This is the second part in a series I’m writing on basic music theory, following my page on rhythm. It’s aimed primarily at people that want to learn how to write music. Most guides I’ve found assume the reader plays a specific instrument (or any instrument), but modern DAWs make it entirely possible for someone to compose music without playing an instrument. Although I do recommend learning an instrument to anyone who becomes serious about composing, having a basic grasp of music theory beforehand will make learning an instrument much easier, and it may even give you a better idea of what instruments you’d enjoy learning. In any case, my aim here is to make music theory accessible to everyone, regardless of prior musical experience or lack thereof.
This page assumes you’ve familiarized yourself with part one’s Basic Rhythmic Concepts and have at least a basic grasp of time signatures (though you needn’t be able to identify them by ear). It introduces the treble and bass clefs and their pitches; diatonic major and natural minor scales; major, minor, diminished, and augmented chords; a key’s tonic, subdominant, and dominant chords; sharps, flats, and naturals; and key signatures. It’s also a work in progress; I’ve uploaded it to make it easier to solicit feedback from people on its comprehensibility. Expect the final version to be substantially different; it may in fact be multiple pages.
I wrote on my page about rhythm that a note’s height signifies its pitch; the type of note signifies its duration. I was oversimplifying slightly, though: to the left of the musical staff, you’ll see a symbol called a clef. By far the most common of these are the treble clef (𝄞) and the bass clef (𝄢).
The clef you see affects what pitch values are written on the staff. In the treble clef, from bottom to top, the five lines represent the notes E, G, B, D, and F, for which Every Good Boy Deserves Favor is commonly used as a menomnic. The spaces in between the lines are F, A, C, and E, which serve as their own mnemonic.
The bass clef’s notes are, from bottom to top, G, B, D, F, and A, for which the similar mnemonic Good Boys Do Fine Always is used. The spaces are A, C, E, and G, for which the mnemonic All Cows Eat Grass is often used.
The clef is usually found at the left of a musical score, like so:
This is the C♯ major scale, starting on C♯4, the note immediately above middle C. But we’re getting ahead of ourselves. We need to start with an explanation of pitch.
The vast majority of Western music uses what’s referred to as twelve-tone equal temperament. Scientifically, this means every octave is subdivided into twelve equal ratios – more specifically, for those of you mathematics nerds out there, each note’s pitch is exactly 2¹⁄₁₂ (≈1.05946309436) that of the note a half-step below it. If that doesn’t make sense to you, don’t worry; you needn’t understand advanced mathematics to play or write music, though I’ll use some simpler mathematics to explain harmony and dissonance later.
Although the octave is divided into twelve notes, most Western music uses a scale that selects only seven of those notes for the majority of its melodies and harmony. The white notes on the piano correspond to the C major scale (or, alternately, the A natural minor scale). The table below has these highlighted.
| C major within the chromatic scale | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| B♯/C | C♯/D♭ | D | D♯/E♭ | E/F♭ | E♯/F | F♯/G♭ | G | G♯/A♭ | A | A♯/B♭ | B/C♭ |
This immediately raises two questions:
I’ll answer these in the reverse order.
♯, the sharp symbol, raises a note a half-step above its normal value (e.g., A → A♯). ♭, the flat symbol, lowers it a half-step below its normal value (e.g., A → A♭). ♮, the natural symbol, negates either of these symbols and sets a note back to its non-sharp, non-flat value.
If any of the above symbols appears immediately to the left of a note, it’s considered an accidental and lasts until the end of a measure. There are different rules if they are set in the key signature, ordinarily seen immediately to the right of the clef. The key signature applies to all notes of a given pitch (thus, in a key signature specifying an F♯, all Fs become F♯s unless otherwise specified). Generally, naturals aren’t specified in a key signature, but sometimes the key signature changes mid-song (which is called modulation). In such cases, naturals may be specified (although they don’t have to be). Key signature modulation is almost always preceded by a double bar (𝄁), after which the new key signature is declared.
The key signature provides a useful sort of shorthand for musicians. If we had to specify F♯ every measure, not only would it be repetitive, but once an F♮ finally occurred, it’d be a musical Boy Who Cried Wolf of sorts – our brains would have gotten so used to the F♯ that they’d just fill it in. Key signatures and accidentals notate a piece’s most commonly used pitches more logically and concisely while making its outliers stand out more.
