Music question

[icepixie]

Music theorists, I have a question for you. I recently heard Dar Williams's "And a God Descended" for the first time, and I found that there was something really, really musically satisfying about the first line of the chorus, or rather the first two lines, since the melody and arrangement repeats itself. (Here's a clip of the relevant part, with a bit of the preceding verse for context.) It's not necessarily that I think it's pretty, though I do, but rather that it feels very, very right that these notes/chords follow each other in this order. Is there some objective reason why I find it so satisfying, such a particularly strong resolution of the chords involved, or something like that? Or is it pure idiosyncrasy?

Also, in case anyone missed it, the Small Fandoms/Rarepairs/Rarely-written Characters Promote-a-Thon and Request Line is still going on! Come share your rare fanworks and see if other people have written things you never knew you needed!

Comments

[sleepingcbw.livejournal.com]

In the verse, we start out with a generic Pachelbel's Canon sequence (in C major). The bassline goes

do ("the broken glass re-")
sol ("-flects the haze it")
la ("shines like endless")
mi ("holy days")
fa ("struggling to remember")

-- and then we get derailed a bit. Traditionally, we expect another do after the fa -- but instead the bass noodles around fa for awhile (drops to mi and then goes back up).

Then, when the chorus hits, we get the do we expected (although it's... not serving the same purpose as the do we expected, but that's a conversation for another time). Since we all know this progression forwards and backwards, the delay of the bass note we expected builds tension (as does the fact that she sits on fa so much longer than on any of the notes in the progression). Also, at the beginning of the chorus we get a mini-reboot of the sequence we started with (bass: do-sol-la) although it gets rerouted towards the every-other-pop-song-ever I-V-vi-IV at the end.

Non-harmonically, at the beginning of the word "celebrating" you can hear a guitar start a slide up towards do (reached at the beginning of the chorus), which helps. And, of course, when the chorus hits we get tambourines, plus and more vocal lines and a keyboard filling in the textural spaces between the voice/bass/drums in the verse.

[sleepingcbw.livejournal.com]

The move to half-notes in the melody also makes the beginning of the chorus sound like a place of repose, especially when compared to the much faster rhythm in the verse.

[icepixie]

Ah, so it's a combination of factors, many of them having to do with what it comes after. Thank you! I thought it might be that it was echoing something familiar (I'm listening to Pachelbel's Canon now, and am sort of gobsmacked at the fact that the sequence is exactly the same; I totally hear it now, but would never have guessed until you told me) and also being in something traditionally bright and cheery and, I guess, natural(?) like C major. (...I just made a pun there, didn't I?)

although it's... not serving the same purpose as the do we expected, but that's a conversation for another time

...? Would I understand if you explained?

[alto2.livejournal.com]

I'm listening to Pachelbel's Canon now, and am sort of gobsmacked at the fact that the sequence is exactly the same;

I'm not only because I've seen this WAY too many times (I'm sure you have, too?).

[icepixie]

Oh, that thingy! Yes, I have seen it, but the only thing I remember about it was the part where he rants about the eight notes in the cello part...

[sleepingcbw.livejournal.com]

Heh. Yeah, that's because you actually worked on your comps. Those of us who were less diligent can recite it from memory.

[icepixie]

Heh. Good theory, except for the part where it falls apart when I remind you that you were doing three sets, and if I remember correctly still managed to pull a distinction on the English comps. ;)

[alto2.livejournal.com]

I didn't watch it again because, you know, bedtime and didn't really want that floating through my head when I wanted to be sleeping--but he does talk about how the damn thing is everywhere, right?

(I remember my mother telling me one time that if Pachelbel had known the Canon would be the only piece he was remembered for, he probably wouldn't have written it...)

[icepixie]

He does talk about it; I just didn't remember it.

[alto2.livejournal.com]

Ah good. I'm not crazy after all. ;)

[sleepingcbw.livejournal.com]

I'm listening to Pachelbel's Canon now, and am sort of gobsmacked at the fact that the sequence is exactly the same; I totally hear it now, but would never have guessed until you told me

-insert Pachelbel's Rant joke here-

Actually, I find it more annoying when it happens in reverse -- when I'll be playing someone that has a Pachelbel progression in it, and suddenly my brain starts singing R. Kelly's "World's Greatest" along with it. Fortunately I don't have occasion to play that progression very often. :)


...? Would I understand if you explained?

