You must learn your scales and your arpeggios.
Bring the music ringing from your chest and not your nose
While you sing your scales and your arpeggios."
Music Theory is the study of how music does what it does. Almost everyone who has ever heard or enjoyed music is, thus, an amateur music theorist. With that in mind, those of us who have spent a bit of time on the subject thought the rest of you might be interested in hearing what's been said about it.
Wikipedia defines "music theory" as "the study of the practices and possibilities of music." This is quite accurate but not very helpful, since "the practices and possibilities of music" is kind of a nebulous thing. This is especially true because the subject matter of "music" is ever expanding, as people both push boundaries outward and find new innovations within previously-known territory; even those who have studied the field will eventually find that they've fallen behind.
Music theory, like music itself, is both an art and a science. As a science, it's a study of the rules of music. As an art, it's the study of how to use those rules to predict and create emotional reactions within the listening audience. The former is objective, and the latter subjective, but the two harmonize a little more frequently than you might think.
What Even Is Music?
Because humans have been making music since well before the dawn of recorded history, we can unfortunately only speculate on how music began. One theory suggests that music developed in parallel with humans' ability to derive meaning from tone of voice, instead of just the literal meaning of the words. Prehistoric humans then separated these tones from language entirely, and realized they could use them to create moving and meaningful patterns of sounds. The earliest example of a musical instrument yet discoverednote dates back to about 43,000 years ago. The word music itself derives from the ancient Greek word μουσική (mousike), meaning "art of the Muses."
For many of us, music is a large part of our lives. We hear it quite frequently; in fact, given modern technology like smartphones and YouTube, we can hear it basically any time we want. Many of us can sing; many more believe we can. It exists in every known human culture. Even people who are deaf or hard of hearing can experience music through the (loud) vibrations of an electronic instrument. We all have experience of music. But what is music?
In short, "music" is the arrangement of sounds in time. It is an artistic collection of noises meant to create specific and intentional effects in the listener.
From this definition, we immediately learn several things about music. The first is that "pitch" or "tone" is technically not necessary; a group of people playing only drums
are still perceived as music. Second, "instruments" are technically not necessary; the sounds involved must be intentionally created and timed, but there is no requirement that they be created via specific means or implements. Third, since time is such an important part of music, this places a greater emphasis on silence — moments of quiet or stillness can be used for great artistic effect. Finally, more things count as "music" than it first may seem. This definition of "the arrangement of sounds in time" may potentially include more phenomena than purists may agree with — for instance, some might protest the inclusion of rap as a form of music — but it emphatically does not exclude anything that ought to be there. Besides, what even counts as sound?, and what are the rules of how it must be arranged? The avant-garde composer John Cage wrote the composition 4'33 precisely to ask this question.
That said, the vast majority of popularly-consumed music does include things like "pitch" and "instruments" and such. But what are those? Well, welcome to our Useful Notes on Music Theory.
Fundamentals of Music
Here we study the technical ingredients of music.Most sounds in music have a pitch. Scientifically speaking, "pitch" is a measure of the frequency of a noise. Quick physics lesson: every noise is just vibrations in the air around us. The number of vibrations per second (as measured in hertz) determines the frequency. This is physics, and it's not very interesting, so we won't spend much time on it.
Pitches are also understood using the alphabet system of A-B-C-D-E-F-G. There is a relation between pitches and hertz; the official "home base" of music is A440, so called because the frequency of said pitch is 440 hz and it is used as an A. Most instruments are tuned directly according to this pitch (except for the ones that aren't).
Obviously, there are a lot of available frequencies between 0 and 440, and more beyond it. You'll be glad to know that the larger majority of them aren't used. Western notation tends to stick with 88 of them — coincidentally, the 88 heard when you press the keys on a piano. There are a number of ways to notate them, but we're going to stick with a combination of "scientific pitch notation," which actually names them after the piano keys — the lowest being A0 and the highest being C8, and the numbers incrementing every time you have a new C — and "hertz" notation, where a pitch is listed with its hertz quantity — A440, for instance. For the heck of it, we'll use both. At this time we should take a moment to mention that the "scientific pitch notation" name for A440 is A4, so-called because it's the 4th "A" key on a piano (not counting the A0 way down at the bottom; remember, the incrementation occurs at C).
Scales
Scales are series of pitches that feel like they go together. The most normal-sounding scale for most human beings is the "major" scale. The pitches in a scale have very specific mathematical relationships to one another, but again we're not going to bother getting into that.
Pitches are also classified in "half-steps," which is the true indivisible interval in Western notation. The closest two pitches can be together is a half-step, which typically involves a sharp (♯) or flat (♭) sign. For instance, you can have the pitches A and B, and they're directly next to each other as white keys on the piano... but they have a black key in between them. This black key represents the half-step, and is either called A♯ or B♭ depending on the circumstances (There are rules about this that we will get into later). The distance between the two white keys, if they have a black key between them, is called a whole step. These terms are used frequently when describing intervals.
"But what about if there's two white keys without a black key in between them?" you might be asking if you've glanced at a piano recently. Congratulations! You've found a half-step! Now let us help you make sense of why a black key should not be there.
The major scale is composed of specific intervals: A pitch, another pitch a whole step above that, another pitch a whole step above that, a pitch that's a half-step above the third one, three more pitches that are ascending whole steps, and one more half-step pitch that brings us back around. See, the reason that the letters in Western music are only A through G is because the thing above G is another A. So if you had an A major scale starting at A4 / A440, the top of the scale would be A5 / A880. (Pitches double in hertz value when they go up or down this way.) The distance between A4 and A5 is called an "octave," so called because there are eight ("octo") notes between them.
"But what about the black keys?" you might still be asking, and you'd have a good point. As mentioned, the major scale contains a very specific sequence of whole steps and half-steps. Black keys exist because the piano keyboard is designed so that the white keys naturally form a C major scale, with the black keys representing the five notes that are skipped over in said C major scale. A scale that includes the black keys is called a "chromatic" (i.e. "chroma", color) scale, whereas one that includes only the main seven scale degrees (A - G, or their equivalent) is called a "diatonic" scale. So, in conclusion, an "octave," defined as having 8 pitches, actually contains 12 pitches. Music can be weird sometimes.
