Anatomy of a simple musical composition
Limerick is a simple-sounding 19-bar (counting the pickup bar) piece in 4/4. It's slow, at 75 bpm, and its key is F for the first 9 bars and then it modulates to the closely-related key of C for the rest.
[View:https://blogs.msdn.com/cfs-file.ashx/__key/communityserver-blogs-components-weblogfiles/00-00-01-59-08/2465.VID00001.wmv]
The sheet music is here: https://voices.azurewebsites.net/my_music/score/limerick_001.png, and the video is also available on YouTube: https://www.youtube.com/watch?v=xMnqopGn12Q.
Modulating from F to C is an example of modulating to the dominant (up a fifth, or down a fourth) and is done by sharpening the 4th degree (that is, adding an augmented unison) to make it #4, then taking the 5th degree (or dominant, and C is the dominant of F) to be the new tonic, whereupon that #4 becomes the 7th degree of the new key.
In terms of sol-fa, we're modulating from doh to soh. Fah is sharpened to fe and it becomes te of the new key.
Because F and C are such closely-related keys, there are plenty of interesting moments of ambiguity in this piece that we can examine.
Beginning in F, bar 2 moves from F (I) to Am (iii) then in the next bar Dm (vi) back to iii. The roots of the chords have spelled out a Dm in first inversion (F-A-D) which is the submediant triad (the submediant, or 6th degree, is the relative minor). By the way, these minor chords sound pleasant but they're doing a poor job of persuading the ear that F major is the tonality. That's because their roots (3 and 6) are modal scale degrees, and not tonal scale degrees (like 1, 4, 5, and 2 somewhat, are). While playing that Dm (vi) chord, you heard the high F5 note as the melody, and that note is the min3 of the chord. In the next bar (0:09) that same F5 melody note is played again but this time against a Bb (IV) harmony where the F note functions now as a stronger 5th. That's followed by the tonic triad F (I) in the same bar. The F tonality has now been insinuated a little better, but that impression gets even stronger in the fourth bar where IVadd9 (a Bb with a slightly discordant dominant-to-the-key C note in the bass) is followed up by V7 which strongly suggests the F tonality because that's exactly where it desperately wants to resolve.
That resolution comes in bar 6 (0:16) and disappears just as quickly in that bar and the next as we again swing up through a repeat of I-iii/vi-iii. But this time the IV in the following bar moves to the tense V7, leaving the final bar free to spend its entire four beats (0:25) resolving to I and staying there. Phew!
Ok, well that was pretty standard stuff. Now we move into some ambiguous territory. For the second half of the piece, you'll feel that a C major tonality is established, although ambiguously so because we use pretty much the same chords and notes as before (although, we do play B as often natural as we do sharpened, and a G chord plays a cameo as a pretty conspicuous V, or arguably V7).
So, in terms of the new tonality of C, we move (0:29) IV-vi7/IV-IV. Then we move (with that brief resolution) to I-I/bVII-bVIIadd9. What's that flattened leading-tone triad doing there? If we were in F that'd be a simple IV. But in C it's a partial v7 (that is a V7, made into a minor v7 by flattening the third, the B to bB, and then losing the root and with it any 5-1 root movement we'd have enjoyed). But it still functions as a v7 in C, nicely sandwiched between two Is (for I-v7-I). You can hear the resolution to the tonic that follows it. That's taken care of four of what were the eight remaining bars and we're still not entirely sure we're in C. But next there's I (0:42) (with the subdominant F in the bass) to IV (with the submediant A in the bass). Then we take a vi chord (6-1-3) and throw an F (subdominant of the key) beneath it to make it a IVmaj7 (4-6-1-3) and move immediately to a G chord (V) which has its own 3rd, a B note, the leading-tone of the key, in the bass. A IV-V cadence (with those tonal degrees for roots) is actually sufficient on its own to establish a tonality so it's arguable that the ear is now perfectly primed for a C chord and the resolution it will bring. Furthermore, the bass movement over the last two chords from that F to that B (0:47) is a tritone and it spells out the business end of a dominant 7th (the 3rd to the fifth of a V7), which makes the ear even more anxious for a restful C chord. Over the next two bars that's what we get, by way of the nice sus4 of the F note that seems itself almost reluctant to let go of the tension and allow us to slip down to that C.
And maybe this is a case of "you should quit while you're ahead". Or in this case, quit while you're resolved. Because bars 18 and 19 (the coda) of the piece mess with our head a little. An octave higher, the motif of bars 16 and 17 are repeated (0:55) but this time instead of ending satisfactorily in a C chord, we end with a Csus4/F. It's a nod to the key of F that we started with but it feels less like a resolving Fsus2 chord (which is made from the same notes we're playing) and more like what it is: a cheeky little refusal to completely resolve to C by allowing that F to move down the minor 2nd that it wants to to E, and the bass to move to C. If you like, when you play the piece, you can just throw a nice satisfactory C in at the end. It sounds good. But if you prefer "cheeky" then stop where the score does. :)
Btw, the book whose spine you can see in the video is "Applications = Code + Markup" which is a book about WPF by one of my heroes, Charles Petzold.
-Steve