#1
It's about the resolution of the tritone, especially in voice leading. I realized today that I can't explain it in actual theoretical terms because I said to someone who asked, "it sounds better that way" and compensated for my ignorance by just blabbering about resolving the leading tone and why V goes to I etc. So to put it simply, Why does the tritone create tension?? Why does it exist?

thx!!
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#2
I havent studied the tritone but I ll make an educated guess.

If we have the notes C E G# (C augmented chord), the notes want to resolve up or down (in this case to A minor).

If we look at the notes that make up the chord, the C becomes the third in Am, the E becomes the 5th in Am but the G# in Caug becomes the root of A minor.

The G# moves step - wise to the A (the root in Am) and hence the strong sense of resolution.

Equally we can apply the same to a diminished chords

Cdim C E Gb

The C Gb just wants to move to the G and make the C major chord (I think.. DO NOT quote me on that I am positive I am wrong here).
Sat in a lab, curing diseases. They actually LET me play with chemicals!
#3
Quote by Guitardude19

Cdim C E Gb

The C Gb just wants to move to the G and make the C major chord (I think.. DO NOT quote me on that I am positive I am wrong here).
so to quote you...

That's my problem. If someone asked me my own question, I would say something fancy like "see how the diminished vii7 chord say in the key of Dmaj will resolve to I with the 7th of the vii sliding down to the 5th of the I and the leading tone sliding up to tonic" and run away while the person is confused. But why? Where are the correct words to explain why it does that?
Gear:
Inflatable Guitar
Digitech GSP 2101/Mosvalve 962/Yamaha S412V
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#4
Why does the tritone create tension?? Why does it exist?


I hope this is what you're looking for. Are you curious about diminished chords and resolving them or the tritone, which are different things entirely. For example a dom7 contains a tritone in it(3rd->b7). I'm just going to guess the tritone...

the tritone exists because we split up an octave into 12 steps. If you look at an octave, which is extremely strong and consonant for every 1 beat of the tonic you'll hear 2 beats of the octave. Basically we've doubled the soundwaves. Instead of listing it all out, you can see the ratio's on this page...

http://www.sciencebuddies.org/science-fair-projects/project_ideas/Phys_p023.shtml

Why exactly we consider huge frequency rations tension? It's just how western music evolved. At some points in history the dissonance is bad practice, others it's evil, others it's desired, others it's bluesy, others it's neutral.
#5
The physical reason that the tritone causes tension is because of the wavelength/frequency of it, compared with the root. If you go up a perfect fourth, then you raise the frequency by exactly 50%, which creates a nice beat frequency that sounds very pleasant to the ears. The ratio of the root to the fourth in terms of string length is 4:3, which, being a nice, round ratio, is why the two notes go so well together.

On the other side of the tritone is the perfect fifth, which is the same as increasing the frequency of the root exactly by two thirds, or 66.66...%. The ratio of string lengths in this case turns out to be 3:2, which is why a perfect fifth sounds more complete than a perfect fourth, and why, if you play two adjacent strings on the same fret (or going one fret higher on the B string if it is with the G) it will sound more like the perfect fifth of the higher string, and not the perfect fourth of the lower one. It will generally resolve more easily to the fifth, not the fourth.

And that brings me to the tritone, which is (almost) just between those two notes. The formula for it is [length of open string] / ( 2 ^ [# of frets you want to move up / 12] = length of string at whatever fret you choose

If we set the open string's length to one, to make it simple, and substitute in the number of frets to get up to the tritone (6), then we get this equation:

1 / (2 ^ [6/12] ) = 0.7071

Then, if we try to calculate the ratio between them, we get this:

1.414213562 : 1

which does not resolve to a nice, round number like our friends, the perfect fourth and fifth.

This ratio could be thought of as 1 414 213 562 : 1 000 000 000, which would have a very long beat cycle, which would cause for a lot of dissonance.

Of course, the ratio isn't exactly that, as the value I used was rounded by the calculator, but that doesn't even matter, since you would never be able to tune your guitar to such a perfect amount.

But yes, that should (at least partially) explain why the tritone sounds so ugly.

And I really hope nobody posted this before me while I was typing all this **** up.

Edit: Damnit, I so knew somebody was going to post something about this before me...
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Last edited by seedmole at Feb 6, 2008,
#6
The tritone's dissonance is cause by the frequencies being related by the square root of two. This is an irrational number, meaning it cannot be represented by a fraction. The decimal points will continue for infinity decimal places, without forming any pattern. Because of this, the sound waves will not fit together EVER. This will cause the notes to sound very distinct from eachother, but also they will create one of the most dissonant dyads. This is unpleasing to our ears, and therefore we want it to become something more consonant (as in two frequencies which relate in a simple rational way).
#7
Wow, thanks CapiCrimm, seedmole, and isaac_bandits! Hit the nail on the head. It was exactly the kind of explanation(s) I was looking for! thx!
Gear:
Inflatable Guitar
Digitech GSP 2101/Mosvalve 962/Yamaha S412V
My Imagination