Though A4 / A440 is the benchmark against which all instruments are tuned, there is also a second benchmark that is used frequently. It's C4 / C261.63, the C below A440. It's called "Middle C", because it's the one note that basically any pitched instrument can hit, and the one note that basically every human being can sing. (People who play piano and other keyboarded instruments also like C because as mentioned, the C major scale is the only scale that can be played using all white keys. Every other scale requires at least one black key.)
Speaking of scales: as mentioned, there are 11 half-steps in an octave. All of them can have scales built upon them. You can have G♯ major. You probably won't, though; you'll probably call it A♭ major. There are rules about this that we will get into la... Actually, let's just get into them now: The key you are playing in, the scale you are using, is determined by a graphic called a "key signature." It's a visual guide that says, "Replace these white keys with the next black key over." (It also means the score doesn't need to notate every single fundamental sharp or flat in the scale, making it more legible.) The key signature will have sharps if you're supposed to play the next black key up, and flats if you're supposed to play the next black key down. (It will never have both.) This is why the black key between A and B is called either A♯ or B♭: its name is different depending on which key you're in. Now, because there are seven white keys, the key signature can never have more than seven sharps or flats. The reason you'll never have G♯ major is because playing it requires eight sharps: G♯, A♯, B♯, C♯, D♯, E♯ and F double-sharp. Now, you could write it that way... but there also exists the key of A♭ major, which only has 4 flats and uses the exact same combination of black and white keys that G♯maj does. It may be called something different, but it sounds exactly the same, at least in terms of pitches. Every possible key (all 12 of them) can be described with a key signature; if you take a look at the "Circle of Fifths" folder, you'll see that a couple, like B major, actually have more than one common description (it can also be called "C♭major," 7 flats, instead of 5 sharps). Perhaps for this reason, there is a third pitch-description system that assigns every key on the piano a unique number, but we're not going to bother with it because two is enough to start with.
Now, a couple of you readers may be wondering: "But wait. I've heard musicians referring to double-sharps and double-flats before. Don't those actually exist?" And the answer is, yes, they do. There is a sign for double-sharp — 𝄪 — and for double-flat — 𝄫. However, these signs are not used in key signatures because, again, they aren't necessary; anything that can be expressed with double-sharps can also be expressed with single sharps or with flats. (There are some semantic differences between G♯maj and A♭maj, of course — some musicians will swear that key signatures which are represented with flats sound warmer and darker, while sharp key signatures sound brighter and colder. There is some science to this, specifically the fact that the higher a note is, the harder it is to play... but that's true the lower a note is too. By and large, the difference between G♯maj and A♭maj is subjective.)
Modes
(directed viewing: Charles Cornell)
As mentioned, every scale consists of the same mathematical relationships between pitches. So a question that might have occurred to you is, "What if we started the scale on a different place in the cycle?" Congratulations: you have discovered Modes, which are exactly that.
There are seven different modes, since there are seven different pitches you can start on in a scale:
- Ionian — you start on the first scale degree. "Ionian" is its technical name, but this mode is frequently known as "major". C-Ionian would go C-D-E-F-G-A-B-C.
- Dorian — starting on the second scale degree. Dorian in D would go D-E-F-G-A-B-C-D. Dorian in C has the whole steps and half-steps in different places: C-D-E♭-F-G-A-B♭.
- Phrygian — starting on the third scale degree. (We're not going to keep spelling these out because it would take a while.)
- Lydian
- Mixolydian
- Aeolian — this mode also has a nickname: "minor". It goes A-B-C-D-E-F-G-A, which is different from the three-sharp A-major scale (A-B-C♯-D-E-F♯-G♯-A).
- Locrian
Modes are neat, but other than Ionian and Aeolian, the truth is that they aren't used all that often. You'll hear them on occasion, though:
- Dorian: "Scarborough Fair" (probably Covered Up to most tropers by Simon & Garfunkel); "Cavi Cape" from Mario & Luigi: Bowser's Inside Story
- Phrygian: Samuel Barber's Op. 11, "Adagio For Strings" (see TearJerker.Platoon); Magus's Theme from Chrono Trigger (the opening violin figure actually outlines a descending E-Phrygian scale)
- Lydian: Saria's Song/Lost Woods from The Legend of Zelda: Ocarina of Time.
- Mixolydian: the Star Trek theme, "Clocks" by Coldplay, "Hey Jude" by The Beatles ("naaaaa na na na-na-na-naaa" section only)
- Locrian: Björk's "Army of Me" is one of only seven examples listed by The Other Wiki as songs that "have been, or may be, regarded" as utilizing this mode. ("Army of Me" shifts out of Locrian for its choruses.) This scale has has a half-step between its first and second scale degrees as well as a flat 5th — the "tritone," the ultimate Brown Note — and as a result sounsd so weird that basically everyone just avoids it.
Intervals
An "interval" is the chromatic/pitch space between two notes. They are typically defined using numbers; for instance, the interval between the bottom note of a piano and its top note would be... What, a 51st? In practice, intervals rarely get into double digits, because large jumps are physically difficult to perform.
From a practical standpoint, an "interval" has its number assigned by counting how many white keys are between them, counting the notes actually being played. The interval between C and an E is a third, because there's three white keys involved: the C, the D and the E. The same system is applied even if there are black keys involved; a D♯ to an F♯ is also a third, even though there's technically only two white keys — E and F — between them, because if you played them a half-step down — D natural to F natural — it would... yeah, you see where this is going.
(Just like there's a sign for sharp and flat, there's one for natural: ♮. It is used most frequently as an "accidental," which is when you play a note that's a half-step different than what would be in the key normally. Despite its name, most accidentals are deliberate.)
From a technical standpoint, "intervals" are collections of half-steps, which we have already talked about. Every interval you can think of (not to mention all the ones you can't) are defined by how many half-steps they contain. That piano-spanning 51st, for instance, involves 88 half-steps. C to E involves four half-steps, so it's a third; D to F involves three half-steps, so it's... also a third? Hold on a second.
What's the difference? Do they really have the same name? Yes and no. They're both thirds... But C to E is a major third, and D to F is a minor third.
