V7

[lermgalieu]

Why does a V7 sound natural to our western ears while a flatted fifth (which interval is part of a V7) sound so tense? I mean, I know the V7 *does* contain this tension and look for resolution, and I know what rich harmonic possibilities just this contains, however I am just wondering about this dramatic difference in the ear. If you are darkening something up by losing the root, why does it darken it up? I suppose a simplistic/mechanical answer is the having two tones (the 1 and 3 of the V7) from the major scale centers it on a given key whereare a two note b5 could be flip-flopped any which way - by its nature it is de-centered...

Also is this why any given chord must have at least three tones (even if one of them is just an octave above)?

There, at least there's a topic - I can't vouch for whether its a good one or not. Its interesting to me.

[brianrost]

Originally posted by lermgalieu
Why does a V7 sound natural to our western ears while a flatted fifth (which interval is part of a V7) sound so tense?

The tritone in the chord doesn't sound so dissonant because we hear it as part of a stack of thirds.

G7 = G B D F

Notice if I leave out the G note, then it sounds more dissonant...now it's a Bdim triad!

To some extent a V7 chord DOES sound tense, start playing one and your ear wants to hear a resolution to the I chord. The V7 chord was not allowed in strict church harmony hundreds of years ago because it WAS thought to be too dissonant due to the tritone.

Originally posted by lermgalieu
Also is this why any given chord must have at least three tones

Sort of. The tritone in the G7 is the interval B to F. If I play JUST those two notes, no chord is defined unless some third note gives that interval a context.

Chords that would contain both B and F: G7, Bdim, Fdim, Db7, etc.

The other answer is that by definition, a chord has at least three notes. So called root/5 "power chords" are TECHNICALLY not chords simply because they contain only 2 notes.

[lermgalieu]

Hmm, well I guess I am looking for a 'deeper' reason. I feel like you are going down the road of the mechanical explanation I started with - i.e. the tritone in the V7 gives it a tense sound, but one which is rooted and therefore more natural sounding to the ear. On the other hand if you remove the G in a G7 and play B, D, F, and the high B, you are left with Bminb5 which sounds much darker to our ears. The tension is then center stage as it is in relation to the root of the chord rather than to another non-root chord tone.

All this is well and good, however I am trying to get to the deeper reasons of why this sounds like this to us. Why was it not allowed in church harmony back in the olden days?

This question is kind of amorphous, because it reeks of similar questions that lots or writers have asked about our ingrained ideas of beauty and how it has evolved over time (obviously you can ask similar questions as the above about, for instance, blue notes or impressionism).

What is it that makes us have this mental model built in a particular pattern where we hear tension if that model's paramaters are flirted with?

Why *that* pattern?

[lermgalieu]

you said:

Sort of. The tritone in the G7 is the interval B to F. If I play JUST those two notes, no chord is defined unless some third note gives that interval a context.

That's what I meant by

having two tones (the 1 and 3 of the V7) from the major scale centers it on a given key whereare a two note b5 could be flip-flopped any which way - by its nature it is de-centered...

I kind of reject the last option though,

The other answer is that by definition, a chord has at least three notes.

. This is a tautology, which in other words is defining something by its own definition. I am looking, again for something deeper somehow.

All of these questions are probably unanswerable at the level i am trying to answer them, but hell, it beats working.

[Chris Fitzgerald]

Originally posted by lermgalieu
Hmm, well I guess I am looking for a 'deeper' reason. I feel like you are going down the road of the mechanical explanation I started with - i.e. the tritone in the V7 gives it a tense sound, but one which is rooted and therefore more natural sounding to the ear. On the other hand if you remove the G in a G7 and play B, D, F, and the high B, you are left with Bminb5 which sounds much darker to our ears. The tension is then center stage as it is in relation to the root of the chord rather than to another non-root chord tone.

All this is well and good, however I am trying to get to the deeper reasons of why this sounds like this to us. Why was it not allowed in church harmony back in the olden days?

