Dear Kuang, It is not possible to evaluate how you are tuning from your statement that you use perfect fifths to tune pianos. How do you judge your fifths to be perfect? Are ALL your fifths perfect? Do you test your fifths or simply make them sound just to your ear? I would love to evaluate your tuning- not to make a judgment about you or your competence, but from genuine interest to know what you are actually doing, and what musical instincts may be coming into play.... Is it equal temperament? You tell me; do all of your thirds beat at the same ratio? That is, do your thirds progress evenly, as you ascend chromatically? If you are in fact tuning ALL your fifths pure, then all the thirds are also coming out the same size, and likewise all the other intervals... This would qualify as equal temperament, in a way; but common practice at this time is for tuners to make the fifths a bit narrow, a very small and specific little bit! If your fifths are all the same size, and if that size really, REALLY IS pure, your octaves are going to be wider than what is commonly accepted as in good taste. Piano tone is a bit fuzzy around the edges, so to speak, and your fifths may sound pure by direct listening, yet not in fact be truly just; then your octaves might be on the wide side, but still within the bounds of good taste, as it were.... Do you know how to 'test' your perfect fifths? If the fifth is just, and you add a major third, the resulting major triad will have major third that beats twice while the minor third beats three times... If you make it a minor triad, the minor and major thirds will beat at exactly the same rate. If you tune a complete cycle of fifths that meet this test, your octaves will be pretty wide, and I doubt very much that's really what you are describing... But how about you try to describe an actual bearing plan, including tests, for how you are tuning.... or are you depending a lot on melodic intervals, and not being a 'beat counter'? "What is well temperament" is a little easier to answer, I think! (to be thorough , there are about three dozen specific rules, but you may get the idea if I say) If there are no major thirds smaller than just, and no fifths larger than just, and if the smallest third is on C-E, and the largest third is on Gb-Bb, and the thirds change gradually in size, it's well temperament. Here is maybe more theory than you're asking for; Equal Temperament is the vain attempt to make three major thirds add up to an octave. Meantone is the acceptance that two major thirds plus one diminished fourth is VERY close to adding up to an octave. Well Temperament is an attempt to maintain the 'two major thirds plus a diminished fourth' character of meantone, while eliminating the 'harmonic waste' of one or more wider- than-pure fifth(s), and reducing the diminished fourths to a size that we can tolerate. Hope this helps, and I sure want to understand what you are actually doing, it must be interesting! Paul Bailey RPT San Mateo CA 103445.713@compuserve.com >HI, I'm new to this field. Can you explain me the difference between >well temperaments and equal temperaments? I use perfect fifths to tune >pianos. Would that be equal temperament? I appreciate your valuable time. >Kuang On Sun, 9 Mar 1997, Paul N. Bailey wrote: > > Pianos sound better in well temperaments than they do in equal > temperament. > > > >
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