Most intervals come in major or minor flavors. One half-step, C to C♯, is a minor second; two is a major second. We've covered thirds. You can have major or minor sixths (8 half-steps vs. 9) and sevenths (10 half-steps vs. 11). You can have minor ninths, which is just an octave (12 half-steps) plus a minor second. This goes on for a while.
More importantly, though, there are a few intervals that don't come in major or minor variants. Instead, there's only one of that interval, and they are called "perfect." These are the perfect fourth (5 half-steps), the perfect fifth (7 half-steps) and the octave (12 half-steps).
Sharp-eyed readers have probably noticed that there's a quantity of half-steps that has been skipped: six of them. There's a reason for this: six half-steps, exactly half an octave, is called a "tritone" (because it's three whole steps)... and, for whatever reason, it sounds really bad; for proof, look no further than the memetic, Creepypasta-inspiring "Lavender Town" theme from Pokémon Red and Blue (the signature ostinato goes C-G-B-F♯, forming a tritone with the first and last notes). The tritone has been called "el diablo in musica" (the Devil in music) and it is so dissonant that Common Knowledge maintains that its use was actually banned by the Vatican for many years. This is not to say that it cannot be used well and artistically; like the aforementioned Lavender Town theme, the opening titles of The Simpsons uses it (from "The" to "Simp-"), as does the eponymous figure in "Maria" from West Side Story. Let's not talk about Johannes Brahms adding them to the fourth movement of his Ein Deutches Requiem and making them heartbreakingly beautiful. Even the Nintendo Wii makes use of it: the very first of the famed "doot doot doots" from the Mii Channel Theme, in the second measure of the song, are a tritone chordioid, both notes of the interval played simultaneously. Rules are made to be broken, and it's absolutely possible to make tritones work. But it's challenging.
Finally, let's talk a little bit about inverted intervals. Let's say you play a C4 / C261.63, a C5 / C523.251, and an A4 / A440. What intervals do you have? Obviously, there's an octave (12 half-steps) between the two C's, and therefore a major 6th (9 half-steps) between the C4 and the A4... and, therefore, a minor 3rd (3 half-steps) between the A4 and the C5. Every interval has a flipside this way: minor 2nds to major 7ths, major 2nds to minor 7ths, minor 3rds to major 6ths, and even perfect 4ths, which are the flipside of the perfect 5th. The exceptions are the tritone, which is its own inversion, and the octave, the flipside of which is two notes on the same pitch, which typically just means one note. Trying to invert an octave is the musical equivalent of trying to Divide by Zero.
Rhythm
As you may have started to notice, there's a lot of recursivity in music. There are very few discrete concepts that can be defined using normal, natural, real-world explanations; most of it requires a context of other concepts that you then have to learn before the original concept makes sense. Rhythm is no different, so hold on to your asses.
Rhythm, in music, is determined in three ways: meter, tempo and duration.
Meter
In a time signature, the number on the bottom (what's called a denominator in fractions) tells you what kind of note to look for in defining the measure. The top number (the numerator) tells you how many of those notes to look for. Now, note durations in music are always created by dividing by two, so the bottom number will always be a power of 2. The top number, though, could be anything.
The most popular time signature is 4/4, or "common time" (to the point it is sometimes just notated as a capital "C"). The bottom number tells us that we should be looking for notes that are equal to 1/4 of a whole — for instance, a quarter note. The top number tells us that four of these "quarter notes" comprise a measure. A better way of describing it might be to say that the top number tells you what number to count to before the measure is over. In 4/4 time, after you've counted to 4, you get a new measure. The bottom number, on the other hand, tells you what duration to ascribe to each count.
(Yes, we are aware that 4/4, as a fraction, can be reduced to the integer 1. You should not do this. Music can be weird sometimes.)
If "4/4" is the most popular time signature, this implies that there are others that aren't as popular. For instance, there's 2/2, "cut time," (like common time, it is sometimes notated with a "C", except there's a line through it like the U.S. cent symbol "¢") which is typically used for marches. There's also 3/4, which is used for waltzes. There's also 6/8, which is used for really weird marches. 3/4 and 6/8 look like they should sound the same (and mathematically, they are the same length: six eighth notes), but they don't, because #/8 in music is code for "Each subdivision is actually a count of three instead of two; each individual beat sounds like a waltz in and of itself." So while a waltz in 3/4 would be counted as "one and two and three and," 6/8 is a march for aliens who have three feet: "one 2 3 two 2 3, one 2 3 two 2 3." And then we start getting into wacky stuff like 5/4 where you can't even count symmetrically; 5/4 can either be "one and a two and" or "one and two and a". Meters that aren't Common Time or cut time actually have their own page here: Uncommon Time.
Tempo
Tempo is measured in "beats per minute". You take the bottom note of the time signature, and have that many of those notes per minute. Because tempos exist, time signatures are not objective measures of anything; a song that's in 4/4 time can be played at 60 beats per minute or 120 beats per minute. Time signatures determine how the music is structured; tempo determines how frantic it is.
Duration
Finally, there's duration. We've actually already covered this. The most basic unit of duration in music is the whole note. It subdivides into half notes, which themselves subdivide into quarter notes, which subdivide into eighth notes, and basically further on down as far as you desire. Realistically, though, sixteenth notes are about as short as you're ever going to get. Remember, though, that tempo determines the speed of everything; it's possible to have songs with mostly whole notes that nonetheless goes very fast (cf the second-to-last battle song from Final Fantasy X), as well as songs that are mostly eighth notes but go really slow (Ludwig van Beethoven's Moonlight Sonata).
And yes, if you're counting, that FFX song is indeed in 5/4. Moonlight Sonata, however, is not in 12/8, even though it sounds like it should be, what with the constant 3-note patterns. It's because the notes of the ostinato ("continually-repeated musical phrase or rhythm, only, this is music, so most of our terms are Italian loanwords") are written in a completely new duration: triplets. It's possible to notate three notes in a way that says, "Play these three notes in the same amount of time, tempo-wise, as though they were two notes." This can be really useful for occasional rhythmic flourishes. (Which Beethoven didn't do: it takes until halfway through the piece before a traditional, non-triplet subdivision even occurs. Well, Beethoven was more brilliant than we'll ever be; what can you do.)
