# 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 Basic Three-Note 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 chord

# Roman Numeral Notation

• Step 1: pick a scale (key)

• Notate the major chord starting at the root as I

• The minor chord is i (lowercase I) of a minor scale

• There are major 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 chord": 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 chord" 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 chord 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 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. $I^6_4$

• A common addition to a chord 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

• "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 Four Chords 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)