List: Here is the final part of this current series. PURE 5ths Using the Accutuner Part III It was while playing around with altering the A4 stretch numbers that I discovered the possibility of having equal temperament with pure 5ths. For sometime it had been noticed that when the temperament octave was stretched a little more than before that the 5ths would be slightly slower and the 4ths would be a little faster in beat rate. The original experiments were done on my Steinway L which had FAC stretch numbers of 7.0, 8.5, 8.6. By adding 1.0 cents to the A4 stretch number, the center octave was stretched enough to make the 5ths come out pure in almost every case. Now this was at the expense of making the 4ths faster as well as the single octaves. The smooth curve ability of the SAT kept the 3rds and 6ths well in line, but the 10ths were a little faster, but the progression was smooth for all intervals. At first one may object to the wider octaves, but after tuning the piano this way, and playing music, it was not objectionable and the wider octaves prepared the way for slightly wider double octaves than the normal readings would provide. While playing two handed block chords up and down the piano, there was a solidity noted which far outweighed the slightly stretched single octaves in the center of the piano (up to 1.5 beats). By the time I reached the 5th octave, and making the 1.0 cent reset, necessary as explained in previous articles on Altering the Stretch Numbers, the test for 3rds, 10th and 17ths showed a very decided increase in the 17ths over the 10ths. But the payoff was in the fact that the 5ths and 12ths continued to be pure. By the time I reached the octave 6, the 5ths were actually stretched, but the 12ths continued to be pure and the triple octaves were also pure. Eventually the 12ths (octave-5ths) gave way to the pure 19ths (double-octave-5ths). The top half of octave 7 may have been a little too much as single octaves, but the triple octave sounded so good, that it was tolerable. The octave-5ths began to be on the wide side too. There is a difference between our melodic sense of hearing and our harmonic sense of hearing. One can prove this to himself by playing middle C with a short staccato blow and while remembering the pitch, playing the C7. Most of us would rather tune the C7 a good bit higher in satisfying the melodic sense than we would tune it as a triple octave sounded together. This test has been done in many of my tuning classes over the years. Most classes preferred to hear the C7 somewhere around 17 to 30 cents sharp when C4 and C7 are played melodically (one note after the other). This gives a stretch on most pianos which would make even a triple octave beat on the wide side (ie too sharp). By progressively sharpening the single, and double octaves as proposed by this series of articles, there is less difference in beats between the single, double and triple octaves as viewed from octave 7. At this point, I am beginning to think that this is what Virgil Smith is doing or at least approaching when he says he can get pure single, double, triple, and sometimes quad octaves. He definitely does make the 5th and 6th octaves sharper than most of us have been doing. Another interesting discovery during Bass tuning was that in going down below the break, I was able to maintain pure 5ths. Most of you have noticed that the normal Bass stretch using the FAC numbers, provided Bass octaves which are usually stretched to make the 6-3 octave relationship a little wide. During this greater stretch, it was noticed that the 5th above the note being tuned was almost always pure. This should not have been surprizing to me when I consider that for example when tuning C2, the machine is listening to the 6th partial which is also the 4th partial of G2. I already knew that the normal curve of FAC tunings attempts to keep the double octaves fairly clean, so since the partial which the machine listens to is two octaves above a note a 5th higher than the note being tuned, the match is very good. Of course, one should expect some slight variation in all Bass tuning tests, because the inharmonicity of Bass strings usually jumps around quite a bit (ie you can't have everything coming up like roses) during the tuning process. There is almost always a jump as you cross the break between the 2 string unisons and the single Bass Strings. Usually the 17ths and double-octave 7ths slow down or else one is widening the 5th, the octave and the double-octave more than normal. Since starting this series, almost every piano I have tuned has been tuned with the above principles, giving close attention to the sound of the various intervals. The comments which I have heard go more or less like this: "The piano seems to have a bigger, fatter sound, I like it." Perhaps after you get over the shock of the wider single temperament octave, you may like. Of course, if you don't, it's OKAY. I do think you should try before you reject it however. Otherwise, you may never know what you are missing. I've missed it for over 55 years. So, you see, I may have been over-rated as an expert for many years. But, this old dog IS learning some new tricks.
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