Melody
A "melody" is a series of notes (which are pitches assigned a rhythm) which move towards a state of tension and then a state of resolution. Three-Act Structure in musical form! They typically stick to pitches that are found in the key they are using, and often form large, repeating patterns over the course of several measures; but just about any trope in music can be subverted, and these are no exception. Melodies are a prominent part of music, and people spend a lot of time studying them and how they work.
Chords
A "chord" is any set of three (or more) pitches that are meant to be heard simultaneously and take place at the same moment in the music. It should be noted that, while they are meant to be heard simultaneously, they might not be played simultaneously; think about a series of notes played on a harp, an "arpeggio," and you'll see how they form chords despite being sounded discretely.
The most frequently-used chord in Western music is the "triad," which corresponds to the first, third and fifth note of a scale or key and named for the note at the bottom, known as the "root". It doesn't have to be the scale or key that the song is written in; a song that consisted of just that one chord is still two chords short of achieving Three Chords and the Truth, and possibly pretty boring as well. Of course, even "Three Chords and the Truth" has been subverted, by Harry Nilsson's infamous "put da lime in da coconut and drink 'em bot' up" song — to this day, the only one-chord song that has ever gotten anywhere on the Billboard charts. (Dr. Luke is undoubtedly trying to achieve the second — when he's not getting sued by Kesha, at least.) Having said that, the single chord in Nilssen's song is not a straight major triad: it's a chord with four notes, in this case the 7th scale degree.
The I chord — the triad built of the first, third and fifth scale degree, typically represented by the Roman numeral for 1 — is one of the three chords in "Three Chords and the Truth." The other two are the IV chord (the 4th, 6th and 8th/1st scale degree) and the V chord (the 5th, 7th and 9th/2nd). These three together are easy to play and create a very effective Three-Act Structure if played as a "Chord Progression" of I - IV - V - I. The reason the Three-Act Structure works is because I, IV and V chords have specific emotional connotations. The I chord, the "tonic", feels stable and like it's comfortable right where it is. The IV chord, the "predominant" or "subdominant", feels like it's trying to start some trouble. And the V chord, the "dominant", feels as though it has been Left Hanging and wants to "resolve" to something — say, the tonic. (They're also three of The Four Chords of Pop, the fourth being a vi chord — the 6th, 1st and 3rd. This chord is minor, which is why the Roman numeral "6" is in lowercase; the other three are major.)
The study of how chord progressions resolve is an entire branch of music theory in and of itself, called "cadences." There are four main cadences, each with a helpful article:
There are also others listed under our Chord Progression article, such as The Four Chords of Pop, the 12-Bar Blues, and the ever-present "Pachelbel's Canon" Progression.Chord Quality
(directed viewing: Charles Cornell)
When analyzing a chord, a Western-trained ear tends to immediately go to the third of the chord, as it determines the chord's "quality." A major third results in a major chord, and a minor third results in a minor chord, which covers two of the three basic qualities a chord can have.
The third quality is for when a chord doesn't have a third at all. Such a chord is called a suspended chord because it sounds incomplete. Typically, such a chord will have a 2nd instead of its 3rd, or a 4th, leading to the terms "sus4" and "sus2".
Suspended chords feel a lot like V chords in the sense that they feel unfinished and want to resolve to something, typically something with a 3rd. The fun part is deciding what kind of 3rd you're going to resolve to.
Chord Configurations
Chords typically consist of, at the very least, the three pitches in their triad, but they do not have to be configured that way. What if, instead of the 1st, 3rd and 5th scale degree, you played it with the 3rd at the bottom, followed by the 5th, followed by an 8th at the top? Because you get new configurations by turning the chord upside-down, these variations are called "inversions," and every chord has (X - 1) inversions, where X is the number of notes in the chord (Non-inverted chords with the 1 at the bottom are in "root position." This is considered the default state for a chord and is not given special notation). Additionally, you don't have to play them in that particular order. What if you had the 3rd scale degree, a gap, the 1st scale degree, a gap, and then the 5th one? This chord would be in "open position," whereas the more traditional 3-5-1 is in "closed position." Open chords sound more impressive, but are harder to play: if the notes are distributed amongst several instruments (IE string instruments, which have a lot of trouble playing two notes at once), it's harder to keep the pitches in tune with each other; if you're on a keyboard, the chord becomes physically larger and requires bigger hands.
Because chords can have more than 3 notes, it is also possible to have chords that are only "half-open": a 7th chord (1-3-5-7) would be called half-open if you moved the third up an octave (1st, 5th, 7th, 3rd).
Note that there is a strange numbering convention for chords. You are only supposed to add every other note to a chord, though (as mentioned with inversions and closed position) you can absolutely configure them differently once you're done adding them. But the result is that anything beyond 1, 3, 5 and 7 is considered to be from the next octave up, and is numbered accordingly. A chord consisting of 1, 2, 3 and 5 is not numbered that way; it's considered a 9th chord, even if you close it up and play it 1-2-3-5. Likewise, a 1-3-4-5 chord is an 11th chord, and a 1-3-5-6 chord (very common in jazz) is a 13th.
It should also be pointed out that you don't have to include everything in a chord. Theoretically, a 9th chord goes 1-3-5-7-9, but in practice the 7th scale degree is often left out, and if not, the 3rd is. Typically, a chord is reduced to only four pitches. People who are dealing with 13th chords are typically very thankful for this fact, as 6 pitches at the same time may exceed the reach (or quantity!) of their fingers or hands. You can, of course, do the opposite; noted YouTube musician Jacob Collier reported being very excited when he found a chord that involves all 11 scale degrees of the chromatic scale and didn't sound like crap, and a god of choral composing named Eric Whitacre is known for massive stacks of notes; the chord at 3:04 in the linked recording has 14 individual pitches, including 11 diatonic pitches in a row — every in-scale note between E♭4 and A♭5.
