If, like me, you are a repeat viewer of Donald in Mathmagic Land, you will be familiar with the idea that Western music has some correspondence to physical reality. (You will also think you are much better at making bank shots in pool than you actually are. Curse you, Disney!) The twelve-note scale results from regular division of a plucked string, and is thus in some sense “natural.” Musicians will tell you that it doesn’t stop there–that when writing a song or playing a solo, there’s some sense of where it “naturally” wants to go, and though some of this is ear training, there’s some research into the way fundamental aspects of music inherently sound pleasing to our brains. But it’s always been hard to explain how this naturalism works to non-musicians. String theory to the rescue!
I know, I know, “chords represented in four-dimensional space” doesn’t sound like it simplifies anything. But go to Dmitri Tymoczko’s site and watch some of the videos. There, he shows a Chopin chord progression represented as movement around a circle, and since a 12-point circle is a clock, it’s easy to follow. Most chord changes represent slight variations in which some notes are held constant while others change. Again, this sounds dense when written out, but just watch the video.
A Time article about Tymoczko claims that this system can be used to show the similarities between different styles of music, but it seems to me like comparing Chopin and Deep Purple based on chord changes kind of misses the point–rock is about texture, after all. Then again, I learned everything I know about hustling from a cartoon duck.
The Geometry of Music [Time, via Slashdot]
considering that guitars and pianos are technically out of tune in all keys, no matter how well you tune them, by the very nature of equal tempered tuning. I think explaining music through math can be missleading and limiting. Music is an art made by humans, and humans like some pretty wierd shit..
The formula for a Throbbing Gristle album explained!
Not likely.
I know that’s not really being suggested anyway.
and when Donald sports a safari suit, I don’t care..
@NotPop: Yeah, I was going to get into tempered pianos and then decided it was beyond the scope of the post. The dude is a musicologist, though, so I’m guessing he deals with all that even if it doesn’t make it into the Time article.
My old piano teacher loved western music=math stuff, and I still have some nostalgic fondness for it.
However, replicating the movement of notes as the movements of balls around a circle doesn’t do much for me but confirm that different types of chords involve different spacing between the notes. Which…you know, you could get from looking at a staff of music or…listening to it.
Glad to see posts like this. More smart, less snark.
Keep the snark though.
In my experience, you tune a guitar to itself, mostly. But you’ve got to make a few compromises if you’re playing along with other instruments.
First, I use the adjustable bridge saddles to tune the first partial harmonic at the 12th fret, to the fretted note at the 12th. Make sure the strings are broken in, and aren’t still stretching out. Rough-tune till then! When the guitar is settled, I try to get the open D string in tune with the D on a digital keyboard (known correct, hopefully).
Then, I tune the G-string to the D. The open two-note 4th should have NO oscillation. Then check the 5th, fretting an A on the 2nd fret with the open D. There should be about 1 oscillation per second. Most of the time, it will not be. Fretboards aren’t perfect equal-temperament material, that’s for sure! It’s a judgment call, at that point. You might want to play a note or two on the fretboard, that you’re planning to use later, and compare it to the note on the keyboard. If it sounds out of tune, you might want to cheat it a bit with the fine-tuners. On the other hand, I hate it when an open G-chord sounds warbley, so I rarely mess with the perfect open 4th D-G chord, even on badly-made fretboards. Hopefully, it tends flat (most fretboards do), and you can pull notes a little sharp with your fingers. (Most of us do that anyway, especially with vibrato…)
I then tune the A-string to the D the same way, only I usually end up dropping the A to nearly match an A on the keyboard. (Tune low, and go back up, of course…) Then the low E to the A. I don’t even bother with the perfect 4th. I tune it so that the basic thrashing 3-note E-chord sounds right. (E-B-E) Check the low E out against the keyboard, too, but it’s not going to be exactly right. You might want to cheat a little, if there’s blazing dissonance..
For the B-string, I tune it to the G-string, playing an open G and fretting the B string at the 3rd fret. Again, I first tune it to no oscillation, but then, I definitely cheat sharp on this one. If you tune the entire guitar on perfect fourths, the low E and the high E will be badly out of tune, so you’ve GOT to fudge things somewhere, and I do it here, and on the next string. High E tuned to the B-string, but pulled ever so slightly sharp. If I cheat any further, it might be to make certain thirds sound better on jangly, non-distorted things, like “Stairway.”
Even on a fixed bridge, you’ve then got to go back and check the open D against the keyboard. Chances are the entire guitar has gone flat while you were tightening strings. You might have to repeat the whole process two or three times. With a floating bridge, over and over again. Don’t tighten those string locks…
I’ve never had lessons on this, or playing. I don’t own a tuner, either. I don’t like how machine-tuned guitars sound, usually! Professionals tend to cringe at everything from my hand positions, to pick technique, to tuning. I don’t know if my tuning method has any validity, but it’s just an effort to make the guitar sound good on a variety of tunes, and it’s definitely not scientific.
Yeah, music and math are a neat (albeit Beauty-And-The-Geek-esque) marriage. See: Fibonacci numbers.
Rousseau did a really good job of disproving the “naturalness” (as opposed to social construction) of the Western diatonic system in the eightenteenth century…
@AcidReign: yeah, my guitar’s ALWAYS out of tune whenever I tune it by fourths to itself. But I suspect that’s because it’s a shitty Squier.
Who knew that Idolator had so many music geeks in its readership? Sounds like we need more articles like this.
@NotPop: It can be misleading, or in the case of some of Mozart’s (see: Sonata No. 1 in C for an easy one), plenty of Bartok’s (see: “Music for String Instruments, Percussion and Celeste”), Webern (Variations for Piano, Op. 27) and all of Xenakis’ (pretty much any, although it’s not golden ratio related…) work, it can be surprisingly illuminating as well. To suggest otherwise is to suggest that a modicum of understanding about the Christian Mass is superfluous to understanding Bach or most music of his era.
Oh sorry about that… American Idol, Hannah Montana, Britney, MTV, record label death, Trent Reznor. OK, quota filled!