Intro
Having recently started a music theory course I figured it’d be a good exercise to write up my notes as posts and do a little extra research into the covered topics, perhaps summarising 2-3 weeks of content at a time. We’ll start with a look at notes, intervals, scales and triads.
Notes and Octaves
Sound is created by the movement or vibration of air molecules at specific frequencies, the higher the frequency the higher the pitch.
On an 88-Key Piano the range of frequencies produced is typically from 27.5hz to 4186hz, split across 9 Octaves, within each exist (up to) 12 notes representing specific frequencies. Moving up an Octave doubles the note frequency and moving down halves it.
The table below shows the frequency (Hz) of each note within the 9 Octaves:
| Octave / Note | C | C#/Db | D | D#/Eb | E | F | F#/Gb | G | G#/Ab | A | A#/Bb | B |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 16.35 | 17.32 | 18.35 | 19.45 | 20.60 | 21.83 | 23.12 | 24.50 | 25.96 | 27.50 | 29.14 | 30.87 |
| 1 | 32.70 | 34.65 | 36.71 | 38.89 | 41.20 | 43.65 | 46.25 | 49.00 | 51.91 | 55.00 | 58.27 | 61.74 |
| 2 | 65.41 | 69.30 | 73.42 | 77.78 | 82.41 | 87.31 | 92.50 | 98.00 | 103.8 | 110.0 | 116.5 | 123.5 |
| 3 | 130.8 | 138.6 | 146.8 | 155.6 | 164.8 | 174.6 | 185.0 | 196.0 | 207.7 | 220.0 | 233.1 | 246.9 |
| 4 | 261.6 | 277.2 | 293.7 | 311.1 | 329.6 | 349.2 | 370.0 | 392.0 | 415.3 | 440.0 | 466.2 | 493.9 |
| 5 | 523.3 | 554.4 | 587.3 | 622.3 | 659.3 | 698.5 | 740.0 | 784.0 | 830.6 | 880.0 | 932.4 | 987.8 |
| 6 | 1047 | 1109 | 1175 | 1245 | 1319 | 1397 | 1480 | 1568 | 1661 | 1760 | 1865 | 1976 |
| 7 | 2093 | 2217 | 2349 | 2489 | 2637 | 2794 | 2960 | 3136 | 3322 | 3520 | 3729 | 3951 |
| 8 | 4186 | 4435 | 4699 | 4978 | 5274 | 5588 | 5920 | 6272 | 6645 | 7040 | 7459 | 7902 |
Tones and Semitones (Whole and Half Steps)
The distance between notes can be measured using tones and semitones. A semitone (half step) is the distance between a note and it’s nearest neighbour, for example E -> F, A -> Bb, G# -> G. Whereas a tone (whole step) is a distance two semitones, for example C -> D, G -> F, A -> B.
Intervals
Expanding on Tones and Semitones we can categorise the various distances between note in an octave as Intervals, the table below shows name of the interval and the number of semitones it covers.
| Interval Name | Semitones | Example |
|---|---|---|
| Perfect Unison (P1) | 0 | C -> C |
| Minor Second (m2) | 1 | C -> C# |
| Major Second (M2) | 2 | C -> D |
| Minor Third (m3) | 3 | C -> D# |
| Major Third (M3) | 4 | C -> E |
| Perfect Fourth (P4) | 5 | C -> F |
| Tritone | 6 | C -> F# |
| Perfect Fifth (P5) | 7 | C -> G |
| Minor Sixth (m6) | 8 | C -> G# |
| Major Sixth (M6) | 9 | C -> A |
| Minor Seventh (m7) | 10 | C -> A# |
| Major Seventh (M7) | 11 | C -> B |
| Perfect Octave (P8) | 12 | C -> C (Next Octave) |
It is also possible to add or remove semitones from intervals to produce an Augmented or Diminished interval, for example adding a semitone to the Perfect Unison produces the Augmented Unison, (C -> C#) which is equivalent to the Minor Second.
Major Scale
Scales are collections or sets of notes that follow a pattern of tones starting from a root note and generally fit well together (harmonic).
The Major Scale has the following pattern:
T,T,ST,T,T,T,ST (W,W,H,W,W,W,H)
Where T = Tone, ST = Semi-tone / W = Whole Step, H = Half Step
So, starting from C this produces the following collection of notes:
C,D,E,F,G,A,B
We can apply this pattern to any root note to produce it’s Major Scale, for example D Major
D,E,F#,G,A,B,C#
There are lots of different scales, e.g. Minor, Blues, each with their own pattern.
Triads
A Triad is simply a collection three notes (chord), consisting of a root note, middle note (3rd) and a top note (5th).
Major Triads consist of a Major 3rd Interval from Root to Middle note (C -> E) and a Minor 3rd Interval from Middle note to Top (E -> G), CEG.
Minor Triads consist of a Minor 3rd Interval from Root to Middle note (C -> D#/Eb) and a Major 3rd Interval from Middle note to Top (D# -> G), CD#G.
Quick note: You may also refer to notes based on scale degree rather than interval, the scale degree refers to a note in a scale relative to the root. For example in the C Major scale, C = 1, D = 2, E = 3, F = 4, G = 5, A = 6, B = 7 and C = 8 (Octave up) so we could also say a Major Triad consists of the notes 1,3,5