And we haven't even started sharping or flatting anything yet. In addition to major chords (which are defined by having the 3rd be a major 3rd up from the root, and the 5th a minor 3rd above that — there is a mathematical relationship going on here because a 5th is seven half-steps above the root, and "7" does not divide evenly) and minor chords (which have the minor 3rd, 3 half-steps, between the root and the 3rd, and the major one between the 3rd and the 5th), there are also "diminished" chords where both intervals are minor thirds, and "augmented" chords where both are major thirds. Technically, any interval can be diminished (by removing a half-step from its normal value) or augmented (by adding a half-step). And when you start adding on additional members to the chord, all of them can be major'd, minor'd, augmented, diminished or perfect'd (assuming it could be perfect'd in the first place; you can't magically have a "perfect" 3rd just because you're adding on extra chord members).
Chords are another major branch of music theory because the possibilities of adding just about anything to the original triad, not to mention the question of how exactly to invert, open or half-open them, are almost limitless. Chord progressions and chord configurations, in particular, also play into the "art" part of music theory (IE how they will cause the listener to react), because different configurations don't have the same impact. Try going to the apronus.com Flash Piano, clicking the "Advanced" checkbox and then the "Chord" checkbox which appear afterwards, and trying the following chords: C4-D4-E4-G4; C3-G3-D4-E4; E3-C4-D4-G4. (If you unclick "Chord" in between each one, the page will actually save each chord as a button which you can press afterwards, aiding in the comparison.) These three chords are, technically, all the same chord — a C-major with an add9 — but as you can hear, they sound quite different, due to the varied ways they distribute the tension of notes that are near each other, and as such will have different effects on the listener. And then there's the question of what progression you plan to put around this chord. All the same questions we've asked about this Cadd9 can be applied to every other chord in the progression that leads up to it.
This stuff gets complicated, fast, but it's also some of the most fun parts of music.
Some music uses what are commonly referred to as power chords, which are technically not chords, as they are made up of a first and third, and sometimes the octave. Both versions give you two notes, and are more correctly a form of double stop, note (or triple stops). Like suspended chords, they are neither major nor minor.
Harmony is the study of what pitches sound good together and why. This overlaps with chords to a certain extent; the two are sometimes described as the "vertical" aspects of music (since you think about everything that's happening in one moment of time) as opposed to the "horizontal" aspects of melody.
Harmony is typically thought of as being "homophonic" — a melody over chordal accompaniment, like someone singing while playing guitar; or you could go even further and be "homorhythmic," — all parts using the same rhythm as the melody, but different pitches, like your typical SATB choir. But it does not have to be this way; "counterpoint" and "polyphony" are the business of creating multiple melodies that sound like they are all independent but are actually crafted to work together. Even admitting that people can do this is probably beyond the scope of this article; some of the greatest composers in history, like Johann Sebastian Bach and Giovanni Pierluigi di Palestrina, made their name solely by perfecting counterpoint (examples: Bach, Palestrina); in fact, Bach is rated by many the finest composer ever because of his mastery of this stuff. Entire styles of composition — canons and fugues — are devoted to the business of repeating the same melody with enough variation to create entire musical pieces. Do Not Try This at Home, at least until you've figured out how normal harmony works, but once you have, this is a place to go.
Consonance and Dissonance
Pitches that sound good together — 1, 3 and 5, for instance — are called "consonant" pitches. More often than not, though, they're not called anything at all, because the default in Western music is that all the pitches in any given chord are going to sound good together, always. When something doesn't sound like it fits in — when something sounds "dissonant" — it's kind of a big deal. Dissonant intervals are notes that are within one whole step of the basic notes of the triad — AKA, anything that isn't 1, 3 and 5. Given that 7th chords exist, it is obvious that this doesn't stop people from subverting the rule, and dissonant chords can sound very cool in the right context (for instance, the add9 in the previous section, which hopefully you enjoyed). However, as with all subversions, one should treat with care, and not attempt to subvert unless they're already comfortable with the rules.
Part of the reason you want to be careful with dissonance is because of another phenomenon called "voice leading".
(directed viewing: 8-Bit Music Theory)
Despite its name, "voice leading" is not unique to sung music; the word "voice" in music theory refers to a distinct line/part/aspect of music within the larger piece (bass, harmony, melody, etc). Voice leading is, instead, the business of controlling the number of pitches that change every time you switch chords. The more big jumps each voice has to make, the more dramatic and unstable a song sounds... which can be cool, but there are also going to be times when you want it to be smooth and calm. For instance, if you're doing a standard Authentic Cadence using Three Chords (and the truth), you're going from 1-3-5 to 4-6-8 to 5-7-9 back to 1-3-5. There are some consecutive numbers between those three chords, right? You could have one voice (say, a viola) go 3, 4, 5, 3 (or even 3, 4, 5, 5), and another (a violin) go 5, 6, 7, 8. Smooth, right? And easier for those musicians to play, which they probably will not complain about. And, of course, you can keep things really smooth by starting to reconfigure the chords themselves. If you put the 4-6-8 chord in 2nd inversion (1-4-6) and the 5-7-9 in 1st inversion (7-9-5), your bottom voice can play 1-1-downto7-backupto1, which is about as unchanging as it's possible to get.
Dissonant chord tones complicate these moving lines, or shut off movement lanes that would otherwise be available, because they have specific places they want to resolve to. In the above example, our hypothetical viola could go 3-4-5-5 or 3-4-5-3; both are viable voice-leading paths. But if we add a "dominant 7th" to the V chord — 1-3-5-8, 4-6-8-11, 5-7-9-11 (AKA 5-7-2-4), 1-3-5-8 — you've got this added 4 you have to resolve, and it almost has to go down to the 3rd — the "suspended 4th" is a well-known and extremely resolved-sounding chord progression. So whatever your other voices or instruments are doing, they have to be on either 1s or 5s in that final chord because the 3 is already taken. (You could double it, but one of the rules of voice-leading is also that you are not supposed to double the 3rd, because the results just sound weird.) And that's even before we get into things like "parallel fifths/octaves" (which is when two notes are a fifth or octave apart and then move in the same direction by the same interval; this sounds bad to most people), "hidden fifths/octaves" (two notes moving by different intervals but still in the same direction to finish a fifth or octave apart; this also sounds bad except in specific circumstances), "tritones" (covered already), and other various messes.
