ToddK -> RE: easier to play with capo? (May 28 2010 16:09:00)
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quote:
So you're saying that this happens even with high end guitars? i think maybe you arent sure what equal temperament is. It does not matter how great the guitar is, or how great your intonation is. Equal Temperament is a musical tuning system that divides the Octave into 12 geometrically equal steps. Each step is one semitone. When moving up one step, the frequency (or pitch) increases by 2^(1/12). Using this system, the Octave (12 semitones) is perfect, because 2^(12/12) = 2^1 = 2, an exact doubling of frequency. But the Fifth (seven semitones) is 2^(7/12) = 1.498 times the root. A perfect fifth, on the other hand is exactly 1.5 times. The difference is small, but it is significant. If you want to hear this, play the 6th string 7th fret harmonic. Now stop the string at the 7th fret and play the assisted harmonic at the 19th fret (effectively the new 12th fret). This note will sound very slightly flatter than the 7th fret harmonic. In Equal Temperament tuning, the slightly flat note is the correct pitch. A common reaction is that Equal Temperament must be 'wrong'. Surely it's better to use perfect intervals instead? •The theoretical problem with this is that you are then restricted to very simple music that remains mostly in one key. If you progress through the 'cycle of fifths' (C, G, D, A, etc) by perfect intervals, when you finally get back to C (after 12 steps) you'll find that it's a very different C from the one you started on! However, by slightly flattening each fifth, after 12 steps you'll arrive back exactly where you started. Thus Equal Temperament slightly compromises every interval (except unison and octave) so that all keys are equally acceptable. This brilliant invention is what made Western music so harmonically rich and varied. •The practical problem, for a guitarist, is that your instrument has a fretboard layout mathematically designed for Equal Temperament. Unless your open strings are correctly tuned, all your 'cross-string' intervals become arbitrary
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