time considered as a sequence of many-named values (modulo twelve)

January 18, 2011 in Graphics, Music

E__F__*__G__*__A__*__B__C__*__D__*__E

B__C__*__D__*__E__F__*__G__*__A__*__B

G__*__A__*__ B__C__*__D__*__E__F__*__G

D__*__E__F__*__G__*__A__*__B__C__*__D

A__*__B__C__*__D__*__E__F__*__G__*__A

E__F__*__G__*__A__*__B__C__*__D__*__E

so here’s a picture of the neck of a guitar.
i’ve been drawing it a lot; here it is in cold type.

it looks all wrong already and will no doubt be
munged up altogether by the miracle of the
god-damn internet by the time anyone sees it.

but in the meantime, i can cut-and-paste to produce
displays like
E__f__*__g__*__a__*__b__c__*__d__*__e

b__C__*__d__*__e__f__*__g__*__a__*__b

G__*__a__*__ b__c__*__d__*__e__f__*__g

d__*__E__f__*__g__*__a__*__b__c__*__d

a__*__b__C__*__d__*__e__f__*__g__*__a

e__f__*__g__*__a__*__b__c__*__d__*__e

where i’ve boldfaced the notes of a
C chord. on paper i mostly draw circles
around scales or chords or individual notes;
i also use a certain amount of underlining.
bold face comes into play, too.

there are some examples in my last post but one
(with mistakes intact… i know of three so far). anyhow,
this looks very much like the music-theory-for-guitar
tool of choice. chord diagrams are common of course
but they generally leave off the names of the notes.
for me, right now, these are pretty close to being
the whole point. sure, i’m mostly working out
*numerical* relationships (like the gaps in a
minor scale: 0, 2, 1, 2, 2, 1, 2, 2 [or the absolute
numbers 0, 2, 3, 5, 7, 8, 10, 12])… but their
instantiations in specific examples long known
to me by kinesthetics are there to make
the results vivid and memorable.

so. the high three notes on the chord in the diagram
are GCE; the middle three are EGC; the high notes
are CEG. these are so-called “inversions” of the
C-major chord. by putting the “tonic” note–C–
at zero and counting so-called “half-steps”
(notes on the piano without regard to
color-of-key… one-fret differences on
the guitar; steps from the 12-tone “chromatic
scale”), one arrives at
0,4,7 for the root-in-the-bass inversion;
-5, 0, 4 for the root-in-the-middle;
and -8, -5, 0 for the root-in-the-treble.

the “negative number” approach is probably
pretty unusual but comes very natural to *me*.
it would be just as true… but maybe less useful…
to say that these patterns are described by
047, 059, 038. (one has moved the “0” to
the bass-note-whatever-it-is; one drawback
of this notation is that we can’t “read off”
the name of the chord as easily).

also one is of course working “modulo 12”:
twelve half-steps above any given note
is the next-higher note having the same name
(and twice the so–called “frequency”:
the string vibrates twice as fast).
in “mod 12” arithmetic, 12 is replaced
with 0; other numbers with their
remainder-on-division-by-twelve.
it follows that, for example
-8 = 4 (mod 12) and
-5 = 7 (mod 12), so
the weird-looking -8, -5, 0 inversion
turns out to be nothing but
4, 7, 0… the E, G, C by
their ordinary chromatic-scale names
(with C at 0).

e__F__*__G__*__A__*__B__c__*__D__*__E

B__c__*__D__*__E__F__*__g__*__A__*__B

g__*__A__*__ B__C__*__D__*__e__F__*__G

D__*__e__F__*__G__*__A__*__B__c__*__D

A__*__B__c__*__D__*__E__F__*__G__*__A

E__F__*__G__*__A__*__B__C__*__D__*__E

in raising the CEG from the (ordinary, first-position)
C-chord of the first display by 12 half-tones,
we of course get another 047-inversion
C-major chord. for the C and E this is
accomplished by going one string higher
and seven frets higher… but for the G
by going one string higher and *eight*
frets higher… this is due to the quirk
in tuning known to all guitarists: the
gaps between strings are 5,5,5,4,5
(in the standard tuning; of course
there are many others… a few of
them known even to me).

guitar players will recognize the resulting
“shape” as an F-chord slid up seven frets.
i’ve been looking into the relationships
among the long-familiar “shapes”…
that, essentially, *follow* from the
5,5,5,4,5 pattern. and having a blast
doing it.

but. i exaggerate for rhetorical effect.
the *real* result of all this scribbling
and calculating is that i’m not thinking
about *money* or *social life* or any of the
million other things i can never seem
to get any satisfaction out of (but
can sure as hell get incredible
amounts of *frustration* out of).
if this isn’t “having a blast”,
well, it’s mostly the closest
i can expect (and lucky to get
even this).

i “had fun” typing all this up, too: same effect.
until i got to the part about my actual life,
i was solving little abstract “problems”
like “how can i say this clearly” or
“how many notes apart are C and E”
or what have you and using the results
to make *improvements* in the manuscript
for this blog post. the feeling that
one is making *something* better
in this crazy life, even something
as meaningless as a blog post,
is the feeling of *something going right*,
and damned hard to get. but…
better than a poke in the eye with
a sharp stick… when we feel “good”,
we’re mostly really feeling *nothing*.

this is, i think, how “obsession” works.
why are so many math-heads nutjobs?
because so many nutjobs become
math-heads… it’s the only thing that
makes the voices-in-the-head quiet down.
musicians too.

a very lucky few in each field of endeavor
are able to find other people that’ll care
about what they’re doing. most of us
have to be content with the doing itself
and count ourselves lucky to get it.
god knows it beats TV.

probably i’ll become a better guitar player
from all this. and, sure, i’ve had some
satisfaction *playing* for other people;
there is *some* investment-paid-off quality
to be had from all the hours and hours
of this-is-no-good, not-this, not-yet,
work-work-work, beavering away.

but that’s guitar. the real motorcycle
one is working on is a motorcycle
called “teaching-and-learning”….
where i can sometimes convince
*myself* i’ve gained some momentary
“insight” into some part of The Art…
but i emphatically do *not* feel myself
becoming a better teacher. (of others;
*maybe* of myself though heck knows
i’m still a very slow learner like always
and anyhow, this is better described
as being-a-better-*student*).

so it’s very frustrating. meanwhile, the students
most in need of my help are the very ones that
avoid me the most effectively etcetera etcetera.

nothing will bring you peace but the triumph of principles.
stated more clearly: nothing will bring you peace.

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