This gets extra confusing because, if properly written, voice leading can trump the needs of functional harmony. The listener will accept a walking line that makes sense even if that walking line involves pitches that don't make sense in context. For instance, let's say you're writing a harmony for the bridge of the classic cheesefest Close To You (you know, "Why do birds suddenly appear") as performed by Carpenters, and specifically addressing the bridge section where the melody goes 5-6-7-6-5. Your harmony could go 1-7-6-7-1. Theoretically, you should not do this, because you're going to end up with a chord spelled 6-1-3-7 (and another spelled 7-1-3-6), which doesn't sound good in and of itself... but the listener won't care very much because the two voices have, in and of themselves, such strong and sensible motion. (To showcase this even more, a couple of exceptions to hidden fifths/octaves specifically involve walking lines, and this kind of movement is also critical to handling dissonance in counterpoint.)
Finally, dissonant notes, "color" notes, "chromatic" notes, are tricky to use because they're hard to play. When musicians hear dissonant notes, they tend to go "Oh, Crap!", because all their training is that this should not be happening. So, even if they're supposed to do it on purpose, they may have trouble doing what they're told. (Obviously, additional training and experience will help with this... but "additional training and experience" may not be something your musicians can obtain at short notice.)
There are many, many, many instruments used for music, starting with one's own voice and hands (clapping them together or slapping other things for percussive effect) and going on from there.
All instruments have one thing in common: a surface that vibrates to produce sound. Since this isn't a useful taxonomic metric, instruments are typically grouped into a number of categories based on additional features they all have in common with each other:
- The human voice is powered by the vocal cords, which vibrate to produce pitch. Consonants and vowel sounds are shaped by the mouth and tongue. Certain consonants are "plosive" (like P and T) while others are "sonorant" and can actually be held on a pitch (M and R). The original instrument, the human voice is quite versatile and should not be underestimated; there is an entire field of music, A Cappella, which utilizes nothing but singing. Voices are typically sorted into Voice Types, both for musical and dramatic purposes. While voices can be used in relatively unregulated quantities, it should be pointed out that they are often used in very close configurations of harmony: an experienced singer typically has a vocal range of about two octaves, a 15th. If you run a bow over the strings of a violin, you will find that it has a range of a 14th — long before you start putting fingers to strings to increase their pitch. The human voice is also very powerful, because it can transmit information not just via pitch, tone and timbre, like other instruments can, but also by lyrics. This means it is possible to overuse voices if you're not careful, overwhelming the listener with too much information that they can't meaningfully parse.
- Stringed Instruments have, as the name would suggest, strings. However, they also have wooden bodies, the bottom panel of which vibrates to create sound, and the strings are manipulated by a "bow." Pitch is controlled by using a finger to manually shorten the length of any given string.
- Woodwinds are powered by the human lungs. In most of them, the vibrating portion is called a "reed"; some woodwinds have two reeds. Reeds need to be replaced frequently, and creating new ones by hand is something any woodwind player eventually masters. Flutes are strapped into this category because they have more in common with woodwinds than anything else, even though their reeds are built into the body of the instrument and do not need to be replaced.
- Brass instruments are also powered by human lungs, but involve a tubular resonator which creates sound, the length (and pitch) of which is changed by the control mechanisms on the instrument. This, not metallurgical composition, is the defining element of a brass instrument (hence why saxophones are woodwinds, and why a traditional wind quintet includes a French horn; earlier ancestors of it, "natural horns", did not have this feature).
- Keyboard instruments are clumped together because they're played by a person sitting in front of a bunch of keys. Each key is attached to an individual noise-making mechanism that is tuned to a specific pitch. The mechanisms themselves vary: on a piano they are strings which are struck by a hammer apparatus; in an organ they're connected to a phalanx of woodwinds; on a harpsichord they are strings which are plucked. So as you can see, here's where the category criterion starts to change from "They make noise the same way" to "They are played the same way".
- Percussion is the family of things that are whacked. From drums to gongs to tambourines, they all have one thing in common: you hit them, and the thing that you hit vibrates to make noise. Percussion instruments are typically thought of as being without pitch, but the family also includes the xylophone, the vibraphone, the marimba, and most kinds of bell (technically, the piano also belongs here, which further shows how the categories are breaking down).
- Plucked Strings are not really a classification that is recognized internationally (you won't find an article on them on The Other Wiki, for instance), but is a way of differentiating between bowed string instruments and things like guitars, ukulele and the harp (seriously, when's the last time you saw someone playing those with a bow?). Again, the only major difference is the way the strings are manipulated, but the change opens up a lot of techniques (harp glissandos, rhythmic guitar strumming, etc) while roping off others.
Each instrument is played a certain way, and having things in common with other instruments does not guarantee much of anything. A guitar has 6 strings and a ukulele has 4, so you can't play things exactly the same on them. And forget things like "piano vs. harp". While a piano has 11 keys per octave, the harp has 7 strings and sharps or flats them using pedals; it can't deal with accidentals nearly as easily as a piano does, and a comparatively chromatic piece, easily played on piano, can be ruthlessly challenging on a harp ("My working title for this piece was 'Pedal Hell' ").
Application
Now that we've gotten some of the basic elements of music, we can talk about how to put them all together.There are a number of different genres of music, such as Jazz, Classical, Klezmer, Rock & Roll, musical theatre, and more.
A scholar named Philip Tagg has divided music into three basic categories:
- Art Music is meant to be listened to attentively and may require a certain amount of music-theory background to appreciate.
- Popular Music is meant to be enjoyed by the masses, not just music students; is disseminated via mass media; and is typically sold as a product meant to turn a profit.
- Traditional Music, sometimes called Folk Music, is transmitted orally and derives from a particular culture or region. It is sometimes called "World Music".
") exist in the Art Music category, while extremely complicated works exist in Popular and Traditional Music (cf Dragonforce's "Through the Fire and Flames").Genres are further subdivisions within each of these larger categories. Most genres are defined by combinations of the things already discussed: specific chords or cadences, specific rhythms, specific instruments, specific time signatures, specific techniques, specific languages or lyrics or subject matter, and so on. For instance, "Rock and Roll" music is defined partially by how it uses drums, whereas a song does not qualify as a Barbershop composition unless dominant-7th chords are used enough times.
