I’ve been saying that any note can be the “one” note to guitar students for years but it occurred to me recently that if that’s true, then that one note has two functions at the same time! Number theory says that it is the tonic, because that’s what the one note is- the tonic in a sequence of notes that moves up (or down) to its octave. So at the same time, the one note is the tonic for the octave ascending as well as the octave for the descending sequence below it. The same numeric sequence, ascending or descending is available from that first note!
Here’s an example. Play one twice. Go up to flat 3 then down to 1 again. Now down to b7 and continue down to sharp 5 then down to 5…
With a little imagination you can hear the first part of the lick from “7 Nation Army”
You can see how useful it might be to understand the notes as numbers! Shifting that sequence of notes to start at a different one note simply means changing your sequence to another key.
Most guitarists, when we start, tend to think about notes and chords as patterns but I’m beginning to wonder if it might not be more useful to think about them as numerical relationships.. not “instead” but rather “as well as”.
Here’s another simple example: We can play 1. 7, 1 and 2 on any one string easily.
1 of course would be your tonic, whatever note that is. 7 in a major scale is a half-step below the 1, so that’s simply the next fret down toward the headstock. Back to 1 again, so a fret back up toward the body. Now 2 is a whole step above 1, so two more frets toward the body gets us that note, and back down to 1 again to resolve our sequence: 1/7/1/2/1. Sounds nice, right? The key that we’re playing in has the same name as the 1 note.
Here’s the cool thing about that. If you can play it in one place on the neck, you can play it in pretty much anywhere else on the neck, even on one string (you have to make sure that your major 7th note is available, at least on the open string). It’s kind of ironic that this idea is true, independent of any key sequence simply because is available in every key sequence.
If you have either a naturally good ear or a well-trained one, this might seem obvious to you. But if you don’t have a natural ear or you haven’t trained your ear well yet, understanding that you can hear note sequences, melodic or chord tones as a series of numbers that relate to one anther might be profoundly impactful for your self improvement on guitar.
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Here’s an example of how you might employ some ideas about numbers.