This, in turn, is part of why most of the notes have two names: raising C by half a step and lowering D by half a step are two ways to refer to the same pitch, but they’re semantically different: the key signature of the passage affects which one is more logical to use (it wouldn’t make sense to use both F♯ and G♭ in the same measure). D, G, and A are the only notes with a single name because they’re the only ones sandwiched between two black piano keys. Here are the notes again; this time, white piano keys have lighter backgrounds.
| The white keys on the piano | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| B♯/C | C♯/D♭ | D | D♯/E♭ | E/F♭ | E♯/F | F♯/G♭ | G | G♯/A♭ | A | A♯/B♭ | B/C♭ |
And here’s a third presentation, with only one name for each white key.
| The white keys on the piano, simplified | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| C | C♯/D♭ | D | D♯/E♭ | E | F | F♯/G♭ | G | G♯/A♭ | A | A♯/B♭ | B |
Again, the highlighted keys correspond precisely to the C major scale. Scales using the same ratios as C major are referred to as diatonic major scales, meaning they feature the following intervals in the following order:
| Diatonic major scale intervals | ||
|---|---|---|
| # | Interval | Notes |
| 1 → 2 | WHOLE STEP | C → D |
| 2 → 3 | WHOLE STEP | D → E |
| 3 → 4 | half step | E → F |
| 4 → 5 | WHOLE STEP | F → G |
| 5 → 6 | WHOLE STEP | G → A |
| 6 → 7 | WHOLE STEP | A → B |
| 7 → 1 | half step | B → C |
Each scale, in turn, has modes, or variants starting from different notes of the scale. The diatonic major scale is also called Ionian mode; the other ubiquitous mode is Aeolian mode, or the natural minor scale, which starts at the major scale’s sixth degree (A, in the case of C major) and runs up an octave to the next A:
| Natural minor scale intervals | |||
|---|---|---|---|
| Major # | Minor # | Interval | Notes |
| 6 → 7 | 1 → 2 | WHOLE STEP | A → B |
| 7 → 1 | 2 → 3 | half step | B → C |
| 1 → 2 | 3 → 4 | WHOLE STEP | C → D |
| 2 → 3 | 4 → 5 | WHOLE STEP | D → E |
| 3 → 4 | 5 → 6 | half step | E → F |
| 4 → 5 | 6 → 7 | WHOLE STEP | F → G |
| 5 → 6 | 7 → 1 | WHOLE STEP | G → A |
I’ve written a of the diatonic major scale’s modes, but it’s quite technical and advanced and may not be entirely comprehensible without more theory knowledge. In brief, the diatonic major scale’s seven modes are:
| Modes of the C major scale | ||||||||
|---|---|---|---|---|---|---|---|---|
| # | Name | 1→2 | 2→3 | 3→4 | 4→5 | 5→6 | 6→7 | 7→1 |
| 1 | Ionian | W | W | h | W | W | W | h |
| 2 | Dorian | W | h | W | W | W | h | W |
| 3 | Phrygian | h | W | W | W | h | W | W |
| 4 | Lydian | W | W | W | h | W | W | h |
| 5 | Mixolydian | W | W | h | W | W | h | W |
| 6 | Aeolian | W | h | W | W | h | W | W |
| 7 | Locrian | h | W | W | h | W | W | W |
| Modes of the C major scale | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| # | Name | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 1 |
| 1 | Ionian | C | D | E | F | G | A | B | C |
| 2 | Dorian | D | E | F | G | A | B | C | D |
| 3 | Phrygian | E | F | G | A | B | C | D | E |
| 4 | Lydian | F | G | A | B | C | D | E | F |
| 5 | Mixolydian | G | A | B | C | D | E | F | G |
| 6 | Aeolian | A | B | C | D | E | F | G | A |
| 7 | Locrian | B | C | D | E | F | G | A | B |
The word chromatic is derived from the Greek word ΟΟΟΞΌΞ±ΟΞΉΞΊΟΟ (romanized: khrΕmatikΓ³s), meaning either relating to colour or relating to one of the three types of tetrachord in Greek music. Bearing this in mind, it occurs to me that some readers may find it helpful to see the chromatic scale’s twelve degrees represented with twelve equally spaced Oklab hues: C, C♯/D♭, D, D♯/E♭, E, F, F♯/G♭, G, G♯/A♭, A, A♯/B♭, B.
