Oddities of Music Theory

This thread is to post and discuss the "odd" theoretical/trivial things we find in different languages of music. When I say "language," I'm referring generally to any syntax that is specific in its treatment of pitches, intervals, and notation, but we can refer to just about any characteristic of music that's specific and/or significant to the language - pretty open field for pointing things out. For example, the tonal language of the common practice era would be a "language" of music. And for an example of something I find "odd" about this language, let's talk about the sonority of the German Augmented 6th Chord.

First, let's create a Gr+6 chord in the key of C Major on the root of F#. We typically see augmented 6th chords voiced in first inversion. So, beginning with the third of the chord, we have Ab, then C (a major third above it), the Eb (the 7th), and finally the F# above that (the augmented 6th). Respell this augmented 6th chord by changing the F# enharmonically to Gb, and now we have an Ab-C-Eb-Gb chord... the sonority of a dominant 7th. The sonority of a Gr+6 sounds exactly the same as a dominant 7th chord, but because of how we spell the chord and where it typically occurs in a progression, we label it differently.

Of course, in context, how the Gr+6 chord resolves is why we spell it differently (the F# resolves up to G instead of down to F), but it's still "odd" that the language needs this level of complexity in offering two different labels for the same sonority for the purpose of explaining how the pitches should resolve. I digress...

What have you found that's "odd" in the music languages you've studied and used?

I didn't find that funny at all.

In fact I didn't even understand the second paragraph with all that dominant 5th harmonic german sonority fish interval stuff.

Do you understand the word "sonority" at all? I'm referring to how a German Augmented 6th chord is identical in sonority to its dominant/enharmonic equivalent - they sound exactly the same. The only difference is how a Gr+6 is spelled and how it resolves. It seems like a lot of work for something so trivial as how the significant interval (minor 7th or augmented 6th - enharmonically no different from one another) of the sonority resolves. In a dominant 7th chord, the 7th resolves a half-step lower. In a Gr+6 chord, the 7th of the sonority (spelled as an augmented 6th) resolves a half-step higher. It's "odd" that the distinction needs to be so theoretically complex, and it amuses me that it is.

Well, there is no enharmonic equivalence in meantone temperament, which means that Gr+6 and D7 are not the same chord. Since meantone temperament has been widely used in the past, it isn't hard to deduce how possibly the Gr+6 chord entered the harmonic language - in a "softer" manner, that is.

I think it really depends on the system you're using.

There's a lot of very complicated context-based analysis choices depending on what you're trying to analyze. For example a modulation from Cb major to F major using the Cb dominant (Gb) as enharmonic to F major D7. Of course it's not just that simple, since dominant forms make things more complex, specially if you're using Riemann function analysis.

There's also stuff in Riemann that seems redundant, but technically has a purpose. For example parallel functions are "mirrored" in gegenklang functions, yet there's a specific use for the terminology depending on the context. Gegenklang functions are linked in major 3rds, while parallel are linked in minor 3rds. Problem of course is when say an E minor chord is both the Dominant Parallel AND the Tonica Gegenklang from C major, but this has to do with the context in which that chord appears in. When it substitutes the tonic then you can call it gegenklang (like in an interrupted cadence) but when it substitutes the dominant (as a furthering of a basic cadence for example) you can call it dominant parallel.

But it gets a lot more complicated with "typical" interrupted cadences, which you'd just normally name the VI from the scale in Riemann it has two names depending if you're in major or in minor. In minor, of course, all the names from the degrees change and all the relationships get switched around.

It's kind of hard to get into it but after a bit I think it's the best system to analyze a lot of music, even if you have to keep wrestling with details like how to name things specifically. Nevermind all the symbols and junk that gets added.

Gegenklang = contra-parallel? That is, the mediant chord could be analyzed as Dp or Tkp, depending on the context, right? Here, the labeling system is a bit different visually: iii would be written as T_III or D_III, depending on the function. For example: T-T_III-S-D, T-S_II-D_III-T. There is also this "unclear function" thing, for example vi between T and S, in which case it would be labeled as T-TS_VI-S or T-W-S ('W' comes from mirrored 'M' for mediant).

I have Riemann's Harmony Simplified, but I think it lacks some explanations on contra-parallel clangs.

