Brian Wilson wrote: > Sounds really good.... thanks > Can you also work out the theoretical speed of 3rd, 10th, 17th etc. > something like C4 and E4. I have answers with my calculations, but it may > seem that your answers may be slightly different. Interesting... > conflicting published versions.. now I want to burn those books! > So I have another question... my "stretch" as been described as conservative > by a concert tech, and he asked me for "more stretch" and unfortunately the > answer was not in English, but he showed me more stretch from F4.I listen to > many recordings and I have to tell you that my favourite CD was recorded at > Carnegie Hall unfortunately no name of pianist, but the stretch is huge... > and it sounds fantastic. First, I'm no tuning authority. There are legions of folks out there that are more knowledgeable, certainly more debative, and demonstrably more skilled than I'll ever be at that corner of this profession. But I have at least tried to pay attention as I slogged through the years of seemingly random misinformation and resulting mutant reality as it morphed through a sort of cheezy Lon Chaney Jr full moon $2.98 special effects sequence regarding tuning. "Stretch" has always been the most mutant concept of the lot, meaning anything imaginable, depending on who was stretching what. As the pixie dust began to eventually settle, and the view showed the first signs of clearing up somewhat, I realized that the "stretch" was going to be defined not by someone's arbitrary and exclusive cognitive insight into the vast cosmic mystery, which tended to be the universally useless (to mere mortals) ultimate answer through most of my professional existence, but by where the test intervals fell. WOW! You mean there's something about this tuning thing that actually makes some sort of organizational sense, where how loud you can shout and how much dense smoke you can generate actually counts less than what you can demonstrate? You mean something like stretch can actually be defined procedurally, and is dependent rather than definitive? Bingo! That's what I want! From my trailer park "sharpened hammer" maintenance man perspective (remember this when you reply), thirds, sixths, tenths, and seventeenths are incremental smoothers, suitable for negotiating equal proportions to intervals within an otherwise determined octave stretch. Fourths, fifths, octaves, and double octaves are stretch indicators, and about the only useful ones available to the aural tuner beyond the temperament octave(s). Splitting the fourth and fifth after the initial octave rough in gets you in the ballpark quickly, and lets you know when you can realistically spend time on the faster beating intervals for further refinement. Further refinement does not, however, significantly change the 4th/5th/octave relationship that effectively defines octave stretch. Tuning to what the piano claims it wants, by this criteria, results in everything falling into place quite pleasantly, with the fourth and fifth beat rates being essentially similar throughout the scale. Too easy. That can't be right. All I can offer is that you explore it aurally and find what you find. If you find anything different, post what you did and what you found as a result for someone else to explore. Pumpkin time, Ron N
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