Dentes.
— The teeth of the neck · 25 chords · Drop C —
the teeth.
Twenty-five chords from one night in September, on a guitar tuned to Drop C, each read back out of its recording note by note and drawn as the shape that holds exactly those notes. Tap a shape and its strings are built from noise and strummed. Tap the take and you hear the hand that played it.
A fretboard is a row of teeth. Press a string behind one and it bites: the string can only ring from that wire to the bridge, and the note is whatever length is left. A chord is six bites taken at once, and a shape is the memory of where the teeth were. Three witnesses stand behind every tap on this plate: the rule that placed the teeth, the law that says why they work, and the loop that lets a browser pluck a string.
Vincenzo Galilei, lutenist and father of Galileo, gave the lute a rule in his Dialogo della musica antica et della moderna (1581): divide the string by eighteen and set the first fret there; divide what remains by eighteen again, and keep going. Each tooth takes an eighteenth of what is left. Twelve of them land a hair short of the octave. The rule leaves 50.4 percent of the string where equal temperament leaves exactly half, about an eighth of a semitone flat, and it could be laid out with nothing but dividers and a straight edge.
Marin Mersenne, a Minim friar in Paris, wrote down why the teeth work in Harmonie universelle (1636): a string's pitch rises as its length shortens, rises with the square root of its tension, and falls with the square root of its weight. Halve the length and the frequency doubles. Every fret is that law, applied with a finger.
Around 1979 Kevin Karplus and Alex Strong found that a plucked string could be made from almost nothing, cheap enough to run two or three voices at once on an 8080A microprocessor. Fill a short delay line with noise and let it circulate, averaging each sample with its neighbour as it comes around. The length of the line is the pitch; the averaging is the string losing its brightness. They published it in Computer Music Journal in 1983, and Stanford licensed the patent. Every strum on this plate is that loop, run in your browser at the moment you tap. None of the strummed notes is a recording.
The comb in Cylindrus is a row of steel teeth, each tuned by its length, each struck once by a pin. The fretboard turns that inside out: one string, and a row of teeth that choose its length. Plate XXXI is the method, what the hands practise. This plate is what the hands made.
The shapes are inferred. The take is not.
How the shapes were found. A recording says which notes sounded, not which fingers made them. Each shape is the most compact way to fret exactly those notes in Drop C; the hand may have used another. Where a chord caught a note still ringing from the one before, or an octave slipped, the shape leaves that note out and marks it in red. The take keeps everything.
the tooth is the note.
The rule. The law. The loop. Tap a shape. Then hear the hand.