Do you understand the word "sonority" at all? I'm referring to how a German Augmented 6th chord is identical in sonority to its dominant/enharmonic equivalent - they sound exactly the same. The only difference is how a Gr+6 is spelled and how it resolves. It seems like a lot of work for something so trivial as how the significant interval (minor 7th or augmented 6th - enharmonically no different from one another) of the sonority resolves. In a dominant 7th chord, the 7th resolves a half-step lower. In a Gr+6 chord, the 7th of the sonority (spelled as an augmented 6th) resolves a half-step higher. It's "odd" that the distinction needs to be so theoretically complex, and it amuses me that it is.

They don't sound the same in 19-tet. :)

Well it all depends on the function intended, the scale used, and the progression. Or I could swear that sometimes musicians just label stuff the easiest they can think of in the moment. What I've always been interested is the next: I'm from Europe and I think most of you westerners know that we use a slightly different system than you. The most notable difference I would say is that in our european system the A# or Bb is called B while the natural B is called H. Now this just seems illogical to me, the natural A minor scale would go: A-H-C-D-E-F-G-A Now why would anyone sane put H after an A. How did this came to happen? Did they have a different natural scale that was more important that included A# so they named it B instead of the natural B?

I have Riemann's Harmony Simplified, but I think it lacks some explanations on contra-parallel clangs.

I think Riemann himself didn't specify a lot of the stuff.

the language needs this level of complexity in offering two different labels for the same sonority for the purpose of explaining how the pitches should resolve.

That's exactly why a Gr+6 isn't a Mm7 chord.

It's also why we label diminished chords by the "root" pitch: it's determinate upon the tones that are being used to resolve. Speaking solely from sound, there are only three diminished chords. But we don't label them "C dim, C# dim and D dim" like we do with the whole tone scales because diminished chords can usually have very specialized functions, namely as a viidim chord.

Of course, this really is only important to theorists. ;) Composers who use this stuff aren't quite as concerned with spelling things 100% "right." I read lead sheets all the time with progressions that are "wrong," but nobody including me cares. It's pretty necessary to know, but not necessary to practice all/most of the time.

They don't sound the same in 19-tet. :)

:)

Surely there are more odd things in the theory of music that amuse us... or are we so uptight that we need to debate the reasons why we label Gr+6 chords differently than we do V7 chords? Really?

I really didn't think it was "debate-worthy" when I posted, just something that amuses me about how we conceptualize music. People, lighten up.

I find it annoying when people mention a scale, (like fore example, mixolydian b6) and call it Mixolydian b13... my rule, is to only talk about extended tones when talking about chords. but thats just me being monkish...

Isn't there actually a diffrent function implied when one spells a chord B Add9 as opposed to B add2 for example?

It also gets on my nerves when people call the circle of fifths the cycle of fifths... But actually, the term cycle of fifths makes more sense, I'm just not used to hearing it. After all, what is circular about the circle of fifths? Maibe just the diagram thats often used to iluistrate it.

KG:

Laziness. :P Jazz writers are lazy. They write whatever they feel like, it's 2 to 1 it'll be labelled differently than it should. I guess 2(? never seen that) and 4 lean toward implying suspension, 9 and 11 leave no doubt that they are tension tones.

I've learned in my jazz studies that theory is a different animal in jazz. I'm sure you have too. The rules turn into guidelines. I mean, how many different ways can you write "C major chord" in a lead sheet? :lol:

Could someone explain in brief ... why the various "TET" systems exist? Do people still use them? I've seen as far as 171-TET! Never heard it, though...how practical are those? All I know as far as practicality is concerned is perfect and tempered, for voices/strings/winds and keyboard instruments, respectively. Just temperment is also interesting, but not practical outside of period performances.

Could someone explain in brief ... why the various "TET" systems exist? Do people still use them? I've seen as far as 171-TET! Never heard it, though...how practical are those? All I know as far as practicality is concerned is perfect and tempered, for voices/strings/winds and keyboard instruments, respectively. Just temperment is also interesting, but not practical outside of period performances.

Er, they're just different pitch systems. There's no reason why any of it shouldn't exist, but that of course doesn't mean you have to use it.

As for using whatever systems there's a lot of ways to make it quite practical, depending on what you're writing for. If you do, say, electronic stuff you can be really picky about frequencies and pitch systems, where if you're writing for different instruments you have to take their limits into account (and who's going to play it.) Why don't you go and listen to some microtonal music and see how other composers have put to use in regular instruments all these different tuning things.

But remember, if it's for "practicality," why even bother to play instruments when we can just listen to a CD?

Right. I didn't know how else to word it. :P Of course, they're never not going to exist.

