Music theory handbook

This is intended for my personal use only and they are NOT guaranteed to be 100% correct

reference:

Notes, Scales, Keys

Scale is a way to organize notes into forming a key.
Most common scales minor scale and major scale.
For each key, it has a “center” where it is based on, called tonal center.
Major / minor key formation:
Major scale: 2, 2, 1, 2, 2, 2, 1(return to beginning)
Minor scale: 2, 1, 2, 2, 1, 2, 2(return to beginning), shifted 2 positions from major * 2 is move up 2 notes, called **full step** * 1 is a **half step**
It’s formed like this because notes sound good in this way
The ONLY way to tell a key is Major or minor is to follow that sequence, something starts with G could actually be C major key
Relative keys:
For a major key, it has a related minor key that uses completely all the same notes but sounds different.
- Major -> minor: find 6th note and take its minor key
- minor -> major: move up 3 steps

Perfect Fifth:
- Root + 5th.
- It’s perfect because the frequency ratio is 2:3 and is considered consonant
- Notes with perfect 5 added have more “power” to it and sounds more “rich”
Perfect Fourth:
- Root + 4th (Inverted 5th)
- By itself, it has a tendency to fall to 3rd.
6th & 3rd:
- have the power to determine if the current chord is major or minor
How inversion works in interval:
- [Interval + x = 9] where x is the inverted interval, and the major/minor quality of the interval changes.
  - Eg: minor 6th <–> Major 3rd
  - Except 5th and 4th: Perfect 5th <–> Perfect 4th

For each key, it has a sequence of notes being played that loops (For C Major, it’s CDEFGAB)
On each note of that sequence, there is a related chord that derives from the key ON that note.
The quality of the chord has NOTHING TO DO with quality of the key we are currently using
Notes DO NOT NEED to be in the area on keyboards (C1-B2, C2-B3, …)
- V in C major can be C3, E3, G3 or E3, G3, C4 or G2, C3, E3 …

Types:
- Major chord: root + 3rd + 5th of the Major key that is using root as tonal center. Denoted by M
- Minor chord: root + 3rd + 5th of the minor key that is using root as tonal center. Denoted by m
- Diminished chord: root + 3rd + diminished 5th (a normal 5th down a step). Not widely used. Denoted by dim
In each key, for note I to VI, the quality (major / minor) of chord follows this pattern:
For Major key: M – m – m – M – M – m – dim – M – …
For minor key: m – dim – M – m – m – M – M – m, shifted 2 positions from major
Otherwise, it is unpleasant to hear.
Inversion in triads
What and why
- Reordering notes in a given chord
- This can help create a smoother upward/downward transition between chords
- make the change in notes during a chord progression as little as possible
Types:
- First inversion: move I up an octave. Represented by subscript 6
- Second inversion: move V down an octave / I, III up an octave. Represented by subscript 6/4

Use root, 3rd, 5th, 7th
Types:
Major 7th:
- If the base triad is a major chord, follow the major key and add 7th note of that major key
- add 4 steps from V to get VII, 11 steps from root
- Maj7
Minor 7th:
- If the base triad is a minor chord, follow the minor key and add 7th note of that minor key
- add 3 steps from V to get VII, 10 steps from root
- min7
Dominant 7th:
- When base is a major chord but a minor 7th is added
- “Dominant” because it has a strong tendency to fall back to a more tonic state
- A strong tendency to “resolute” to a more tonic chord.
- Makes people feel alerted?
- Each dominant 7th is related to a particular key.
- Represented by 7
Psycho chord:
- Mainly used in a movie called Psycho
- When base is a minor chord but a major 7th is added
- Not widely used in diatonic chord progression.
- Represented by mM7
Again, this has a pattern similar to that of triad:
For Major keys: Maj7 – min7 – min7 – Maj7 – 7 – min7 – dim7 – Maj7
For minor keys: min7 – dim7 – Maj7 – min7 – min7 – Maj7 – 7 – min7, shifted 2 positions from major

Major Triads:
- M – m – m – M – M – m – dim – M
- I – ii – iii – IV – V – vi – vii^o – I
  - i – ii^o – III – iv – v – VI – VII – i for minor triads
Capitalized numbers: 1, 4, 5 are only in Major triads; 3, 6, 7 are only in minor triads
Major 7th chords:
- Maj7 – min7 – min7 – Maj7 – Dom7 – min7 – dim7 – Maj7
- I7 – ii7 – iii7 – IV7 – V7 – vi7 – vii^o7 – I7
  - i7 – ii^o7 – III7 – iv7 – v7 – VI7 – VII7 – i7 for minor 7th chords
Capitalized numbers: 1, 4, 5 are only in Majors where 5 is Dominant; 3, 6, 7 are only in minors where 7 is Dominant
Chord progression is represented by linking the chords with their corresponding roman numbers
For a given chord pregression, it sounds similar regardless of the current key being used

Cadences: short combinations of chords
- Authentic: V – I
- Plagal: IV – I
- Half: (…) – V
  - Sets the tension
- Deceptive: V – (…)
  - Creates twist
Common progressions:
- I, IV, V
- I, vi, IV, V
- ii, V, i
- I, vi, ii, V
- I, V, vi, IV
- I, IV, vi, V
- I, iii, IV, V
- I, IV, I, V
- I, IV, ii, V
Borrowing:
- For I, vi, ii, V in C major (CM, Am, Dm, GM), Dm can be seen as I of D minor, thus a V of that I can be added (substitute AM with A7), the finalized progression can be (CM, Am, A7, Dm, GM)
- Use the chords of same number in parallel key (CM <–> Cm, DM <–> Dm, …)
Substitution:
- V can be substituted with (G, B, D)
  - bII, the Major chord of 2nd down half a step. Tritonic substitution / Napolitan 6th (Db, F, Ab)
  - V7 (G, B, D, F)
  - Vaug (G, B, D#)
  - Vº7 (G, Bb, Db, E)

Minor scales are sometimes changed in some ways because 5th related chords sound good
(inverted) V-I is good because:
- It has a 7th, which has a strong tendency to fall to 1st
- It has a 5th to 1st motion
- shared 5th
Changed by moving 7th up a half step, and all the chords that used that 7th is changed, resulting in changes in chord patterns:
Changed to m – º – + – m – M – M – º – m
- Where + is moving the 5th in that major triad up a half step
When building melodies, 6th is also raised half a step to avoid the gap btwn 6th and 7th being to big

It can show how “similar” are two keys
- “similar” in the sense of sharing same notes
- The most similar keys are always a 5th away, hence the name
Can choose chords in similar keys when needed
But not changing keys