are more subtle, the listener will sense gradual evolution or relative stability. A convincing musical form is not possible without many degrees of stability and novelty.

Continuity vs. Surprise example
Beethoven, 3rd Symphony, 1st movement, m.65 ff: Here the change to a new motive (with 16th notes) is in the foreground, but the common repeated notes (upper strings and winds) continuing from the previous passage provide an audible link in the background.

Sources of Connection or Novelty
Any audible musical element can participate in creating connection or novelty. Among the most obvious to the listener, and thus the most useful, are: register speed (note values or harmonic rhythm) motives timbre

Register example Ravel, Pavane pour une infante défunte, m. 13: The 2nd theme is quite similar in character to the first theme, but the fact that the oboe opens up a new register (even though the change is quite mild) creates an effect of freshness.

Speed example Beethoven, Sonata, op 2#1, 2nd theme, m. 20ff: Most of the novelty here comes from the accompaniment, which is in steady 8th notes for the first time.

Motives example Brahms, 3rd Symphony, 1st movement, m.3 ff: the arrival of the new theme in vln. 1 provides foreground novelty, while the imitation of the melodic profile of the opening chords (now in the bass) adds an element of continuity in the background.

Timbre example The best example of this Ravel's Bolero: over an extremely repetitive and predictable structure, novelty is mainly the result of timbral variation at each presentation of the theme.

Rate of Presentation of Information (1)
Closely related to the effects of articulation is the issue of the speed at which new elements arrive, and the prominence of the changes: if articulation is brusque, change will be more striking.

Rate of Presentation of Information (2)
In general, the psychological effects of the rhythm of presentation of new information to the listener allow the composer access to a continuum of character effects ranging from very restless to very calm. The quicker the pacing of new events, the more demanding is the job of the listener, and consequently, the more exciting the effect.

Beethoven’s 6th Symphony

I chord in the key of F Major.
III chord in the key of d Minor (melodic) IV chord in the key of C Major. IV chord in the key of C Minor (melodic) V chord in the key of Bb Major. V chord in the key of Bb Minor (harmonic, melodic) VI chord in the key of A Minor (natural) VII chord in the key of G Minor (natural)

CS 791 Multisensory Computing 15 September 2002

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