| Modes of the C major scale | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| # | Name | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 1 |
| 1 | Ionian | C | D | E | F | G | A | B | C |
| 2 | Dorian | D | E | F | G | A | B | C | D |
| 3 | Phrygian | E | F | G | A | B | C | D | E |
| 4 | Lydian | F | G | A | B | C | D | E | F |
| 5 | Mixolydian | G | A | B | C | D | E | F | G |
| 6 | Aeolian | A | B | C | D | E | F | G | A |
| 7 | Locrian | B | C | D | E | F | G | A | B |
Notes are sometimes followed by numbers that represent what octave they belong to. C4 is defined as middle C. Since the diatonic major scale is considered the center of Western harmony, and the white keys on the piano are in turn given foremost importance, the note below C4 is not B4 but B3. (This should qualify as a violation of the Geneva convention against OCD sufferers.) The note above C4, meanwhile, is C♯4. Thus, the entire chromatic scale goes C4, C♯4, D4, D♯4, E4, F4, F♯4, G4, G♯4, A4, A♯4, B4, C5.
It may be helpful to understand that octaves are based on the fundamental ratio of 2:1. That is, Western music defines the pitch of A4 as 440 Hz. A3, found an octave below A4, is 220 Hz, or 440 / 2. A5, found an octave above A4, is 880 Hz, or 440 * 2. Several other foundational intervals approximate other superparticular ratios; these ratios were first specified by the Pythagoreans approximately 25 centuries ago.
In the following table, “P” stands for “Pythagorean” (i.e., the “ideal” ratios), “M” for “Modern” (i.e., the twelve-tone equal temperament employed by modern tuning), “R” for “Ratio”, and “Q” for “Quotient”. Mathematics nerds may find it interesting that our modern twelve-tone equal temperament is within about 0.0015 of the Pythagorean ratios for perfect fourths and fifths, while its ratios for the major and minor third are off by approximately 0.01.
| Mathematical Foundations of Harmonic Intervals | |||||
|---|---|---|---|---|---|
| Interval | PR | PQ | MR | MQ | Difference |
| Perfect fifth | 3:2 | 1.5 | 2⁷⁄₁₂ | ≈1.49830707688 | ≈-0.00169292312 |
| Perfect fourth | 4:3 | 1.3333… | 2⁵⁄₁₂ | ≈1.33483985417 | ≈0.00150652083 |
| Major third | 5:4 | 1.25 | 2¹⁄₃ | ≈1.25992104989 | ≈0.00992104989 |
| Minor third | 6:5 | 1.2 | 2¹⁄₄ | ≈1.18920711500 | ≈-0.01079288500 |
In short, the ear finds these superparticular ratios pleasing. However, drifting too far from these fundamental ratios results in dissonance. The tritone, which is simply a √2:1 ratio, is so dissonant that it historically was the interval most commonly called diabolus in mūsicā (Latin: “the devil in music”), although contrary to popular belief, it was never banned, nor could composers be excommunicated just for using it. Jazz bassist and music theorist Adam Neely has called the minor ninth the most dissonant interval; its ratio is 2¹³⁄₁₂:1 (≈2.11892618872).
However, understanding harmony and dissonance doesn’t require fully understanding the mathematics behind them. It can help, but the important point is this: the ear finds octaves, perfect fifths, perfect fourths, and thirds pleasing, while intervals that stray too much from these in specific ways feel unsettling. A few examples:
A suspended second (sus2) chord (e.g., C4, D4, and G4) consists of a major second (e.g., C4 to D4), a perfect fifth (e.g., C4 to G4), and a perfect fourth (e.g., D4 to G4). The first of these intervals is somewhat dissonant, but the other two intervals are consonant enough to make the chord harmonic overall.
However, this chord also carries with it an expectation of a resolution. Since it does not clearly establish tonality, it is usually followed by a resolution to either its respective major or minor chord.
A suspended fourth (sus4) chord (e.g., C4, F4, and G4) consists of a perfect fourth (e.g., C4 to F4), a perfect fifth (e.g., C4 to G4), and a major second (e.g., F4 to G4). Everything said above about the suspended second chord also applies to the suspended fourth.
