Music Theory

Notes and the Clefs

Notes

    The piano started at C1 before A and B were added, so in order of the piano, the octaves start at C.

    ex. A3 B3 C4 D4 E4 F4 G4 A4 B4 C5

Treble Clef

    The spiral circles around G

Bass Clef

    The two dots are on either side of F

Alto Clef

    The wherever the middle of the clef symbol is, is middle C (C4)

Time Signatures

Simple meter: the numerator beat is divisible by 2 eighth notes (1, 2, 3, 4, 8)

Compound meter: the numerator beat is divisible by 3 eighth notes (6, 9, or 12)

Duple - 2 pulses

Triple - 3 pulses

Quadruple - 4 pulses

Scales and Key Signatures

tonic - supertonic - mediant - subdominant - dominant - submediant - leading tone(subtonic m) - tonic

  1^ 2^ 3^ 4^ 5^ 6^ 7^ 8^

Transposition- preserves scale intervals while shifting to a new pitch level

    Major

W-W-S-W-W-W-S

    Minors

1. Natural minor

W-S-W-W-S-W-W

2. Harmonic minor

Raise the 7th scale degree a semitone

The 6th and 7th scale degrees create an augmented 2nd

3. Melodic minor

Ascending- Raise the 6th and the 7th scale degrees

Descending- Revert back to natural minor scale

Circle of Fifths

Flats get added → BEADGCF ← sharps get added

With every counterclockwise turn around the circle, the tonic pitch descends five steps and one flat is added (one sharp is taken away)

With every clockwise turn around the circle, the tonic pitch ascends five steps and one sharp is added (one flat is taken away)

Relative key: major and minor keys with the same key signature

Parallel key: major and minor keys with the same tonic

• Scale degrees 3, 6, and 7 are a semitone lower in the parallel minor

Identifying Keys

    Look at the key signature to narrow down options to one major and the relative minor

    Look for accidentals (is it a type of minor or are the accidentals random?)

    Look at the highest note in the treble line and the lowest note in the bass line, what is the arrival note?

    Do the accidentals agree with either the major or minor scale, or does it align with a different key?

    Collect the notes you see and line them up to create a scale, identify a potential matching scale

Writing Chords from Keys

• Look at the key and determine the root from the roman numeral (ex. D: IV is key of D major and the fourth chord, so we know the root of the chord is the fourth note, G)

• Spell out the rest of the chord in it’s root position (ex. IV is major so spell a perfect fifth and a major third from G)

• Adjust notes up or down the octave to fit the figured bass notation (ex. a 6 marking means the third of the chord is now the root)

Intervals

Interval: A distance between two notes

• Named after how many lines and spaces the interval spans

    ex. an interval spanning two lines and spaces is a second

• Size: Total number of lines and spaces spanned between the two notes including where the notes rest

• Quality: Precise number of semitones between the two notes

Harmonic interval: Two notes played at the same time (harmony)

Enharmonic interval: Same number of semitones, different number of scale steps (at least one is dissonant)

Natural interval: Written without intervals, only white notes are played

Inverted interval: Two notes are reversed in position (one moves up an octave or one moves down), done by dividing the octave into two smaller parts

• When an interval is inverted, the sizes add up to nine

  • A second inverted turns into a seventh, a fourth inverted turns into a fifth, a sixth inverted turns into a third…

Melodic interval: Two notes are played one after the other (melody)

Simple interval: The interval notes fit within an octave

Compound interval: The interval is farther than an octave

Numerical interval

    1. Major/minor

• 2nd, 3rd, 6th, 7th

Major intervals contain one more semitone than the minor interval

• In a major scale, all intervals after the tonic are either major or perfect

• In a minor scale, all intervals after the tonic are either minor or perfect except for the major second between scale degrees 1 and 2

Augmented interval contains one more semitone than the major

Diminished interval contains one less semitone than the minor

    2. Perfect

• unison, 4th, 5th, 8th(octave)

Augmented intervals contain one more semitone than the perfect interval

Diminished interval contains one less semitone than the minor

Consonant Intervals:

• Major and minor 3rds and 6ths, perfect 5ths and 8ths (perfect 4ths are context-dependent)

• Considered ‘resting points’; all other intervals are considered dissonant

    Perfect consonances: perfect unisons, perfect fifths, perfect octaves

    Imperfect consonances: major and minor thirds and sixths

Determining Interval

1. Odd or even

Odd: Both notes are on lines or both notes are on spaces

Even: One note is on a line, one note is on a space

2. Size

How many semitones are within the interval

ex. five lines and spaces = fifth

3. Quality

What can the interval be based on size

ex. a 6th can only be major, minor, augmented, or diminished, but not perfect

4. Scale

Think of the low note of the interval as the tonic of a major scale and check if the higher note is included in that scale’s key signature

ex. E and C# —> E major has four sharps and C# is one of them. Intervals in major scales are either major or perfect and since E and C# is a 6th, it can’t be perfect, making E and C# a major 6th (M6)

Triads

Triad: A chord made up of three notes 5/3

• Can be major, minor, augmented, or diminished

  • Major and minor triads have a perfect fit between the root and the fifth, the quality comes from the quality between the root and the third

    • Perfect fifth = major or minor, minor third= minor triad, major third= major triad

  • Augmented and diminished chords have major and minor thirds between the root and the third, so name comes from the quality of their fifth

