The pleasure of music comes from similar themes and devices as does the pleasure of stories and humor (and, to some degree, games). That is, from establishing expectations and then surprising the audience by doing the unexpected; and from the development of suspense and relief. With stories—including funny ones—these effects emerge from the dynamics between characters, from conflict, and from playing with the ambiguity of double-meanings before clarifying the intended interpretation.
In music, the story characters are the Elements that we learned about. And the drama comes from manipulating the perception of a tonal center (which I'll explain later on this page) to set up expectations, ambiguities, and the excitement of musical suspense; and then either surprising the audience with something exciting or novel, or giving them the relief of resolution.
In the pages of this Harmony section, you'll see concepts illustrated with examples in the form of little snippets of music. Sometimes the exact rhythm and notes will be important, and in those cases the example will be written as score. Other times, I'll write down chords and notes inline in the text using a notation of plain ANSI letters and digits (meaning that, for example, I'll indicate "flat" with a plain letter "b" instead of with a special "♭" glyph). Next I'll describe the meaning of all the notation that you'll see on the pages that follow.
An upper-case letter (A-G) on its own represents a major triad. C is a C major triad; A is an A major triad. To indicate a minor triad, the lower case letter "m" is appended (sometimes "min"). So, Cm and Am represent C minor and A minor triads, respectively.
The names of extended chords (you extend a chord by adding further thirds above it) end in "7", "9", "11", and so on. A dominant seventh chord is written in the form C7. Major and minor sevenths are written in the forms CM7 and Cm7, respectively. A minor major seventh is written in the form CmM7.
To indicate an augmented or diminished triad (or seventh) in a chord, "aug" and "dim" are used, respectively. For example Caug, Cdim, AaugM7, Adim7, Adimdim7 ("an A triad with a minor third and diminished fifth, extended with a diminished seventh"). Suspending and adding to a chord are indicated with the shorthand "sus" and "add", respectively. For example, Csus4 or G7add6.
By default, a chord is intended to be played in root position (the root of the chord in the bass: the lowest-sounded note). When a different note than the root is intended to be in the bass, that's indicated with a slash character ("/") and the root note. So, C/E means a C chord played with the right hand, but with an E note in the bass played with the left hand. And G7/B means a G7 chord with B in the bass.
There are times when an upper-case letter (in the range A to G) represents a note instead of a chord. For example the "E" in "C/E" is an E note, and not an E chord. Because a slash is always followed by a note—and never by a chord—the meaning is perfectly clear in that case. And there are other cases where it's clear and unambiguous. For example, I use a plus ("+") character between notes to indicate notes played at the same time. I never use a plus character between chords (because it would not make sense). So you can be certain that D+G+C means "a D note, a G note above it, and a C note above that played at the same time".
If it's important to be clear which octave the notes are in, then a single digit is appended to the note letter to indicate the octave number on the piano into which the note falls. C1 is the C natural note in octave 1; that's the lowest C natural note on a piano. C4 is the C natural note in octave 4; that's middle C on a piano. So, D4+G4+C5 means "D4, G4, and C5 played together". By the way, I'll never specify a note in octave 7—that means that I can write dominant seventh chords in the form C7 without ambiguity.
When you alter a note, the resulting octave number respects the octave number of the natural note's piano key, which may not be that of the resulting piano key. Take C4 (middle C) as an example. If you flat that note (subtract an augmented unison) then the resulting piano key is physically in the next octave down: octave 3. Despite that, the resulting note is not named C3b, nor Cb3, and certainly not B3. Its name is C4b: the C in octave 4, flatted. The note an augmented unison above C4 is C4#.
I use a hyphen ("-") character to separate any notes and/or chords played in sequence. The notes in a broken chord, or a chord sequence, or any combination of the two, will be notated in this way. Octave numbers are used to make it clear where notes, rather than chords, are meant. So, D4-G4-C5 means "D4, G4, and C5 played one after the other in sequence". And D-G-C, which has no octave numbers, must therefore mean "the chord sequence D followed by G followed by C".
When it's obvious we're not talking about a chord (we're talking about the notes in a single monophonic voice, or in a scale, or in a chord) and when the octave numbers are irrelevant or obvious, then octave numbers will be omitted even for notes. For example "the melody C4-D-E" can only mean "the notes C4, D4, and E4 played in sequence". And "the melody C-D-E" can only mean "any C, D, and E, played in sequence".
When analyzing a harmony in its general form, the concepts of scale formula degrees and the intervals between them are too abstract to be represented in score. Score was designed to capture particular notes in a particular key. So when I'm talking about scale formula degrees and intervals I'll use textual notation, too. For intervals, I'll use the short names you saw on the Intervals page. For example, maj2, min3, per5. For scale formula degrees, I'll use arabic numerals (1-7) and they'll be either natural or alterered in relation to the natural degrees of the major scale formula. So, for example, 3 means "the third degree, or mediant, of the major scale formula". In the context of a minor scale formula, 3 means "the third degree, or mediant, altered from a min3 above the tonic to a maj3 above by sharping it". A scale formula degree can be prefixed with an alteration symbol such as "b", "#", "dim", or "aug". So, b3 means "the third degree, or mediant, of the major scale formula altered from its natural maj3 above the tonic to a min3 above by flatting it". In the context of a minor scale formula, b3 means simply "the third degree, or mediant".