This list omits an important three-note chord type: the augmented chord. Augmented chords do not appear in the diatonic major scale or any of its modes, so I’ll address them below. Let’s first return to the B-D-F diminished chord above. If we throw a G below those notes, we wind up with G-B-D-F. This is a G seventh chord. From G, we have a major third, a perfect fifth, and a minor seventh; from B, we have a minor third and a tritone; and from D, we have another minor third. This chord feels far less dissonant than the diminished chord, but it also carries an expectation of a resolution: the ear expects C major to follow it.
If our key is C major, then C major itself is the tonic or root chord of the scale. The fifth chord of the scale, G major, is called the dominant chord. The dominant to tonic progression is the single most common chord progression in music, and it’s the easiest way to establish the home key.
I want to be extremely clear here, though: although I’ve spent a long time explaining what creates harmony, dissonance is not inherently bad. In fact, in many cases, it can be what you want. Two particularly famous examples of this include John Williams’ theme for Jaws and Bernard Herrmann’s theme for Psycho. Another great example is Krzysztof Penderecki’s Threnody to the Victims of Hiroshima, which uses droning dissonance to incredibly unsettling effect. The point shouldn’t be to avoid dissonance entirely; it’s to avoid it where it’s unwanted.
(“Krzysztof Penderecki” is pronounced roughly “Kshishtoff Pendetetski”, but native English speakers can be forgiven for pronouncing his first name “Krishtoff”, since English never places “ksh” together within a single syllable – the closest you’ll find is something like “Berkshire”, which uses them in separate syllables. If all else fails, just don’t rhyme his last name with “Becky” or pronounce the z’s as z’s and you won’t embarrass yourself too badly.)
Additionally, there’s a difference between blue notes (i.e., acceptable dissonance) and sour notes (i.e., fingernails on a chalkboard), but until I’ve delved into non-diatonic scales, any explanation I could provide would boil down to (with all apologies to Justice Potter Stewart) “I know it when I hear it”. In some cases, sour notes may even be what you want – there are no universal rules in music, apart from “there are no universal rules in music, apart from ‘there are no universal rules in music, apart from…’”. The point isn’t to avoid any particular kind of interval entirely: it’s to know how the interval makes listeners feel, so you can employ it to its greatest effect.
Ordinarily, key signatures must follow certain rules. It is not permitted to mix flats and sharps; moreover, notes must be flatted or sharped in a specific order, following what’s referred to as the circle of fifths.
| A Basic Presentation of Key Signatures | |||
|---|---|---|---|
| # | Major | Minor | Accidentals |
| 7♯ | C♯ | A♯ | F♯, C♯, G♯, D♯, A♯, E♯, B♯ |
| 6♯ | F♯ | D♯ | F♯, C♯, G♯, D♯, A♯, E♯ |
| 5♯ | B | G♯ | F♯, C♯, G♯, D♯, A♯ |
| 4♯ | E | C♯ | F♯, C♯, G♯, D♯ |
| 3♯ | A | F♯ | F♯, C♯, G♯ |
| 2♯ | D | B | F♯, C♯ |
| 1♯ | G | E | F♯ |
| ♮ | C | A | |
| 1♭ | F | D | B♭ |
| 2♭ | B♭ | G | B♭, E♭ |
| 3♭ | E♭ | C | B♭, E♭, A♭ |
| 4♭ | A♭ | F | B♭, E♭, A♭, D♭ |
| 5♭ | D♭ | B♭ | B♭, E♭, A♭, D♭, G♭ |
| 6♭ | G♭ | E♭ | B♭, E♭, A♭, D♭, G♭, C♭ |
| 7♭ | C♭ | A♭ | B♭, E♭, A♭, D♭, G♭, C♭, F♭ |
This table provides several demonstrations of the circle of fifths. G is a perfect fifth above C; it’s also the key above C in this table in both the major and minor columns. Continue traveling upwards by fifths and you’ll find D, which is the next row in the table. Up from that we have A. And so on.
This applies in the accidentals column as well. B♭ is a perfect fifth above E♭, which in turn is a perfect fifth above A♭, and so on. The same applies for the sharps, but in reverse order. And another corollary applies here: wherever I’ve written “a perfect fifth above”, we can replace it with “a perfect fourth below”.
