Just a place to jot down my musings.

Monday, May 12, 2014

Guitar tuning and contravariance

I’ve been fiddling around with a guitar for a few years now, trying to occasionally produce a few notes that sound mildly musical. Since I don’t usually get anything done unless I put immense pressure on myself, I decided to record myself playing and singing a song ("Daaru Desi" from the Bollywood movie Cocktail) that would force me to actually learn some chords.

There was only one minor hitch: the song is in G♯m.

The opening riff involves the chords G♯m and D♯, which have to be played with barre chords on the 4th and 6th frets of the guitar. This raised two issues:
  1. My barre chords are atrocious
  2. Whereas in the opening riff the D♯ is clearly lower than the G♯m, playing them on the 6th and 4th frets means the D♯ sounds higher than the G♯m.
After much shedding of sweat and tears (fortunately no blood), I was on the verge of giving up, when I accidentally played the chords on the 5th and 7th frets. This of course shifted the song up by a semitone, and resulted in me playing the Am and E chords (on the 5th and 7th frets). I was now out of tune with the original song, being too sharp by a semitone, but since I didn’t really care about that, I now had the option to play the Am and E chords in open position. This then had the further consequence of making the E lower than the Am—just as the opening riff demands.

I realized I had almost cracked the puzzle of the song. All that needed to be done was … what? Retuning the guitar so that the Am open position on the regular tuning became a G♯m instead, and the E open position on regular tuning became a D♯ instead. All I had to do was to tune every string a semitone flat. (This is apparently called the E♭ tuning.)

With this new tuning in place, I was able to play the song in the same key as the original—and was able to play it using mostly open position chords.

Now, if this were all, it wouldn’t make for a great story. What got me excited, though, was the fact that I had realized a deep truth about tuning and music:

an instrument’s finger positions contravary with its tuning

In plain English, it sounds commonsensical: if you lower the tuning of a string, you’ll have to play at a  correspondingly higher position on the string to produce the same frequency earlier. Hmm, now it doesn’t sound that exciting at all. Oh well.


1 comment:

  1. I'm excited! I realized the same today and found your post. It's quite logic if you think of the tuning as the base and the fret as the coordinate of a vector. Retuning the guitar corresponds simply to a change of base. Intriguing indeed!

    ReplyDelete

Why pearls, and why strung at random?

In his translation of the famous "Turk of Shirazghazal of Hafez into florid English, Sir William Jones, the philologist and Sanskrit scholar and polyglot extraordinaire, transformed the following couplet:

غزل گفتی و در سفتی بیا و خوش بخوان حافظ

که بر نظم تو افشاند فلک عقد ثریا را


into:

Go boldly forth, my simple lay,
Whose accents flow with artless ease,
Like orient pearls at random strung.

The "translation" is terribly inaccurate, but worse, the phrase is a gross misrepresentation of the highly structured organization of Persian poetry. Regardless, I picked it as the name of my blog for a number of reasons: 
1) I don't expect the ordering of my posts to follow any rhyme or reason
2) Since "at random strung" is a rather meaningless phrase, I decided to go with the longer but more pompous "pearls at random strung". I rest assured that my readers are unlikely to deduce from this an effort on my part to arrogate some of Hafez's peerless brilliance!

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Cambridge, Massachusetts, United States
What is this life if, full of care,
We have no time to stand and stare.
—W.H. Davies, “Leisure”