Very few (if any) musical acts ever stick to a single genre. True, an act may be predominantly country, or electronic, or choral, but almost everyone mixes and matches based on the kind of music they wish to create. "Genre Mashup," in that sense, should actually be considered the norm rather than an exception. This is especially true as various acts gain popularity and the landscape shifts to accommodate them.
A song does not have to stay in the same key for its entire duration. If it doesn't, it's called a "key change" (in common parlance) or a "modulation" (in technical-scientific-music-speak).
Modulations typically follow specific rules that are similar to those of voice leading: specifically, the two keys should be as similar as possible.
- Under the rules of Art Music, of the sort that Mozart followed, this means that the new key should be a fifth higher or lower than the original, because the new key signature will only be different by one sharp or flat. (More on this mathematical fact shortly.)
- Under the rules of Popular Music, it's possible to simply go up one half-step or one whole step — the so-called Truck Driver's Gear Change. If you go up a whole step, the resulting key will be two sharps or flats different than the original one, but a half-step key change typically involves changing from a key signature written in sharps to one written in flats, or vice versa. From the standpoint of technical music, the two keys have nothing to do with each other... But it works artistically because they sound so similar.
- The Art-Music standard is that a song should change to its "relative major/minor" key, which means the song should, if it starts in minor, switch to the major key that is a minor 3rd up — such as a song in A minor becoming C major — and if the song starts in major, move to the minor key a minor 3rd down — e.g. C major down to A minor. This is because of the modal relationship discussed earlier: the Aeolian mode, the one starting on the 6th scale degree of the matching Ionian scale, is minor. In other words, the key signature for a key's relative major/minor is identical to that of the initial key... And in terms of making the fewest number of changes to a key-signature graphic, "none, you're just thinking of a different note as being tonic" is hard to beat. Modern examples example of this technique can be heard from the Act II opener to Dr. Horrible's Sing-Along Blog, "My Eyes", in which one character sings in minor and the other in major (and, at the end, they duet); and in "Suteki Da Ne" from Final Fantasy X, in which the verses are in minor and the chorus in major.
- Popular Music rules allow you to simply flip between the major and minor of any given key — "Happy Together" by The Turtles, "The Sign" by Ace of Base. These are called "parallel major/minor" keys, and, again, typically involve flipping from a sharp key signature to a flat one, but it works because the tonal center is maintained (unlike the relative major/minor keys, where the key signature is maintained).
- This is also a good time to introduce the concept of "melodic minor," which is neither a key nor a mode but rather a modification. "Natural minor," a.k.a. Aeolian mode, has three scale degrees that are different than major: in addition to the lowered 3rd scale degree which defines the minor sound, they also have a lowered 6th and 7th. "Melodic Minor" re-raises those two notes so that the only difference between it and major is the 3rd. Again, though, "Melodic Minor" is not a key with a signature; it has to be denoted using accidentals.
- This is also a good time to mention the "Picardy Third." If you've ever heard a song that spends most or all of its time in minor, but then throws the chord of its parallel major right at the end just to feel more complete (e.g. "Happy Together" by The Turtles), well, that's a Picardy Third. There, done with that bit.
This gets interesting because now we're going back to physics and math.
When two separate instruments play two separate pitches, and the pitches are perfectly in tune, they will create a sympathetic vibration together — AKA, another pitch. This pitch called an "overtone". Its exact hertz is determined by what the two "real" pitches are, but typically follow the "harmonic series." The harmonic series is... complicated, so we'll just link you to a helpful YouTube video that explains it.
The reason this is significant is because harmony has a basis in nature. We don't think these things sound good because Humanity Is Insane, we think they sound good because physics. It's math that makes things sound good. And you can't argue with math.
"Can I create overtones using only a single instrument?" you may ask, and that is a very good question. The answer is that it depends on the instrument. First off, even on instruments that can make more than one pitch (EG violin or guitar), there's Some Dexterity Required to play them perfectly in tune. Second, even on keyboarded instruments, pitches are not perfectly in tune. Pianos use equal temperament, which is the best compromise that makes any given key sound like it's in tune with any given other key... but they're only approximations. To create an overtone by pressing (say) F5 and G5, you'd have to tune them just sliiightly different than if you wanted to create an overtone between F5 and G♯ 5/A♭5... and so on for all 85 other keys on the keyboard. While synthesizers could potentially be programmed to tweak the hertzage of any given key depending on what other keys are being played at the same time, this also assumes that proper tuning could be achieved for any given chord — eg, for the third of a chord to tune properly to the fifth might require the third to be at 1,234.5 hertz, whereas to tune properly to the 7th it might need to be 1,256.7 hertz. (The linked YouTube video actually covers this too.) Technology Marches On, but we have yet to invent an instrument that can make two pitches sound like one pitch — or have them near each other but still sound good.
This is a simple way to add color to a song.
Let's say you have a IV chord — 4-6-8 — in first inversion: 6-8-4. You know what would be a similar chord? A vi chord, 6-8-3. Two of the three pitches are the same, after all. So, where you'd normally use the IV-in-first-inversion chord, you write a vi chord instead. The important part is that the vi chord is essentially pretending to be a IV chord in this case — it's serving the same harmonic function.
In general, you can substitute Chord B for Chord A as long as they have two pitches in common. However, that's where things start getting really wacky, because the pitches can include chord extensions. Did you know you can substitute a F♯7 for a C7? They both share E♮ and A♯. "But hold on," you may say, "A dominant-7 C chord doesn't have an A♯ in it." And you'd be right... but it does have a B♭ in it, and B♭ Lives A Double Life as A♯. When the same piano key has two names, said names are described as "enharmonic equivalents." (Also, F♯7 for C7 is a tritone substitution and it's pretty out there, but it's a good demonstration because it shows just how dramatically you can use this technique.)
The Circle of Fifths is not really a musical figure in and of itself; instead, it's a tool that helps you put together harmonies and chords. It does this by listing all 11 notes in a chromatic scale (that is, white keys and black keys) and showing how each one is a perfect 5th (7 half-steps) above one pitch and a perfect 5th below another. If you keep going around the Circle of Fifths this way, you'll end up right where you started, which is pretty neat.
