Random ramblings about guitars
Mar. 7th, 2009 10:23 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
mmcirvinI'm going to say some more things about guitars. Most of my statements are going to be either wrong or idiotically elementary, but I'm saying them so that people who know stuff will be provoked to say something interesting.
If you poke around online, you will find an amazing profusion of pages whose authors have self-constructed systems, patterns or mnemonics they use for playing. A lot of it seems almost like crackpot science literature, except that in many cases the authors seem to actually be competent guitarists, so the systems are presumably working for them if not for anybody else.
I think that a lot of the reason for this fever-dream creativity is just that the fingerboard of a multi-stringed instrument possesses a symmetry: for a guitar, it's the operation in which a fingering moves down to the next lower string, and up five frets toward the bridge (or four if it's from the B to the G string), which maps a note onto an identical note. If you keep doing this you'll fall off the fretboard before long, but the resulting collection of symmetries can be turned into a symmetry group in the mathematical sense if we imagine an infinite continuation of the fretboard in all directions, or join it into a torus by factoring out some octaves, identifying the high and low E strings with each other and fret 12 with the nut. I suppose it's not a very interesting group then, really just a complicated action of Z5. But it's sort of like a gauge symmetry—you can apply it independently to every note.
What that means is that you have a huge amount of leeway to decide what fingering you're going to use to play a given sequence of notes. And it seems like a lot of what goes on in getting proficient is to come up with a private toolkit of fingerings you like and that work well with your hands (in other words, the symmetry-breaking element is the player). With immense practice, these scale patterns also eventually overlap in your head to get you familiar with all the notes on the entire fretboard. Textbook examples are just the starting point, though of course it's really all I've got so far.
But I'm starting to independently notice stuff. When I read about the five pentatonic boxes I pretty quickly figured out what this guy is going on about, that the symmetry action on the toroidal fretboard lets you generate all five from the first one they teach you—but it's not in the order that lets them fit together like puzzle pieces on the fretboard, it's in a different order in which you always skip over a box. That helped me understand why the root note shows up where it does in the different boxes, since the root is always going to move over one string in the order of generation. (Earlier, I'd realized that a similar action could generate most of the standard open chord shapes from a few basic prototypes, which helped me learn them, even though knowing something visually with your forebrain is one thing and knowing it by linking ears and muscles is quite another.)
I also figured out the commonality between the C major diatonic exercises in the instruction book I have, and some of the other stuff I'm reading. The C major scale played partly with open strings near the nut is a superset of what I think of as pentatonic box 4 in C major (there are a million contradictory numbering systems but I call it box 4). It's also a superset of box 1, the first one they teach you, in G major, since the only difference between C and G major is the F/F# which isn't part of the pentatonic scales. But if you're playing C major pentatonic it's box 4.
Anyway, some other pages used "blues in A" as an example, which was A blues starting up at fret 5, and that's basically A minor pentatonic (plus the tritone, D#). So I started playing around in box 1 for A minor, which is also a box for the relative major, C major. It took me an embarrassingly long time to figure out that box 1 at fret 5, and box 4 at the nut, fit together seamlessly into the same C major pattern—the bottom of one and the top of the other form box 5. So apparently I now have some slight familiarity with a pentatonic scale pattern all over more than half of the fretboard, not to mention its major/minor diatonic extension here and there. Now I just have to get used to transposing it in all directions...
Thinking about the fretboard in terms of a symmetry group reminds me of the idea of a tonnetz. I was wondering today if the tonnetz started out as something like the idealization of the fretboard of a viola da gamba, but looking at Euler's first diagram makes me think that it didn't.
Anyway, around the same time I accidentally rediscovered one of these little six-note scale patterns on two strings (scroll to about halfway down the page). Reading about them on that page a couple of days ago, I realized that the "Ionian", "Lydian" and "Mixolydian" ones are none other than Guido's hexachords reborn, apparently as a means of shredding like Steve Vai! Well, the Lydian one isn't exactly the same because these are all modes of the same major scale and you run into the old issue of B. But if you do what Guido did and replace the B with a B-flat there, they are totally his C, F and G hexachords. I have no interest in shredding like Steve Vai but I like discovering this stuff.
