Brian: I am going to post the beat rates I calculated under the "Do Fourths Beat Faster?" Topic, but want to reply to some things in this post separately. First, sorry I did not include the other beat rates that you asked for. I did the beat rates for my own education, using a calculator, and do not have the time to go further. Second, I agree with you that fourths should beat progressively faster in the temperament. I want to share with you just how accurate this can make a temperament. Take a fourth that is 2 cents wide and beats 1bps. To beat 2bps (as fast as the fourth one octave higher) the fourth would have to be 4 cents wide. For the fourths to be progressive each fourth must have a beat rate a twelfth root of 2 (or about 1/16th) faster than the one below it. To determine how many cents this is, simply multiply 2 cents by 1/16. The result is 1/8th of a cent. Each fourth must be within 1/8th of a cent of the width of the ones chromatically above it and below it to beat progressively. Major thirds are 14 cents wide and need only be within 7/8th of a cent of the width of the ones chromatically above it and below it. Chromatic fourth can be 7 times as accurate as chromatic thirds! But this should all be "tempered" with reality. In shorter piano, the fourths may not double each octave and a wider octave stretch will increase the width of the fourths. Also, a practical limit of setting a string securely, without any "leaning" is probably 1/3 of a cent. So practically speaking, contiguous fourths should be progressive, if chromatic fourths cannot. You mentioned hearing two beat rates when listening to fourths. The slower beat rate is the 4:3 partials, the faster is the 8:6 partials. Which to listen to? Well, you could listen to both. I experience this as the "color" of an interval and notice it more in fifths. The ratio of the two different beat rates is what I experience as color and can be used to tune fourths and especially fifths without tediously listening to beat rates. Instead equal color in the intervals can be tuned. It doesn't work so well on shorter pianos, though. On Sun, Feb 8, 2009 at 9:16 AM, Brian Wilson <pianocare2 at bigpond.com> wrote: > Hello list > > > > It is nearly midnight here and I just travelled 58 kilometres to try a > little tuning. > > Piano 1 was tuned last Wednesday at a venue approx 35 kilometres from its > usual home. It has had a 20 degrees Celsius change in temperature and > changes of humidity of 40%. The piano is ok except for a couple of unisons. > This piano exhibits 4ths increasing in speed. I checked the intervals from > F3 to C#5. More on that soon. > > Piano 2. I moved forward the tuning programmed for Tuesday and performed it > tonight. I will still probably tune it on Tuesday, Friday, and every day the > week after. It will also be moved on Thursday 19th returning approx midnight > 28/2. > > I fitted a strip to the complete piano except for the single strings. That > is not what I usually do. I tuned the piano as per I usually do..aurally. I > then dusted off the PRCT and programmed it for this piano. I let it decide > what it wanted to do. I asked for the 4 setting, even though I know this > piano likes a bigger stretch. Full blush from F3 to A5… I then used the > "right ear" and found that I was less than 0.20 out on every note. Fastest > spinner as well. FYI I tune aurally 99.99% of the time and a few of my > professional musician customers would sack me if I tried using an ETD on > their pianos. A bit conservative here! > > I was also armed with a metronome. > > The F3 A#3 4th "sounded like" 1 beat per second as well as the C4 F4 and the > E4 A4 and the A4 D5. All "sounds like1 beat per second" however to listen > closely, they do change in speed. From a "slow" 1bps to a "fast" 1bps. In > the 5th octave I realised why I don't take a lot of notice of the 4ths. Not > really usable for me but there is a faster beat. To quote from a book "At > A61 the 4th and 5th are no longer audible", Then I turned on the metronome, > and as I started to work out the speed, a friendly violinist came and said > hello. Wanted to know what was I doing and that he had never seen a piano > tech with a metronome. In short, he became my conductor. Armed with a > capstan driver for a baton, he waved the beat for me. His answer.. he > conducted faster on my listed intervals. He laughed at me and told me to > keep doing what I normally do. And that my client is happy with my work. > Advised me to go home and get a life. Ha > > Not really happy with my 5th octave I spun the piano around and opened up > right at the wall. No false beats, but there is a fast beat and a slow beat > in these 4ths. Which one do you listen to? No wonder I use the 10th to 17th > here. I have to agree with the quoted book. > > So after being accused of ranting and shouting and then reading that in a > decent aural tuning 3rds 4ths 5ths 6ths 8ve 10ths 12ths double octaves etc > all falling into a reasonably sane relationship that the 4ths and 5ths beat > at pretty much the same speed, respectively at pretty much the same speed > throughout the scale. Pretty much the same, close to seems to be the same is > not definitive. Close enough is not good enough. So I have largely ignored > the slight insults. > > To quote Wayne Jackson that you would lose marks in a tuning exam. Yes, you > would fail the Yamaha and Kawai tests. To perform a temperament without a > "slight" increase in speed in the 4ths would fail. No doubt on that. I am > talking a small amount of increase. I advised a colleague to read my text > books when he started in the industry. He bought himself a metronome and a > piano and he spent hours tuning intervals to the speed listed in the text > books. Well, he is a fantastic tuner and he too has passed tuning tests with > flying colours. He went against the status quo and he came out on top. Many > of what I consider to be extremely good technicians tune very very similar > to me. Oh I forgot, Japanese, German and English technicians as well. > > Now I too can claim to have performed numerous tunings. The bottom line is > that … I have passed tests by my peers, factories, visiting technicians, and > more than any thing else I could possibly have some satisfied clients. I too > could claim experience that would be verified by my colleagues. To receive > compliments from "masters" in Germany may be worth something. > > Back to the pianos: Piano 1 Steinway Model D Hamburg s/n 440474 Piano 2 > Steinway Model D Hamburg s/n 452140 Client: The Queensland Orchestra, > Brisbane And the client is not happy, they are extremely happy with my work > and all associated details for their music productions. And they are happy > with other technicians that tune for the concert hall venue. And he tunes > quite similar to me! > > I must perform a decent tuning and the speed of the intervals closely > matched the theoretical values. > > Must sleep, have to leave home in 4.5 hours for another high end piano. Or > do you think I should start another career because I don't conform to your > beliefs? > > -- Regards, Jeff Deutschle Please address replies to the List. Do not E-mail me privately. Thank You.
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