- anyone read Evan Valens "The number of things: pythagoras, geometry
and humming strings"? From the sixties, it is a good introduction to
some of the things that impact is here on this list. I particularly
like it as a primer for figurate numbers--best explanation of this
topic by far.
Anyway, I liked this nugget:
In elaborating about the Pythagorean theorem and showing how a square
can be broken down into composite triangles that illustrate the
theorem, Evans uses the example of Egyptian rope stretchers (knotted
in 12, you can approximate right angles by forming the rope into a
triangle of 3,4 and 5 knots).
Taking this example further, Evans says
"the old Egyptian rope trick can be performed in another manner, with
delightful results, by stretching a guitar string around three nails.
The nails are separated by distances of 3, 4 and 5 units. the string
can be tightened by a set-screw at one corner, and small pulleys at
the other two corners will help keep the tension equal on all sides.
When the three strings are plucked they will sound a musical chord, an
inverted minor triad.
if the longest side is tuned to G, the other two sides will sound B
and E. this is the chord sounded by the top three strings of a guitar.
now, this is a most unlikely event. an assortment of guitar-string
triangles of random shapes is not likely to produce even on e sonorous
triad. why should the simplest of right-angled triangles give us on e
of the most common musical chords?"
well, actually it is not a "most common musical chord". technically,
G-B-E is an E-minor chord. nothing minor is "most common". however, I
take his point to mean that the top three strings of a guitar is
in case you are wondering what songs are played in E-minor, Red River
Valley is. If that is not familiar, it is a common enough blues
tuning. Skip James generally played in D-minor or E-minor--they are
roughly equivalent tunings. So to get a feel for what a song sounds
like in this Pythagorean tuning, check out the movie "O Brother Where
Art Thou?" starring George Clooney. Not only does Clooney break his
womanizing-mould and actually act in this movie, it features Chris
Thomas playing a classic delta blues guitarist. Actually this is funny
since his character's myth is build on the legend of Robert Johnson.
However, the song he actually plays in the film is Skip James' "Hard
Time Killin". Anyway, listen to the song and you get a sense of E-minor.
And who said I couldn't connect Pythagoras and the blues? humbug.