Sure. It's not really complicated; it just has nothing to do with the question above. :)

Basically there are three functions of chords: tonic (I, iii), subdominant (IV, vi, ii), and dominant (V, vii). A whole crapload of music goes

tonic -> subdominant -> dominant -> tonic

except sometimes there'll be extra chords in there, like a I hanging out with the subdominants where it doesn't belong, or a V near the beginning that isn't really doing V-ish things. These are called extensions (tonic extensions, dominant extensions, subdominant extensions).

The Pachelbel canon breaks down like this:

C: tonic
G-a-e: either subdominant, or sequential material that doesn't count, depending on who your theory professor is
F-C-F: subdominant (the C is a subdominant extension)
G: dominant

If this song followed the pattern exactly, the chorus would begin on a subdominant extension C. Instead, it begins on a tonic C. (Williams can do that, because F-C is a legitimate ending cadence in pop music -- but for Pachelbel the final cadence has to be G-C, so he can't just stop there.)


Hey, thanks for helping me pretend I don't teach high school for a little while! :)

[sleepingcbw.livejournal.com]

(Wait, oops! Expansions, not extensions. Extensions are something different. :D )

[icepixie]

Fortunately I don't have occasion to play that progression very often.

You and your Webern. :)

Interesting explanation. I feel like one of these days I should check a music theory textbook out of the library or something (and hope that it comes with an accompanying CD, 'cause I never know the songs they use for reference), because I sort of vaguely know the terms and ideas behind them, and basically have just enough knowledge to be dangerous but not enough to really do anything with. It's an annoying limbo.

Hey, thanks for helping me pretend I don't teach high school for a little while! :)

Glad to be of service! :)

[alto2.livejournal.com]

the every-other-pop-song-ever I-V-vi-IV at the end

Ah, as soon as you said that I remembered this:



I presume they're the same four chords? (My brain is full of useless information that only seems to return to the surface at moments like these...)

[sleepingcbw.livejournal.com]

I presume they're the same four chords?

Yyyyyyyup.

(They get bonus points for getting "Torn" right, too. It's in the Pachelbel video, but doesn't actually follow the Pachelbel progression -- just the first three chords of it.)

[asinpterodactyl.livejournal.com]

I was going to post the exact same video. (Thanks, alto2, for beating me to it!)

So yes, the progression I-V-vi-IV shows up everywhere you look, but I don't see this as a bad thing. I think the REASON why it shows up everywhere is that everybody recognizes that it's awesome. People write songs around this progression because people want to hear songs written around this progression.

[asinpterodactyl.livejournal.com]

There's a larger philosophical issue here, which is "why do certain chord progressions sound better than others?". The answer is probably something like "because of the mathematical ratios of the chords' tones", but that just raises a new question -- "Why are some mathematical ratios more pleasing than others?". It's a good question, and I certainly don't know the answer to it.

[icepixie]

"Why are some mathematical ratios more pleasing than others?"

I feel like it has to relate to the idea of the Golden Mean and all that stuff about facial symmetry and particular hip/waist ratios being more attractive than others.

Or perhaps certain chord progressions (and thus mathematical ratios) sound more intentional than others, and thus carry the connotation of communication, which we're wired to respond to?

[sleepingcbw.livejournal.com]

People write songs around this progression because people want to hear songs written around this progression.

I very strongly suspect your causation is backwards here. People want to hear songs written around this progression because it's familiar -- because every person in the Western world has some kind of meaningful context for that progression.

Certain chord progressions don't innately sound better than others. If they seem to, it's a result of cultural bias, not mathematics.

[sleepingcbw.livejournal.com]

Ok, here's a less angry answer.

There's an area called diatonic set theory that deals with the question you're sort of getting at -- why are fifths so important?

The most important reasons are, more or less:
--A perfect fifth is seven semitones, and seven is coprime with twelve (that is, they don't share any factors). As a result, we can't divide an octave equally into fifths (unless we exhaust the whole circle), the way we can divide it into four diminished thirds. This lets us generate reasonably-sized scales based on a single interval; we can create a seven-pitch diatonic based just on the perfect fifth, but if we wanted to make a scale out of repeating augmented thirds we wouldn't get too far.
--The perfect fifth builds a diatonic scale within the chromatic scale such that, if you keep following the diatonic scale, eventually you get to a fifth that's too small -- in C major, the diminished fifth between B and F. There's only one of these, though -- and because there's only one of them, we can use it to figure out which key we're in aurally. When we hear that interval, we automatically know it's between scale degree 4 and scale degree 7 (whereas with, say, a major third, there are tons of possibilities) -- and therefore we automatically know where 1 is. That's why a dominant seventh points to its key so strongly; it has both of the pitches from that key's unique interval. Supposedly, IV and V sound less stable than I for this same reason -- because IV has the sd 4 from the tritone, and V has the sd 7.

