Theory

Ratios in music

Music is all about ratios

The choice of 12 semitones per octave comes from the fact that going up 12 "perfect fifths" (3:2 ratio) is almost exactly the same as going up 7 octaves (2:1 ratio)

the chromatic semitones are equally spaced by have each note be the same ratio higher than the preceding note, so that the product of 12 of these ratios equals 2:1 (octave) exactly.
- Mathematically this ratio is the twelfth root of 2.

Tonic

Music is built around the tonic. Some notes are ok with being away from the tonic, but others give a strong push towards ending up at a tonic. Notably, the leading tone of a scale wants to point back to the tonic. If the tonic is the most grounded note of the spectrum, then the leading tones serve to add gravity to the music. That is, they send the progression back to the tonic center.

Metronome

The goal of playing with a metronome is not to rely on it, it's to develop your internal sense of space and time

try setting your metronome on beats 2 & 4, which forms the backbeat of most popular music. Then, try setting it only on beat 4. Then try putting it on the "and" of beat 4. Then try putting it on the first beat of every second bar. Doing this allows you to really feel the space between the beats and how the music fits in it.

The root of the relative minor is 3 semi tones below the root of the relative major

ex. A minor is relative minor of C major because A is 3 semi tones below C

Plagal cadence - when IV (subdominant) chord resolves to the I (tonic)

Functions

From Function

Go to text →

A function describes the relationship between a chord and a tonal center, all in the context of the harmonic progression.

Tonic function

stable chords of a key.
In major: I iii vi. They are stable because their triads (ex. C E G) all contain the key's third scale degree (ex. Here, all C E and G chords contain an E).
In minor: i ♭VI⁶ ♭III Has 3rd but no 4th

The third is the most important note for defining the scale's overall sound (modality)

Subdominant function

bridge chords between other 2 functions. These chords take you away from home rather than lead back home.
In major: ii IV. How these chords feel changes depending on if we are using triads or 7th chords. The IV triad contains the root of the key, giving it a little more stability. Meanwhile, the ii lacks the root, making it sound more adrift. The 7th of that chord happens to be the tonic, giving it more stability
Has 4th but no 7th
Chord contains the tonic note of the mode (c)

Common melodic resolutions are 5 -> 1, 2 -> 1, 7 -> 1

In minor, the 4th is usually a iv⁷

Dominant function

unstable chords that provide tension and point back to tonic. Main engine that drives songs forward.
- it is unstable because of the characteristic leading tone
in the major scale, if we add a 7th it adds even more instability, thus making it have more gravity in wanting to point back to the tonic (ie. it makes the dominant function of the V scale even more dominant by making it a V⁷)
- ex. In C Major, it doesn't matter if we use a G or a G7 as our V chord, since both of them contain a B, which is the leading tone (ie. 7th scale degree) of the C Major mode.
In major: V vii°. They both contain the 7th (leading tone) and 2nd degree of the scale. These notes circle around the tonic and want to collapse in toward it.
Has 7th but no 3rd

Playing the V keeps the music from resolving

In Minor

In minor keys, though, we actually have two forms of the seventh scale degree:

Natural minor: The seventh degree is a whole step below the tonic (e.g., in A minor, it’s G). This G doesn’t have the same strong pull towards A; instead, it has a more subdued, ambiguous sound.
Harmonic minor: To create a similar tension to major keys, we raise the seventh scale degree to create a half-step leading tone (e.g., G# in A harmonic minor). This leads to a V7 chord that can still pull strongly toward the tonic in a minor key (E7 in A minor, for instance).
Doesn't really exist in natural minor, because there is no leading tone in minor, which dominant needs. However, the harmonic minor scale does include a leading tone, which effectively brings back the sense of wanting to resolve to the tonic.
- this is only partially true, because the V chord can still create tension to make us want to return to a i. It all depends on context really.

Scales

Children