The circle of fifths, incidentally, is also a neat guide for writing key signatures. As mentioned above, C major / A minor is the only key that can be played on a piano with all white keys; its key signature is a complete and total blank. But if you go clockwise around the Circle of Fifths, the next entry — the one at 1 o'clock — is G major (or its relative minor, E minor). This key signature involves 1 sharp. Likewise, the key at 11 o'clock, Fmaj / Dmin, has a key signature of 1 flat.
The reason this works is because each pitch has a logical relationship to each other pitch. The Circle of Fifths simply illustrates that, making easy for you to figure out the most efficient way to get where you're going.
Much has been discussed about the Circle of Fifths and how moving around it can be used to create specific emotions in the listener, which is — again — the whole point of why we're studying music theory in the first place. For a fairly rapid, if mind-blowing, dive into the subject, watch Adam Neely's talk on the "brightness" of modes, followed by the 8-Bit Music Theory's study of use of deliberate brightness and darkness in the soundtrack of Persona 5.
The circle of fifths is most useful when attempting to change keys. As mentioned previously, dominant chords feel unstable, and have a chord they want to resolve to — specifically, a fifth down. Consequently, the V chord of your new key can be a very effective way of setting up the upcoming transition. Which, by coincidence, leads us to...
, Adam Neely)With this topic, we have officially graduated into more advanced music theory — in fact, secondary dominants are, almost literally, the foundation of jazz. This concept makes plenty of sense on paper, but can be difficult to implement in actual composition. Fortunately, we've already discussed its two ingredients: Chord Substitution, and the Circle of Fifths. "Secondary Dominants" is when you do a Chord Substitution (IE Chord B pretending to be Chord A) that is specifically meant as a V-I authentic cadence, with the Chord Substitution coming from a different key.
That's still kind of a lot, so let's explain.
One of the best ways to emphasize the importance of a chord is by having something resolve to it. Obviously, if you want to emphasize your I chord, you precede it with a V chord. But what if you want to emphasize something else, say a iii chord or a V chord? Simple: precede it with a major chord that is a fifth above it. The problem is that dominant resolutions don't work unless chord-that's-fifth-above is in major, which isn't true for these two example chords. If you are sticking to white keys or diatonic scale degrees, the chord that is a fifth above a iii chord is a diminished 7th, which just doesn't sound very good; likewise, the V of 5 is ii, which in diatonic scale degrees is minor.
Thus, secondary dominants. The scientific explanation is that we are borrowing chords from other keys to create a secondary, artificial, dominant resolution to a chord that isn't I. The practical explanation is that we are just taking chords and making them major by adding on accidentals. Let's say we're in C major, and trying to have a V of V, for a chord progression of II - V - I (two authentic cadences in a row). Our naturally-occuring ii chord is D minor, D-F-A. A major II chord isn't naturally found in, well, basically any key (you need a mode for it), but D-major as a chord in and of itself does in fact occur in various places — Dmaj, for instance. Technically, we are importing it from Gmaj where it serves as the naturally-occurring V chord to G, which is the chord we are trying to resolve to; technically speaking, we are shifting, for this one chord, into G major, a shift so swift that a key-signature change isn't necessary. (Nor, frankly, would it be practical, because — due to the nuances of music notation — key-signature changes are only allowed to apply to entire measures, and "one chord" is typically swifter than a measure.) It's a secondary dominant.
When you import a chord to make a secondary dominant, you almost always use a dominant 7th chord, because it feels extra-unstable and leads the listener to expect the authentic cadence. This is especially important if you are trying to do the secondary dominant of a IV chord, because the V-of-IV is... I, which is about as opposite of "unstable" as it's possible to get.
One of the... interesting elements of music is that almost everything has more than one name, or more than one way of describing it. Here we're going to go over some of them.
- Major and Minor: As mentioned, these are technically modes. It is acceptable to refer to something as being in "G Aeolian," though most people will look at you funny if you do.
- Enharmonic Equivalent: This is when the same pitch goes by multiple names. The piano key right below an F, for instance, can either be called "E" or "F♭". And we've been over black keys way at the start. This is, obviously, annoying, but is also important for spelling. If you're trying to spell a C-E-G chord, well, obviously, "C-F♭-G" isn't right. (It doesn't even have a vowel in it.) Of course, it also gets worse than that, since that E we were talking about earlier could also be a D𝄪 (double-sharp). Fortunately, it won't be often.
- Enharmonic Equivalents are typically only seen in one context: weird and rapid key changes. This can be jazz, or it can be a Truck Driver's Gear Change. As mentioned when we discussed "voice leading," music is easier to perform if as few notes change over time as possible. In certain circumstances, you'll find a note that's in common between your two keys... except that in one of them it's a G♭ and the other it's F♯. It'll sound fine to the listener — in fact, it'll sound more stable, because (again) the less change, the better, and the performer will be happy once they realize that they're just supposed to stay on the same note... but it might take them a while to figure that out.
- Augmented, Major, Minor and Diminished Intervals: As mentioned previously, you can augment and diminish any interval whatsoever. See where this is going? A perfect 4th is 5 half-steps, a major third is 4 half-steps... A "diminished 4th" is also 4 half-steps. Again, this is mostly necessary for spelling. The notes in a chord always have to be in thirds above the root of that chord, so at times you may need to fake your chord's spelling with (say) an augmented 3rd, because you're just not allowed to have a 4th.
Further reading
There is a lot more to be learned about music theory then has been covered here, and even in most of the topics we have covered there's more to learn. The good news is that there are a lot of resources that will allow you to do so. On YouTube alone there are a ton of content creators who spend time on music. On a scale of "easy" to "complicated" — or, perhaps, on a scale of "Stuff we've covered here, but in more detail" to "jazz" — here are some people to visit:
- Michael New
- GUIM
- Ongaku Concept
- Adam Neely (who arguably belongs further down the list, but also belongs up here because the breadth of his analysis is quite wide)
- 8-bit Music Theory
which provides notation software that runs in HTML5. This means that you can actually write your own sheet music in your browser. While we do not claim that this article has given you enough training to start writing your own music, Noteflight will let you mess around with notes and simply see what things sound like, which is really where all musicianship starts. If you want something more full-featured, check out the open-source MuseScore.