Harmony and Chords

Harmonies

  • Polyphony: more than one note being sounded at a time

  • Can get a long ways with a MiniMoog playing monophonic, but even then a band is helpful, so probably polyphony

  • A bunch of the scale setup — in particular, "equal temperament" — is desiged to make polyphony sound good

Consonant Intervals

  • In a major scale

    • Third (four steps up from root) is roughly 5/4 the frequency of the root

    • Fifth (seven steps up from the root) is roughly 3/2 the frequency of the root

    • These intervals have a reasonably regular wave structure with periods 4 and 3 root cycles respectively, so sound "pure"

  • In a minor scale

    • Minor third (three steps up from the root) is roughly 6/5 the frequency of the root with period 5
  • Note the "roughly": the equal temperament compromise means that these frequencies are a little off and periods are thus long

  • Thirds are particularly bad, being about 1% (1 cent) off. This would be considered borderline "out-of-tune" for a guitar

The Guitar Fretboard

  • Let's look at a guitar fretboard

  • Note that the spacing of frets is not even. Why?

  • Note that a third is 1/6 of the way down a string, and a fifth 1/3 of the way

  • Markers are at the minor third, fourth, fifth, sixth intervals, double marker at the octave, then repeat

  • Intonation: adjust the length of each string at the bridge to make the marker positions right — different from tuning by adjusting string tension

  • Pickup position matters (hence two sets of pickups) — why?

The Tritone Chord

  • There can be only one — well, one major, one minor

  • 1-3-5 major, 1-3♭-5 minor

  • Note that we have abandoned note names here: a "C major chord" and a "D♭ major chord" have frequencies in the same relationship, but with a different base pitch

  • In other words, we pick a scale, then use the root, third and fifth notes of that scale to make a tritone chord

Roman Numeral Notation

  • Step 1: pick a scale (key)

  • Notate the tritone major chord starting at the root as I

  • The tritone minor chord is i (lowercase I)

  • There are (obviously) tritone chords that start on each note in the scale: notate these I, II, III, IV, V, VI, VII

  • Except typically you make the chords out of notes in the scale, so the normal thing would be I, ii, iii, IV, V, vi and…uh vii°

  • vii° is a "diminished tritone": 1-3♭-5♭ (starting from note 7)

  • For minor scale would be i, ii°, III, iv, v (or V in classical), VI, vii°

What Do Chords Sound Like?

  • Major chords sound happy, minor chords sound sad

  • Diminished chords are kind of spooky and mysterious-sounding

  • (The "augmented tritone" 1-3-5♯ sounds like it's going somewhere — you'll hear it occasionally)

Octaves and Inversions

  • It is common to use octave notes of the tritone to add to a chord, either above or below. A big "chord stack" is its own thing

  • It matters which note is on top in a tritone chord:

    • 5 on top is the "root chord": 1-3-5 notated e.g I

    • 1 on top is the "first inversion": 3-5-1 notated e.g. $I^6$

    • 3 on top is the "second inversion": 5-1-3 notated e.g. $I^6_4$

Adding Notes

  • A common addition to a tritone is the 7 tone of the scale, either flatted ("natural seventh") or not ("major seventh")

  • The are several different Roman Numeral conventions floating around for sevenths: see this chart for one such

  • The inversion notation gets messy; let us not care

  • The 9 tone, 11 tone, 13 tone may be added for increasing dissonance. This is mostly a jazz thing

More About Minors

  • "Relative minor" starts on 6 of major: has same key signature

  • "Parallel minor" starts on 1 of major: has different key signature

  • (Other minors start on other tones)

Pop

  • Cast a big net here: Pop intermingles with Rock, Rock is inspired by world rhythms, Blues, Jazz, and (yes) Country

  • Pop is noted for its simplicity: I, IV, V chords dominate, vi, ii, iii (or III) (relative minor) chords are frequent

  • Pop is typically not notated with Roman Numerals, but with named chords in a particular key. Often a melody in standard musical notation is used — a "lead sheet"

  • Even when full music is provided, the lead line (melody) will typically be on a separate staff, and the lettered chords will be included

  • Here's an example: Let My Love Open The Door by Pete Townshend

  • The bass line is also commonly included. Pop bass line is often just root note of current chord, in rhythm

  • More could be said about bass, but time…

Chord Motifs Are Reused In Pop

  • Many of you will have seen

    by Axis of Awesome. Let's see if we can get something more out of it

  • Common Pop chord progressions

    • Four Chords: I-V-vi-IV

    • Blues: I-IV-I-V-IV or so

    • 50s: I-vi-IV-V

    • Pachelbel: I-V-vi-iii-IV-I-ii-V

    • many more

Pop, Key Changes, and the Circle Of Fourths

  • We are playing in equal temperament so that we can shift keys during a piece

  • Common pop motif: jump up the circle of fourths 1-4 steps, eventually walk back down or jump back

  • Dark Side of the Moon by Pink Floyd:

    • Verse: I-IV7-I-IV7-I-I7-IV-iv-V-V7-I

    • Chorus: IV-V-♭VI-IV (repeat)

Fancier Pop Chords

  • It's not all just formulaic: some songs have really fancy chords

  • I'm a big fan of Supertramp: they do a bunch of this stuff — diminished chords, diminished sevenths, fancy key changes, etc

Computer Things

  • When analyzing music:

    • Be aware that a lead sheet is a viable product

    • Chords are hard to sort out of pop music, since there's so much other noise and so many harmonics for each note (freakin' guitars)

    • Top note is usually melody, bottom note is usually bass and gives tonic of chord

  • When generating music:

    • Chords come first, bass second, melody third

    • The melody should be in the scale corresponding to the chord: some "accidentals" are fine

Captain Obvious Says

  • This is just a starting point: go find out more things

  • "To the Obviousmobile" (gets in Obviousmobile)

Last modified: Thursday, 23 May 2019, 12:30 AM