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MaryAnn wrote:How do you deal with that? These people are in their 50's and 60's. This kind of thing is a constant in the groups I play in, which are of necessity amateur groups.

MaryAnn wrote:I did the guitar thing many years ago in a bluegrass band I was in....I woudl retune the guitar when I played it so that the chords were as in-tune as you could get them (fretted instrument; can't get it perfect) What was weird was that he sang in tune, so there wasn't anything "wrong" with his ear, just his concept.

Just Intonation is the system of tuning pitches to the simplest (and most beautiful) possible intervals. This simplicity may be both appreciated aurally, since the just-intoned intervals are strikingly clear and consonant; and understood conceptually since the intervals can be defined in terms of simple arithmetical relationships.

Perhaps, for some readers, a bit of basic acoustics would be useful at this point. All pitch relationships (intervals) may be described by a comparison of the relative speeds of vibration of the individual pitches. Imagine any two voices or instruments. One plays a pitch that vibrates 770 cycles per second and the other plays a pitch that vibrates 392 cycles per second. The relationship between the two pitches is 770 to 392 which is reducible to 55 to 28---a fairly dissonant interval that sounds like a very large major seventh. Now magine the same two instruments playing 800 and 400 cycles per second respectively.

800 to 400 or 800/400 is reducible to 2/1 which is alled the octave, a very consonant interval. All intervals, from the octave to the most dissonant, may be defined by such fractional relationships. Generally, it may be said that the simplest fractional relationships sound the most consonant, and the most complex relationships sound the most dissonant. In Just Intonation, the perfect fifth is 3/2, the perfect fourth is 4/3, the major third is 5/4, the minor third is 6/5, etc.

Just Intonation is not the system used to tune instruments in current Western culture. These small-number-ratio intervals do not exist on the piano or other Western fixed-pitch instruments, as well as in virtually all Western music of the last couple centuries. In the current Western tuning system of 12-tone Equal Temperament, the octave is divided into twelve equal intervals which must be at least slightly out of tune in order to accomplish the desired equality.

The reason that equality necessitates "out of tuneness" may be understood by further examination of the multiplicative, not additive, nature of pitch relationships. As music theory is commonly taught, one adds and subtracts pitches to and from one another: i.e. a major third plus a minor third equals a perfect fifth. This language of common music theory is cleverly designed to obscure (in the name of simplicity) the actual multiplicative relationships of intervals by having the musician add exponential values without necessarily
understanding that one is even dealing with exponents. In 12-tone Equal Temperament, the smallest interval (minor second) must be of a size that will produce an octave (2/1) when multiplied by itself 12 times. The equal-tempered minor second is the twelfth root of 2 or 21/12, the major second equals 21/6, the minor third equals 21/4, the major third equals 21/3, etc. The musician who thinks an equal-tempered major third plus a minor third equals a perfect fifth is actually expressing: 21/3 X 21/4 = 21/3+1/4 = 23/12+4/12 = 27/12. And thus musicians, many of whose mathematical abilities stop at counting, can innocently practice logarithms.

In Just Intonation, on the other hand, the math is much simpler. One multiplies a major third by a minor third to obtain a perfect fifth: 5/4 X 6/5 = 3/2 (perfect fifth). One divides a perfect fourth by a major third to obtain a minor second: 4/3 ÷ 5/4 = 16/15. Compared to 3/2 and 16/15, 27/12 and 21/12 sound unfocused. For anyone who has the opportunity to make an aural comparison, the just-intoned intervals will be clearer and more consonant than the equal-tempered. This doesn't mean that all just-intoned music will be consonant. Unlike 12-tone Equal Temperament, Just Intonation is an open system to which any number of tones may be added.