(There're other criteria dealing with the way the diatonic pitches are spaced among the chromatic pitches, with how we spell intervals and what sizes are allowed, etc, etc, but these are the big two for this conversation.)

As a result -- or so we theorize -- it's easy for us to organize information in a seven-pitch diatonic within a twelve-pitch chromatic, and to build that diatonic, we move by fifths. However, there are other sizes of diatonic and chromatic scales that work, too. More to the point, caring about the location of tonic is itself a culturally-constructed value. These mathematical benefits don't speak to the 7d/12c being intrinsically superior or more natural; it just means that system contains certain features we're culturally-disposed to exploit.

If we accept that certain intervals are more pleasing in the absence of cultural context, we're necessarily making a value judgment about music without actually dealing with the music itself. When you say that certain mathematical ratios are more "pleasing" than others, you're writing off Debussy and Bartok as less "pleasing" in their raw materials than Natalie Imbruglia. That's what Schenker was doing; his writings are meant to further the perception of common-practice tonality is intrinsically superior to everything else. Unless you're prepared to write off everything else, though, it's dangerous ground.

[asinpterodactyl.livejournal.com]

Okay, first an apology and clarification. I don't believe that cultural context has no influence on what music people find pleasing. Rather, it has a HUGE influence. I apologize that I failed to convey that clearly, and in doing so, got you all upset. Sorry! No cultural imperialism intended! Would you like a cup of tea?

To continue my clarification, though, while I believe that cultural context has a huge influence on what music people find pleasing, I don't believe that it completely determines what music people find pleasing. I think, rather, that people's taste in music is determined by a complicated mixture of many factors.

One of these factors, the factor I was getting at in my earlier comments, is the fact that when we look at the physical frequencies of pitches certain very popular intervals, we find that they're all mathematical ratios of low integers.

For example, an octave is two frequencies in a 2:1 ratio. A perfect fifth is two frequencies in a 3:2 ratio. A perfect fourth is two frequencies in a 4:3 ratio.

Now, I'm not totally sure about what this implies, but it seems like the evidence points to this conclusion: Humans are probably are hard-wired wired to pay attention to these particular frequency ratios, and this attention affects our taste in music.

It doesn't determine our taste in music. It just affects it.

[sleepingcbw.livejournal.com]

Hey! I'm failing so badly at prompt replies this year. My apologies.

Anyway:

If what we're reacting to is the smallness of the natural numbers in the ratios that make up musical intervals, then why can't the average listener tell the difference between equal temperament and just intonation? We can't really argue that the listener ought to prefer JI, since recordings are built to suit the instruments available, and the instruments available are must more likely to be in ET, so listeners are more accustomed to ET -- but if the numerical intervals really make that big of an aural difference to us, then just intonation ought to sound better instinctively, or at least vaguely more correct somehow. And it doesn't, since most non-musicians can't tell the difference; it's something one has to be trained to hear.

For that matter, if this is true, why isn't extended just intonation a much bigger deal? I've never conducted this kind of experiment myself, but I'm guessing the average person couldn't tell the difference between Partch or Johnston and a more aribitrarily-microtonal composer. Logically, if the ratios themselves matter, Johnston should sound more "correct" than Ligeti, but I doubt we'd find that in practice.

Also, if the exact intervals matter, why do they only matter for pitch, not for rhythm or any other facet of the musical experience? Cowell's Quartet Romatic (http://www.youtube.com/watch?v=ZUgCure2uKo) organizes its rhythms by the overtone series (e.g., one instrument on half notes, one instrument on half-note triplets --> 3/2 ratio --> rhythmic "perfect fifth"), and it's... absolutely an acquired taste.

There's no evidence that we're hard-wired this way. It's a pretty idea -- like the doctrine of affects or the music of the spheres or the undertone series -- but just because it's pretty doesn't make it true.

[icepixie]

Yes, I think you're right. In H's Music History class, we talked about this concept; I'm pretty sure the term chord progression wasn't involved, but we discussed why and when such things became popular. (For our "why," I think we settled on something similar to your comment below, that it was some kind of instinctual math-related thing.)