Here are some analyses that I've made of others' (and my) music. Below this list of links is a section that explains how to read the notation
that I use in my analyses.
When analyzing a piece of music, the functions of the chords and
scale degrees used is very important, as is the modality. But the
specific note used as the tonal center is not important, because that
can be changed without affecting the essence of the music. Consequently,
analytical tools that eliminate the use of any specific note
or chord from the picture help you get down to the essense of the music,
and help you see how it works. For this, you can use: the roman numeral system to
represent chords of various formulas built on various scale degrees; the arabic numeral system for scale degrees
themselves; and intervals for the distances between things.
Here's how to interpret the notation I use in the analyses above. The contents of a pair of brackets represents one bar. If there's just one chord per bar then you'll see
just one chord symbol within a pair of brackets. If there's a chord-change per half-bar, then you'll see two chord symbols in a bar (the first chord gets beats 1 and 2, and the second chord gets beats 3 and 4). If you see four chord symbols in brackets, then each chord gets a beat. The notation "." means that the chord from the previous beat, half-bar, or bar, should be repeated or sustained.
Each syllable of the lyrics (if any) is written out, with its scale
degree (relative to the key, and using arabic numerals) vertically-aligned above
it. If a series of melody scale degrees spells out a chord, then the chord
(again, relative to the key, and written using roman numerals) appears
immediately before the series, on the same line. If the harmony is some chord
other than a tonic chord then, vertically-aligned above the key-relative melody
degree or chord symbols, the symbol is written again, but this time in terms relative to the
harmony. And then, vertically-aligned above that, are the chords of the harmony.
The harmony-relative melody line (the line immediately below the harmony) is a
kind of "disagree-o-scope", which highlights where there is disagreement or
agreement between the melody and the harmony. So, for example, if V7 is in the
harmony (V7's formula is 1-3-5-b7) then there is agreement whenever the
harmony-relative melody line contains any of 1,3,5, or b7. If it's 1, then
there's root-agreement. If the harmony-relative melody line contains degrees
that are not of-the-formula, then there is disagreement.
In the song structure sections, a number at the beginning of a line of text indicates the bar number within the section. Each phrase is put on its own line so that you can see what I consider to be the length of a phrase, and where each phrase begins and ends.
Theories
I'm still working on this set of ideas, so I'll keep updating this content as my understanding changes. I have some data to back these ideas up, but I need a lot more data (analyzing existing songs, and doing my own experiments) before I'm certain that they're meaningful. Some of these ideas are just my definition and name for something I've read about. The rest could well be recognized things, too: I just haven't come across them yet in my books.
disagreement. This is when there is disagreement between the melody note and the harmony (because the melody note is not a note of the harmony chord);
or between the chord that the melody is spelling out, and the harmony chord.
Disagreement means tension, and the anticipation of resolution is often very
enjoyable. Singing 4 over I (which I notate as I+4), or singing 6 over V
(which I notate as V+2, because 6 is 2 relative to V), are examples of disagreements. Sometimes, the melody spells out an entire chord that's different from the harmony chord (for example, playing V but singing the notes of I, or of iii). You could view that case as a single disagreement, or as a series of disagreements.
agreement. The opposite of disagreement. When the melody note is a note of the harmony chord;
or the chord that the melody is spelling out is the harmony chord. Singing 4 or 6 or 2 over IV (IV is 4-6-2), or singing 1 or 3 or 5 over I, are examples of agreements.
I would notate those examples IV+1, IV+3, IV+5, I+1, I+3, and I+5,
respectively.
Agreement following disagreement, is of course particularly, enjoyable.
root-agreement. The special case of agreement when the melody note is the root of the harmony chord. Singing 1 over I
(I+1), or singing 4 over IV (IV+1), are examples of root-agreements.
leading melody. A leading melody is a melody that
either occasionally, or habitually, gets ahead of the harmony. In each instance
of leading: first, the melody changes so as to cause disagreement; then, the harmony changes so as to restore agreement. The melody pulls the harmony along, with
a moment of
disagreement before the lagging harmony catches up. This idea
conjures the image of an over-energetic dog dragging its sluggish
owner along by the leash. I know that the term pushing
exists for analogous ideas in drumming, and for changing chord a half
beat before the bar's end. But you can only get ahead of something
if you're leading (or pulling) it, so that's the term I prefer.
leading harmony. A leading harmony is a harmony that either
occasionally, or habitually, gets ahead of the melody. In each instance
of leading: first, the harmony changes so as to cause disagreement; then, the
melody changes so as to restore agreement.
hierarchy of time-units. The smallest time units are divisions of the beat. A bar is a time unit that's a collection of beats. A line (or phrase) is a time unit that's a collection of bars. A section (for example, verse, pre-chorus, chorus, bridge) is a time unit that's a collection of lines or phrases.