There are many stories about that subject, and little way to tell which were true. One theory is that a tritone is an interval made of six half-steps - and six, as we all know, is THE DEVIL'S NUMBER. Many referred to the interval as "Diabolus in Musica", as evidenced in the following link to a page relating the interval to the painting of Heironymous Bosch:

http://music.research.home.att.net/Bosch_Music.htm


Another theory that is a bit more scientific was put forth by composer Paul Hindemith, who devised a system of harmony which revolved around the relative consonance and dissonance of intervals as evidenced by their placement in the harmonic series. According to Hindemith, intervals are inversionally equivalent, so that a minor 2nd is exactly as dissonant as a Ma 7th, etc.. By Hindemith's standard, the tritone rated as even more dissonant than the minor 2nd, since the tritone is first found in the series as a "dirty" overtone (the 11th partial), and doesn't occur naturally until much higher in the series. I can't remember how he reconciled the tuning of the 7th partial (the b7), which was also "dirty" however.

Another theory of dissonance involves using the circle of fifths as a guide of just how dissonant key centers and - as some would have it, notes themselves - are to each other. For instance, if you want to play intentionally "outside" of a major key, all you need do is to play a Major pentatonic scale based on the note a tritone away from tonic - this will give you the exact five notes not contained in the major scale itself. As you get closer in on the circle, you'll find that the closer you get, the more notes the pentatonic scale have in common with the original key.

Spooky stuff, eh?


This question is kind of amorphous, because it reeks of similar questions that lots or writers have asked about our ingrained ideas of beauty and how it has evolved over time (obviously you can ask similar questions as the above about, for instance, blue notes or impressionism).

What is it that makes us have this mental model built in a particular pattern where we hear tension if that model's paramaters are flirted with?

Why *that* pattern?

I can't answer definitively, but I'd guess somewhere along the lines of Hindemith's theory. While the concept of "dissonance" can be called subjective, i also believe that we are hearing a healthy dose of math when we hear music, and the tritone may well be the musical equivalent of Pi or some such.

Interesting topic.

[Sam Sherry]

LG Inquireth:What is it that makes us have this mental model built in a particular pattern where we hear tension if that model's paramaters are flirted with?

Nothing more or less than cultural conditioning. The Lydian or #4 mode is equally "natural" when we consider that the string harmonic series contains a #4 but not a natural 4 harmonic. And Gregorian chant, which is not built around three-note chords, sound plenty "harmonic" to these ears.

In many parts of the globe, the "tension" you refer to is not a factor or plays out in other ways. Much Asian music sounds to westerners as if it has a five-note scale, although it is equally possible to hear many notes westerners perceive as microtones in it. Much other, highly-sophisticated Asian music is built on "microtones" but westerners perceive it as only having one "chord" going on. And check out Bulgarian music -- quartal harmony, "mircotones" and a generally rockin' sound!

Why was it not allowed in church harmony back in the olden days?

It is so easy to picture that the bright fella who thought up the idea of introducing a "third" tone to choir practice was promptly flayed. It's entirely possible that the course of Western music was shaped by the fact that Mario didn't like #4 and Mario was the bishop's cousin and the bishop was the pope's pal.

I am looking for a 'deeper' reason. I feel like you are going down the road of the mechanical explanation . . .

Before we leave mechanical explanation, let's spend one more minute on mechanical function. The Western major scale is a tool which generates major I IV and V chords for happy polka action. The IV chord of the Lydian #4 mode, as you point out, is a half-diminished chord, not a major. That means that a composer utilizing the Lydian mode needs to step outside the mode-tones to generate a polka-approved IV. If yer tryin' ta Keep It Simple, the classic western major does the job.

[Edited to remove music-theory brain-fart.]

It's a great topic, LG.

[lermgalieu]

I think I am following you guys (although I am a little foggy on my partial overtones, Chris). Some great info here...

I think the whole thing about the Lydian scale is fascinating...

I think the thing about Hindemith is fasinating...

And I especially want to know who Mario was.

I'm the kind of guy who 'makes the chords weird' in the band and then stops the guitar players and insists everyone play that other note that really defines the chord. Or that everyone remove the root or play it inverted or whatever.

