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Harmonic postions

Discussion in 'General Instruction [BG]' started by dlloyd, Aug 16, 2005.


  1. dlloyd

    dlloyd zzzzzzzzzzzzzzz

    Apr 21, 2004
    Scotland
    I thought it might help some here if I posted a list of harmonic postions and their qualities.

    I get confused with intervals above a 13th, so I broke them down to octaves + additional interval for simplicity.

    The numbers are calculated fret positions above the fretted position rounded to one decimal place.

    Code:
    	        octave	        good	12.0									
    octave +	perfect 5th	okay	7.0	19.0								
    	        2 octaves	good	5.0	###	24.0							
    2 octaves +	major 3rd	flat	3.9	8.8	15.9	27.9						
    2 octaves +	perfect 5th	okay	3.2	###	###	###	31.0					
    2 octaves +	minor 7th	v.flat	2.7	5.8	9.7	14.7	21.7	33.7				
    	        3 octaves	good	2.3	###	8.1	###	17.0	###	36.0			
    3 octaves +	major 2nd	okay	2.0	4.4	###	10.2	14.0	19.0	26.0	38.0		
    3 octaves +	major 3rd	flat	1.8	###	6.2	###	###	###	20.8	###	39.9	
    3 octaves +	dim 5 	        v.flat	1.7	3.5	5.5	7.8	10.5	13.7	17.5	22.5	29.5	41.5
    3 octaves +	perfect 5th	okay	1.5	###	###	###	9.3	###	15.2	###	###	###	43.0
    As a brief explanation, when you play a harmonic, you are subdividing the string length into equal parts. The twelfth fret harmonic is exactly half the length of the string, so when you touch that harmonic, you are dividing the string into two equal parts and sounds at a frequency twice the fundamental. The seventh and 19th fret harmonics divide the string into 3 equal parts and sounds at a frequency three times the fundamental. And so on.
     
  2. Vorago

    Vorago (((o)))

    Jul 17, 2003
    Antwerp, Belgium
    Thanks, I'm printing it right now! :)
     
  3. dlloyd

    dlloyd zzzzzzzzzzzzzzz

    Apr 21, 2004
    Scotland
    If anyone needs higher order harmonics than that, you can calculate the fret postion with this formula:

    12*(log(2)(x/y))

    Where y is the order of harmonic (fundamental = 1) and x is a positive integer less than y, that y is not divisible by.

    for example x/y can equal 1/3, 3/5, 2/7 but not 2/4 (because that's the same as 1/2).
     
  4. dlloyd

    dlloyd zzzzzzzzzzzzzzz

    Apr 21, 2004
    Scotland
    There's a slight error on that page, which is probably a typo.

    They state the seventh harmonic of C is an out of tune B#3. Using equal temperament to calcualte C from open A on the bass:

    55 Hz(A)*2^(3/12) = 65.41 Hz

    Multiply that by seven, you get 457.84 Hz, which is a pretty flat Bb3 (466.16 Hz)

    edit: In fact, the figure next to the text shows the seventh harmonic as Bb. So it's definitely a typo.