There are two ways to indicate the same scale formula degree in different octaves. I can use an apostrophe (a plain text version of a prime symbol) to indicate "an octave higher". So 1' is the tonic in the octave above 1. Like octave numbers for notes, the "prime" notation for scale class degrees respects the octave of the natural scale formula degree in question. So, for example, the scale formula degree an aug2 above 6 is #7, and not #7'. The other way of indicating "an octave higher" is to add 7. So 8 is the tonic in the octave above 1; 9 is the supertonic in the octave above 2, and so on. That notation makes it clearer why the scale formula degree an aug2 above 6 is #7 and not #14.
Note the subtle distinction between the meanings of intervals and scale formula degrees, despite their similar notation. For example, compare min7 and b7. Min7 means "a minor seventh", but that says nothing about what notes it occurs between. And b7 means "the seventh degree of the major scale formula flatted from its natural maj7 above the tonic to min7 above". So while the interval from 1 (the tonic) up to b7 is a min7, so is the interval from 2 up to 1'. Similarly, while 4 sounds like it wants to resolve to 3, that doesn't mean that every per4 wants to resolve to a maj3. Some do, and some don't, as we'll see.
So we've seen how scale formula degree numerals are used relative to the tonic of a scale formula. The same numerals are also used relative to the root of a chord. So, a major triad can be said to have the formula root+3+5. That can be read: take the root note, the note a maj3 above the root, and the note a per5 above the root, and play them together. Similarly, a minor triad has the formula root+b3+5.
A chord formed on a scale formula degree uses Roman numerals instead of arabic numerals. So, the chord formed on 1 is I. It is written in upper-case to indicate that the triad is major. The chord formed on 2 is a minor triad, so it's written ii. Then iii, IV, V, vi, and viib5. The "b5" at the end of "viib5" reminds us that the chord is diminished (it has a flatted 5) and not just minor.
We can extend, alter, and add to a scale formula degree chord, too. For example, V7add6. The 6 is the submediant of V, remember, not of I. Another example: ii is root+b3+5, but II is root+3+5. In the major scale formula, sharping that b3 gives us the chromatic degree #4. But, as we'll see, II has a very important function in the harmony of many of the songs and classical pieces that you know and love.
Scale formula degrees and the chords formed on them give us a general way of thinking about music and analyzing harmonies than we could get from chords formed on notes. We're able to think about the function of each degree and chord with respect to the tonal center, and we can extend that understanding across different tonalities (the key of the music) and modalities (for example, the major or minor mode, although there are others).
Earlier on this page I promised to explain what I meant by "tonal center", so this segment is an overview of the concept. And on later pages we'll use more examples to really look at the idea from every angle.
Melody and harmony (the voice and the instrument, in a song) work as protagonist and antagonist to tell a story. One leads the other, they clash, one pulls the other back or they move forward together or they continue to clash or they clash in a different way. All this is very dynamic; each little piece of drama happens quickly and the story is always moving forward, always moving somewhere new.
Two (or more) voices in a harmony work the same way, blurring the line between what's melody (each individual voice) and what's harmony (the interplay and drama between the voices). In this case, the voices perform the roles of protagonist and antagonist.
Music weaves different tonal centers together (including centers within centers) over time (often moving at a fast pace). You can think of those centers as wrestling, or battling, or dancing. They pull and tug and clash and resolve with one another, and that's the drama of music.
In Elements, we talked about scale formulas. Redefined in terms of harmony, a scale formula is determined by:
A scale formula is abstract because it exist in terms of intervals, not notes. To make it concrete, you substitute a note for the origin. Then the tonic tone becomes the tonic note, and the diatonic tones become diatonic notes. When a tonic note applies to an entire piece of music (or large parts of a piece, if there's a key change), then that's known as the key. If necessary you can say "local tonic note" (or local tonal center, in the abstract) if you need to be clear that you're talking about a tonic note that's not also a key. Some local tonic notes are so local that they are nothing more than the root of a single chord.
For example, in the key of B, play the chord sequence B-A-E-E7/D-A. The key is B, so that's the global tonic note of the whole sequence. In the subsequence containing the two A chords, and the chords between them, you establish a local tonic note of A. While playing the E chords the tonic note is E. So, at first there is one tonic note in effect (B). Then two tonic notes (B and A) are in effect at the same time, but at two different levels of hierarchy. Then three tonic notes (B, A, and E) are in effect at the same time, at three levels of hierarchy. These different levels—local to global—work in a similar way as turbulence: small-scale, local effects add up and create effects at larger, more global scale.
In a cycle-of-fifths sequence, each chord-root tonic plays a crucial role (root movements down in fifths). But it must end at some larger-scale tonic. Rather than thinking of the key of a piece as determining the options at smaller scales, think instead of the smaller-scale tonics as determining the larger-scale ones. By taking control at the smallest, most local level, the composer exerts control at the global level, too.
You can make a good case for a tonic note by playing diatonic notes together. "Together" could be simultaneously, or just in close enough succession not to lose their effect by having been forgotten or overwritten by some other effect. For example, C4+F4+G4 and the melody C-D-E-F-G both make a good case for the tonic note of C.
I say "make a good case for" because a lot of the time that's the most you can do. Sometimes you can make such a good case that you've established a tonic note beyond argument. No-one would argue that the melody C-D-E-F-G-A followed by the chords G7-C unambiguously establishes C as the tonic note. But the really interesting things happen when the case you're making leaves room for ambiguity, and of course that's done deliberately. Of course, momentarily, that V7 chord is making a case for a major G tonality (even though its b7 is not diatonic to G but all of its notes are diatonic to C). But any case it makes for G is only in a local sense; at best it can only convince us we're in G for a moment, and it has no lasting effect on the sense of what the larger scale tonic note is (at least, in this case).
Anyway, you can use notes from the instruments or voices to make cases for tonalities and it's how you overlay and weave them that makes music.