At this point, I hear some readers asking themselves, “Wait, is all harmony centered around the circle of fifths?” I’m tempted to just answer “yes” and drop the mic, but that’d be a slightly glib oversimplification. Nonetheless, the circle of fifths is a foundational component of musical harmony, and you will start to see it everywhere. In fact, I’d say that after the notes of the treble and bass clefs, the circle of fifths order F-C-G-D-A-E-B (and its reverse, B-E-A-D-G-C-F) is the single most important note order to memorize in music. It occurs everywhere.
Let’s expand the above table. I’ve adapted the following version from my page on modes. In order, its column headers stand for “Lydian”, “Major”, “Mixolydian”, “Dorian”, “Minor”, “Phrygian”, “Locrian”, and “Key Signature”. (The gray “Dorian” column is a pun on a classic Oscar Wilde novel.) Don’t panic about its information density: not all of it will yet be meaningful to you. However, you may note that I presented the modes in a different order from the one seen above, and also that following the modes from left to right results in another passage up the circle of fiths. If you’re wondering whether these facts are related, the answer is an unequivocal “yes”.
| Key Signatures of the Seven Modes for the Twelve-Note Chromatic Scale | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Lyd | Maj | Mix | Dor | Min | Phr | Loc | KS | F | C | G | D | A | E | B |
| F♯ | C♯ | G♯ | D♯ | A♯ | E♯ | B♯ | 7♯ | ♯ | ♯ | ♯ | ♯ | ♯ | ♯ | ♯ |
| B | F♯ | C♯ | G♯ | D♯ | A♯ | E♯ | 6♯ | ♯ | ♯ | ♯ | ♯ | ♯ | ♯ | |
| E | B | F♯ | C♯ | G♯ | D♯ | A♯ | 5♯ | ♯ | ♯ | ♯ | ♯ | ♯ | ||
| A | E | B | F♯ | C♯ | G♯ | D♯ | 4♯ | ♯ | ♯ | ♯ | ♯ | |||
| D | A | E | B | F♯ | C♯ | G♯ | 3♯ | ♯ | ♯ | ♯ | ||||
| G | D | A | E | B | F♯ | C♯ | 2♯ | ♯ | ♯ | |||||
| C | G | D | A | E | B | F♯ | 1♯ | ♯ | ||||||
| F | C | G | D | A | E | B | ♮ | |||||||
| B♭ | F | C | G | D | A | E | 1♭ | ♭ | ||||||
| E♭ | B♭ | F | C | G | D | A | 2♭ | ♭ | ♭ | |||||
| A♭ | E♭ | B♭ | F | C | G | D | 3♭ | ♭ | ♭ | ♭ | ||||
| D♭ | A♭ | E♭ | B♭ | F | C | G | 4♭ | ♭ | ♭ | ♭ | ♭ | |||
| G♭ | D♭ | A♭ | E♭ | B♭ | F | C | 5♭ | ♭ | ♭ | ♭ | ♭ | ♭ | ||
| C♭ | G♭ | D♭ | A♭ | E♭ | B♭ | F | 6♭ | ♭ | ♭ | ♭ | ♭ | ♭ | ♭ | |
| F♭ | C♭ | G♭ | D♭ | A♭ | E♭ | B♭ | 7♭ | ♭ | ♭ | ♭ | ♭ | ♭ | ♭ | ♭ |
Readers may notice a few additional points about this table:
If you’re beginning to suspect that absolutely none of this is coincidental, you’re absolutely right. Furthermore, if you’re beginning to wonder if this chart could be extended above B♯ or below F♭… it could, but many musicians (myself included) don’t like to talk about it. Double-sharp (𝄪) and double-flat (𝄫) symbols exist, but I personally feel their only place in music notation is for pieces that don’t conform to the diatonic scale, so that’s the only place I’ll acknowledge their existence. But this feels like the ideal time to cover non-diatonic scales.
I avoided mentioning one of the four fundamental types of chord above, because it cannot appear in the diatonic major scale or any of its modes. An augmented chord (e.g., C, E, and G♯) contains two major thirds (C to E, E to G♯) and a minor sixth (C to G♯). It doesn’t feel dissonant, but it does feel eerie. It belongs to one of the whole-tone scales, which consists of six equally spaced scale degrees (either C, D, E, F♯, G♯, A♯, or C♯, D♯, F, G, A, B). Whole-tone scales can establish a dreamy or playful mood; because all scale degrees are evenly spaced, they also have no clear root key, which creates a sense of being suspended in space or time.
(To be continued.)