If you poke around online, you will find an amazing profusion of pages whose authors have self-constructed systems, patterns or mnemonics they use for playing. A lot of it seems almost like crackpot science literature, except that in many cases the authors seem to actually be competent guitarists, so the systems are presumably working for them if not for anybody else.
I think that a lot of the reason for this fever-dream creativity is just that the fingerboard of a multi-stringed instrument possesses a symmetry: for a guitar, it's the operation in which a fingering moves down to the next lower string, and up five frets toward the bridge (or four if it's from the B to the G string), which maps a note onto an identical note. If you keep doing this you'll fall off the fretboard before long, but the resulting collection of symmetries can be turned into a symmetry group in the mathematical sense if we imagine an infinite continuation of the fretboard in all directions, or join it into a torus by factoring out some octaves, identifying the high and low E strings with each other and fret 12 with the nut. I suppose it's not a very interesting group then, really just a complicated action of Z5. But it's sort of like a gauge symmetry—you can apply it independently to every note.
What that means is that you have a huge amount of leeway to decide what fingering you're going to use to play a given sequence of notes. And it seems like a lot of what goes on in getting proficient is to come up with a private toolkit of fingerings you like and that work well with your hands (in other words, the symmetry-breaking element is the player). With immense practice, these scale patterns also eventually overlap in your head to get you familiar with all the notes on the entire fretboard. Textbook examples are just the starting point, though of course it's really all I've got so far.
But I'm starting to independently notice stuff. When I read about the five pentatonic boxes I pretty quickly figured out what this guy is going on about, that the symmetry action on the toroidal fretboard lets you generate all five from the first one they teach you—but it's not in the order that lets them fit together like puzzle pieces on the fretboard, it's in a different order in which you always skip over a box. That helped me understand why the root note shows up where it does in the different boxes, since the root is always going to move over one string in the order of generation. (Earlier, I'd realized that a similar action could generate most of the standard open chord shapes from a few basic prototypes, which helped me learn them, even though knowing something visually with your forebrain is one thing and knowing it by linking ears and muscles is quite another.)
I also figured out the commonality between the C major diatonic exercises in the instruction book I have, and some of the other stuff I'm reading. The C major scale played partly with open strings near the nut is a superset of what I think of as pentatonic box 4 in C major (there are a million contradictory numbering systems but I call it box 4). It's also a superset of box 1, the first one they teach you, in G major, since the only difference between C and G major is the F/F# which isn't part of the pentatonic scales. But if you're playing C major pentatonic it's box 4.
Anyway, some other pages used "blues in A" as an example, which was A blues starting up at fret 5, and that's basically A minor pentatonic (plus the tritone, D#). So I started playing around in box 1 for A minor, which is also a box for the relative major, C major. It took me an embarrassingly long time to figure out that box 1 at fret 5, and box 4 at the nut, fit together seamlessly into the same C major pattern—the bottom of one and the top of the other form box 5. So apparently I now have some slight familiarity with a pentatonic scale pattern all over more than half of the fretboard, not to mention its major/minor diatonic extension here and there. Now I just have to get used to transposing it in all directions...
Thinking about the fretboard in terms of a symmetry group reminds me of the idea of a tonnetz. I was wondering today if the tonnetz started out as something like the idealization of the fretboard of a viola da gamba, but looking at Euler's first diagram makes me think that it didn't.
Anyway, around the same time I accidentally rediscovered one of these little six-note scale patterns on two strings (scroll to about halfway down the page). Reading about them on that page a couple of days ago, I realized that the "Ionian", "Lydian" and "Mixolydian" ones are none other than Guido's hexachords reborn, apparently as a means of shredding like Steve Vai! Well, the Lydian one isn't exactly the same because these are all modes of the same major scale and you run into the old issue of B. But if you do what Guido did and replace the B with a B-flat there, they are totally his C, F and G hexachords. I have no interest in shredding like Steve Vai but I like discovering this stuff.
