Chapter 5 - Harmonic Organization 1: Intervals, Triads, and Seventh Chords

• Harmony - The way notes are simultaneously sounded, creating a vertical element to music.
• Counterpoint - A single melody line or linear voice added to another line or voice.

Intervals

• Interval - The distance between two pitches.
  • They can be melodic or harmonic.
  • The exact interval size is described by quantity and quality.
  • Quality - Expressed by a number and determined by counting the distance between one letter name and the next letter name.

Identifying Interval Quality

• All intervals built from the tonic up to notes within a major scale are either major or perfect.
• Perfect intervals
  • Unison
  • Perfect fourth
  • Perfect fifth
  • Perfect eighth
• Major intervals
  • Major second
  • Major third
  • Major sixth
  • Major seventh
• A minor interval is one-half step smaller than major.
• Diminished interval - An interval that is one-half step smaller than perfect or minor.
• Augmented interval - An interval that is one-half step larger than major or perfect.
• Enharmonic intervals - They sound the same but are spelled differently and function differently.
• Doubly augmented interval - When a major or perfect interval is made one whole step larger without changing the letter names of the pitches.
• Doubly diminished interval - When a minor or perfect interval is made one whole step smaller without changing the letter names of the pitches.

If-Then Intervals

• If the top note is in the major key of the bottom note, then it is major or perfect.
• If the top note is a half step lower than the diatonic note would be, then it is a minor or diminished interval.
• If the top note is a half step higher than the diatonic note would be, then it is an augmented interval.
• If an interval is perfect, then both top and bottom pitches are in the other’s major key.
• If the same accidental is added to both upper and lower pitches, then the interval remains the same.
• If an accidental is added only to the bottom pitch, then the accidental has the opposite effect than when added to the note above:
  • If a flat is added to the lower pitch, the interval is larger.
  • If a sharp is added to the lower pitch, the interval is smaller.
• If the lower notes doesn’t represent a standard key, then determine what the interval would be without the accidental and adjust.

• Simple intervals - Intervals that are one octave or smaller in quantity.
  • They are expanded to a compound interval by adding seven
• Compound intervals - Intervals that are larger than an octave.
  • They are reduced to a simple interval by subtracting seven.
• Inverted intervals - Intervals are inverted by transferring the lower note an octave higher or by transferring the higher note an octave lower.
  • Major intervals invert to minor intervals.
  • Augmented intervals invert to diminished intervals.
• The rule of nine - When any simple interval is inverted, the sum of the ascending and descending intervals must add up to nine.
  • A second inverts to a seven.
  • A third inverts to a sixth.
  • A fourth inverts to a fifth.
• Consonant intervals - Stable
• Dissonant intervals - Unstable, the impression of activity or tension.
• Resolution - The motion of the dissonant interval to the consonant that acts as its goal.
• Within any four-part composition, these intervals may exist:
  • A-S, Alto and Soprano
  • T-S, Tenor and Soprano
  • T-A, Tenor and Alto
  • B-S, Bass and Soprano
  • B-A, Bass and Alto
  • B-T, Bass and Tenor

Triads

• Chord - A group of pitches that forms a single harmonic idea.
• Triad - A three-note chord made up of two intervals stacked in thirds.
• Root - The lower note of the chord.
• Third - The middle note because it’s an interval of a third above the root.
• Fifth - The upper note, it’s a fifth above the root.

Building Triads

• Tertian harmony - Harmony built on thirds.

• To build a triad:

  • Build the snowman in thirds above the root.

  • Identify the quality of the lower third as a major or minor.

  • Identify the quality of the fifth as perfect, diminished, or augmented.

  • Identify the chord with the pitch name letter (the root of the snowman).

  • Identify the quality of the triad

    

  

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