For me, I don't know if tritones sound 'odd' at all to me, they are obviously an integral part of lots of music for quite some time now, and jazzers could wonder around in the tritone woods for hours without coming back to the root. I definietley like the sound, but yet I am aware of a dichotomy between the niceties of the major/relative minor harmonic approach and the fact that these niceties make the tritone contrast and sound even better, even more complex, than it would be by itself.

Heck this is probably part of the reason jazz *exists*. That love of these complex sounding chords that relate back to something somehow but at times the listener isn't quite sure how...

Anyway I am rambling. I would *love* to hear more about people like this Hindemith character.

[lermgalieu]

In bizarro world our lydian would be the major scale i suppose.

[Damon Rondeau]

Long as we're walking the byways of musical history, I caution all not to forget the Grecian role in provisioning the Western ear.

Pythagoras (what was that guy on, anyway?) got into a trance one day after hearing a vibrating string. One thing lead to another and, after much cogitation and ciphering, he figured out how the harmonic overtone series works. Much rejoicing in Athens town ensued...

Based on Pythagoras' work, the Greeks took on a hate for certain intervals. Our beloved MAJOR THIRD was an interval you couldn't play (unless you were Spartan, or Trojan or something.)

People more knowledgeable than I will have to say for how many THOUSANDS of years the third was riding the back of the bus, but it was a long time.

Sam's right on the money about cultural conditioning.

Of interest to me is how Pythagoras' work on harmonics lead to non-musical results. All that stuff you've heard about "golden rectangles" and divine proportions in architecture and art all started with Mr. P. The same ratios that Pythagoras laid down went on to become incorporated into Roman and then Renaissance architecture (the "modular" system of measurement and design.)

What will really blow your mind is that those same Pythagorean proportions (and modular measurement system) are thought by many to be the foundation of what we know as the shape of the modern violin. I've been putting together a web page on this (not done yet, no URL to hand out) and how it seems to be reflected in basses as well. I determined a few months ago that basses that look "right" to my eye conform to modular measurement rules (but not in the same way or as strictly as in the other, less ballsy members of the violin family.) Ugly basses don't.

I've spent some time in India and Africa, and I've heard little kids casually humming and singing microtonal stuff that Westerners would need YEARS to learn how to do. To them it's as simple as whistlin' Dixie. I'd imagine our "divine proportions" sound just as weird to them...

Wouldn't this world be a boring place without human diversity in all its glory?

[Darth_Linux]

Originally posted by lermgalieu
All this is well and good, however I am trying to get to the deeper reasons of why this sounds like this to us. Why was it not allowed in church harmony back in the olden days?

Firstly, remember that prior to about the 1400's there was no concept of Major or Minor tonality. The only thing there was were the church modes. There wasn't even sharps or flats except in "musica ficta". Modes are just the C major scale starting on different notes. Because the tuning system they used back then was completely different than what we have now, B was a much different pitch to them than what it is to us now. So, in the music of that era (gregorian chant) which relied upon fourths and unisons, as the music went up the C scale in fourths, when they got to F, the fourth of that, B, was horribly, terribly sour. so the church simply banned that note and used Bb instead.

I hope this somewhat simplified history account is helpful.

[Darth_Linux]

Originally posted by Samuel

That's also quite likely the reason that western composers adopted the Aeolian (Aolian? Ay-yolian?) vi mode as the Factory-Approved Relative Minor. It gives you KIS-ready i iv with major/dominant V.

Actually, it doesn't. If you harmonize a natural minor scale you are left with a minor v and no leading tone, which is why Baroque and Classicals composers utilized the Harmonic Minor scale instead of the natural minor. It makes your V dominant and you get a leading tone to the tonic so you still have vii diminished chords.

You can see a similar problem with the Dorian mode favored by the jazz crowd. On it's own, it has the tri-tone at the 3 and 6, which makes for a super cool sound but you still have a minor v and no leading tone. So what did the jazzers do? They used the Melodic minor scale - you still get the tri-tone at 3 and 6 but you also get the leading tone vii and a dominant V. how cool is that??

[moley]

Originally posted by Darth_Linux
how cool is that??

Very cool indeed.

[lermgalieu]

hey darth, good posts. thanks.