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no subject
Date: 2009-03-08 05:49 am (UTC)This sums up the entire universe of my guitar knowledge. But I enjoy reading your posts about it.
no subject
Date: 2009-03-08 06:41 am (UTC)What that means is that you have a huge amount of leeway to decide what fingering you're going to use to play a given sequence of notes.
Well... yes and no. Theoretically yes. No, however, if you take into account the necessary minimization of movement you need for speed and accuracy. But I have teeny tiny hands and was playing the Spanish/classical guitar with the wider fretboard, thus may have been approaching fingering in a wildly different way than you are.
I always thought I would have been better at guitar had I been better at math.
no subject
Date: 2009-03-08 07:46 am (UTC)People have been shredding for a long time, on a variety of stringed instruments. There is certainly nothing new about that.
I am waiting for when you find out that the guitar is not justly intonated, and learn about the hacks and kludges around this, like the short nut and the Buzz Feiten Tuning System. Don't wait too long; training your ear to hear the difference between just intonation and what you have when you tune a guitar via the fifth fret (or, worse, the 5th and 7th fret harmonics) makes you a much more nuanced player.
no subject
Date: 2009-03-08 12:21 pm (UTC)I don't thing my ears are trained enough to hear the difference between a just and equal-tempered fourth or fifth, but the thirds are another matter. I was a bit shocked when I learned that the thirds we all use today suck so badly. Tuning systems tried to deal with the problem for hundreds of years and then almost everyone decided to just ignore it.
no subject
Date: 2009-03-08 12:28 pm (UTC)no subject
Date: 2009-03-08 12:54 pm (UTC)A while back I thought of the idea of a game like that with a grid of tiny buttons on the controller, for realistic fingering, so that you could actually learn some real guitar playing from the game. Recently I learned that Mattel actually made such a thing, for kids, but nobody likes it; it's too much like work.
no subject
Date: 2009-03-08 06:27 pm (UTC)no subject
Date: 2009-03-08 07:13 pm (UTC)Instead, it's a way of achieving a more accurate implementation of 12-tone equal temperament across the entire fretboard by compensating for physical properties of the instrument that differ from ideal vibrating strings (such as that the tension on a string increases when it is pressed to a fret, or that the strings themselves have mass).
no subject
Date: 2009-03-08 07:24 pm (UTC)It is possible to get into massive flame wars about this, so I will point out that this is just my conclusion after a few weeks of fooling around with a digital tuner, some BFTS guitars, some short-nut guitars that have other tweaks (PRSes), and some regular guitars. It is obviously not gospel truth.
no subject
Date: 2009-03-08 09:45 pm (UTC)no subject
Date: 2009-03-09 01:41 am (UTC)Open position on your standard-construction equal temper guitar is sharp, and it's ugly. The BFTS flattens it out quite a bit, which is important:
It starts to make sense when you think about how guitars are tuned versus how they are played. To tune a guitar, you pluck the string, then let it ring out as you work the tuning peg. You are tuning the sustain and decay of the note.
But is that how you play the guitar? How many whole notes do you let ring out for seconds at a time, when you are playing? I know I sure don't do that much. I'm either strumming chords, shredding, or occasionally fingerpicking or arpeggiating.
The average player, depending on how hard he uses the pick, can sharpen the attack of a note by up to 25 cents, which gradually flattens out during the sustain. Also, consider what you can do with your fret hand. It is a lot harder to flatten a note than it is to sharpen it by fretting it (although it can be done.)
The BFTS tunes guitars to be sonorous in the way that they are actually played. You really don't have to understand it to hear that the guitar sounds better. But if you fool around with it for a few weeks, experimenting to see how this guitar can be played, you begin to viscerally sense the beauty of it.
More here. (http://www.buzzfeiten.com/howitworks/tuningwtbfts.htm)