Can you recommend some discography on microtonal music? You've picqued my curiosity.

Here's a handful of composers:

http://en.wikipedia.org/wiki/Harry_Partch

http://en.wikipedia.org/wiki/Alois_H%C3%A1ba

http://en.wikipedia.org/wiki/Adriaan_Daniel_Fokker

http://en.wikipedia.org/wiki/G%C3%A9rard_Grisey

http://en.wikipedia.org/wiki/Tristan_Murail

Also Stockhausen has worked with microtonal stuff too in his electronic music (his etudes, etc.)

There's quite a lot of literature if you bother to look around a little bit, and can probably find a lot of pieces on youtube!

Can you recommend some discography on microtonal music?

Here is a recent freely released album by Sevish on "Split Notes", a microtonal net label. It's reallly really good in my opinion:

http://split-notes.com/spnt001.php

He uses different equal divisions of the octave (like 22-edo and 13-edo) and also some just intonation scales (using specific frequency ration relationships) in a cool beat oriented way :)

John M

Right. I didn't know how else to word it. :P Of course, they're never not going to exist.

Can you recommend some discography on microtonal music? You've picqued my curiosity.

In terms of "microtonal poineers", I'd say look to Alois Haba, Henk Badings, and Ivan Wyschnegradsky. Also, if you can find it, music by Julian Carillio. Easley Blackwood's "Twelve Microtonal Etudes" is considered a major piece in microtonal history -- though I don't find it all that interesting.

Harry Partch (as already mentioned) and Charles Ives are some early American's dealing with microtones.

The American Festival of Microtonal Music has some CDs out that I think are a good starting place -- aside from the John Catler, Skip LaPlante, and Johnny Reinhard specific albums, they all have a variety of different composers from different periods. So in addition to those "experimentalists" of the early 20th century, more recent works, plus earlier music (Brahms, Bach, Beethoven) in period tunings.

You've probably heard a lot (if you listen to "new music") seeing as Nono, Stockhausen, Xenakis, Ligeti, Scelsi, etc. used microtones. They all used ETs derived from 12tET -- quartertones, eighttones -- and Ligeti also used Just intonation (Hamburg Concerto, Horn Trio).

Spectralists are also microtonalists too (as SSC kinda mentioned as well) -- you can also look at Horatiu Radulescu.

Pascal Dusapin and Maurice Ohana as well.

Wendy Carlos uses scales that don't confine to the octave.

Since most of that deals with ETs, you could also look at Ben Johnston, some Lou Harrison, Kyle Gann, Terry Riely, etc. in terms of Just intonation.

Johnny Reinhard is a "polymicrotonalist", and that, I think, is worth checking out.

Oh, John Cage (number pieces, specifically Ten) and definately Ezra Sims. James Tenney too.

In terms of your question about people using them, yes people use all different kinds of ETs. 18, 19, 24, 30, 31, 36, 41, 48, 53, 72, 96 are the more common ones, I suppose. 205 has been used by several composers in various works.

I've use a multitude of different ETs and non-equal tunings in my work.

----

I don't find the Ger+6 to be much of an oddity. I do think its odd when people refer to it as the Swiss+6... but that, again, has to do with resolution.

KG:

Laziness. :P Jazz writers are lazy. They write whatever they feel like, it's 2 to 1 it'll be labelled differently than it should. I guess 2(? never seen that) and 4 lean toward implying suspension, 9 and 11 leave no doubt that they are tension tones.

I've learned in my jazz studies that theory is a different animal in jazz. I'm sure you have too. The rules turn into guidelines. I mean, how many different ways can you write "C major chord" in a lead sheet? :lol:

Could someone explain in brief ... why the various "TET" systems exist? Do people still use them? I've seen as far as 171-TET! Never heard it, though...how practical are those? All I know as far as practicality is concerned is perfect and tempered, for voices/strings/winds and keyboard instruments, respectively. Just temperment is also interesting, but not practical outside of period performances.

I think that after 24 tet, things start to get hairy practicality wise... But that is no reason not to use tuning systyms with more notes per octave.

The tonal plexus keyboard has 210 notes per octave. =O

Also, for me, rules are always guidelines. The thing is to learn WHY we have the the "rules" that we do, so that you don't just follow them blindly, but know where it acceptable to break them.

For example, Why are paralel fifths and octaves so bad anyway?

Because they reduce the independence of lines.

*reads entire thread*

:mellow:

I nominate this for Unfunniest Thread on YC.