    • Augmented or diminished fifth= augmented or diminished triad, minor third=diminished triad, major third=augmented triad

Chords in a Major Key: I ii iii IV V vi vii^o VIII

Chords in a Minor Key: i ii^o III iv v VI VII viii

Determine triad

• determine quality of the fifth

• determine quality of the third

Writing triads

• write the root

• write a stack of generic thirds above the root

• adjust the fifth with an accidental as needed

• adjust the third with an accidental as needed

degree symbol = diminished

+ = augmented

Inversions

• When the root note is in the lowest/bass position, the triad is in root position

• The triad is considered to be inverted when the lowest note is not the root note

  • Bass vs. Root

    • Bass=lowest sounding note in a chord

    • Root=foundation of the chord, bottom note in root position (stacked thirds)

  • Identifying/writing inversions

    • Bass note is the one that matters

    • Upper voices can be any order or spacing

  • Figured bass- intervals above the bass

    • Root position (5/3) - “ending” “most stable”

    • First inversion 6/(3) - “middle” “going somewhere”

    • Second inversion 6/4 - “least stable”

Determined only by the lowest note of the triad

• Third of the triad as the bass = first inversion, creating a third and sixth above the bass 6/3

• Fifth of the triad as the bass = second inversion, creating a fourth and a sixth above the bass 6/4

• Figured bass symbols: intervals above the bass

Recognizing inverted triads

• move the notes around (octaves) to create a root position triad

• identify the position of the bass

Writing inverted triads

• spell out the chord

• determine which note of the triad needs to be the lowest

Seventh Chords

Four notes stacked in thirds

Quality is determined by the triad quality and the seventh quality

Triad quality is written first, and then seventh quality

Inversions

When the root note is at the bottom, the seventh chord is in root position, shorthand 7 (7/5/3)

When the third of the seventh chord is at the bottom, the chord is in first inversion, shorthand 6/5 (6/5/3)

When the fifth note is on the bottom, the chord is in second inversion, shorthand 4/3 (6/4/3)

When the seventh note is on the bottom, the chord is in third inversion, shorthand 4/2 (6/4/2)

Chords on the Grand Staff

SATB/Chorale style

Written for singers: sopranos, altos, tenors, and basses

Each singer has their usual range, so keep that in mind when writing for each part

Stems for each voice alternate: bass and alto stems point downwards, tenor and soprano stems point up

• Spacing

  • Upper voices should be no more than an octave away from the next closest voice

  • Soprano and alto voices should be within an octave of each other, alto and tenor voices should be within an octave of each other

  • The distance between tenor and bass is unrestrained as long as they fall within their usual ranges

  • Soprano should always be written above or in unison to the alto voice even though the ranges overlap, alto always above or in unison to tenor, and tenor always above or in unison to the bass

Keyboard style

Right hand takes upper voices while left hand plays bass

• Spacing

  • Soprano and tenor distance should not be more than an octave

  • Distance between bass and tenor is unrestrained

Comparison

Realizing Chords from Roman Numerals

1. Spell out chord using letter names'

2. Determine the inversion and the bass note

3. Write the bass note on the staff

Doubling guidelines for triads (three notes but writing for four voices)

Root position: double the bass

First inversion: double any note*

Second inversion: double the bass

    *Never double the leading tone of the key or any chordal dissonance

4. Write the remaining notes in any voice as long as it fits within the proper range

Writing Chords from Figures

The figures represent the intervals above the bass

There can be accidentals that tell you to raise or lower a given note above the bass, an accidental with no figure means it applies to the third above the bass

Notes above the bass do not have to follow the order given in the figure

Voice Leading

Motion

Contrary: Voices moving the opposite direction

Oblique: One voice stays the same, the other moves

Parallel: Same direction in the same intervals

Similar: Same direction, but not identical intervals

    Guidelines

Contrary motion is preferred, mainly between the outer voices (bass and soprano)

Oblique and stationary motion are okay, especially between the middle voices (tenor and alto)

Parallel thirds and sixths are good, parallel perfect fifths and octaves are evil

Avoid similar motion when approaching a perfect interval unless the upper voice moves by a step

No hidden or direct octaves

Upper voices should move smoothly, avoid leaping more than a sixth (leaping in upper voices is okay in sustained chords though)

Avoid augmented intervals between chords

Avoid making the bass leap more than a seventh

Avoid approaching the leading tone with an ascending melodic leap of more than a third

If the leading tone appears in an outer voice, the next chord has to have that voice going up to the tonic, inside voices having the leading tone don’t need to go a step up to the tonic

Chordal sevenths should resolve a step down in any voice (can be shifted to another voice/register and then resolved down, can be repeated and then resolved down)

Musical Narratives

Phrase: basic unit of tonal music communication, a complete thought, a musical sentence

Cadence: musical punctuation, the closing harmonic/melodic/rhythmic material

V → I = authentic cadence, ends at home (tonic) (like a period)

    Perfect (final/complete): ends with root position V/V7 and root position tonic; soprano ends on DO (tonic)

    Imperfect: incomplete in some way, usually either the soprano doesn’t end on the tonic or the dominant isn’t root position V/V7

→ V = half cadence, ends away from home (dominant) (like a question mark)

Not all V → I are cadences, look for where it makes sense (usually pauses, endings, etc)