time-unit borders. Between any two neighboring time units, at any scale, there exists a border. Beats 1 and 2 are separated by a beat-border; beats 1/2 and beats 3/4 are separated by a half-bar-border; bars 1 and 2 are separated by a bar-border; lines (or phrases) 1 and 2 of a verse are separated by a line-border (or a phrase-border); a verse and a chorus are separated by a section-border. A border has zero size and zero time: it's just a location marker.
effect-space. A topological space (similar to a Cantor set) formed by the union of all time-unit borders. At any point in effect-space, musical effects (such as resolving to the tonic) are magnified in proportion to the level of hierarchy of the border representing the point. For example, if you place an effect at a bar-border then it will be more effective than if you'd placed it between any two arbitrary beats (or at any other arbitrary point in time), but less effective than if you'd placed it at a section-border.
Magnifiers exist particularly at one-half, and at three-quarter,
positions within blocks of units.
h-pace (harmonic pace, aka harmonic tempo, or harmonic rhythm). The pace at which the chords change. You can control the amount of energy, interest, or perceived speed, of a song by adjusting the h-pace, even while keeping everything else the same (including, in particular, the actual tempo of the song).
m-pace (melodic pace). The melodic counterpart to h-pace. M-pace is the pace (or tempo, or rhythm, if you prefer) at which the melody seems to change. This is somewhat subjective, but often you can hear that the melody is spelling out the same chord (or other pattern, including droning on a single note) over, say, a two-bar period, and then changing to another chord/pattern for two bars. In that case, the m-pace is per-2-bars (or just "a 2-bar pace"). Other times the chord/pattern might change with a more rapid pace; perhaps once per bar or once ber half-bar. The m-pace can give the impression of a song speeding up and slowing down even if everything else stays the same. And, of course,
you can vary m-pace independently from h-pace for even more creative
options.
r-pace (rhyme-pace). Still somewhat theoretical. But, by changing how frequently rhymes occur, you can control the perceived length of lines or phrases, and then that should affect the perceived pace of the song
for that duration. The limerick form of poetry is an example. It
contains four phrase-units (each unit is four bars of 3/4), but it
sounds like it contains five units (and, that's how you'll see them
written out).
false resolution (or false effect). A disagreement whose melody is repeated in the effect that follows (the disagreement exists only for the purpose of highlighting the effect that follows it). For example, in Just Like Jesse James, the same 2-1 melody is used in a disagreement ("fla-mes": 2-1 over IV) and then it's used again in the very next bar in the resolution to I+1 ("Ja-mes": 2-1 over I).
h-attractor (harmony-attractor). The path that the ear expects the harmony to follow either in order to return to I, or to maintain agreement. It's a kind of force-field or furrow or envelope that you expect a chord sequence to conform to. Your expectation can be in response to the way the chords seem to be going (away from or toward I, for example), or by the way the melody is going. And you can be guided in your expectation either by music you've heard before, or by your intuition. It's important to be able to resist the h-attractor at pivotal points
in a song, especially when you're close to I. But, most times, depending on where in effect-space it happens, and as long as you're resisting agreement (or at least root-agreement),
then you can allow the h-attractor to pull you back to I when it wants to.
m-attractor (melody-attractor). Another force-field, similar to the h-attractor, except this one is in the shape of a melody that will continue to go the way it already seems to be headed, and/or that will agree with the harmony. The m-attractor wants you to serve it; so you have to bring a lot of creative force to bear to resist its pull for those times when you want to develop tension and/or do something unique. You want the melody to serve you, but the m-attractor doesn't make that easy. In a sense, the h-attractor and the m-attractor are two aspects of the same force, because the harmony and the melody are so entangled and influential on one another. One way of demonstrating an m-attractor is to have someone play both the melody and the harmony of an unfamiliar, but fairly simple, piece on the piano using just
the fingers of one hand (or you can use the left hand to play bass also). This will be a sequence of chords and notes where, whenever a chord is being played, the melody disappears into the chord. Now you recreate the sequence of chords and notes that you've just heard, except you use only a single finger (or you sing it). That forces you to pick just a single note where before there was a chord. The series of notes that you play is your
own subjective m-attractor for that piece of music. The m-attractor often causes you to hear the highest note from a harmony chord as the melody, but different people might hear slightly different m-attractors for the same sequence. For example, when playing C-F(second inversion)-G(second inversion), you might hear an m-attractor of C4-A4-B4, especially with the bass playing, or perhaps E4-A4-B4 or G4-A4-B4 without. But C-F-G will probably have an m-attractor of G4-C5-D5 for you.
