Am I correct that when you set the 9th partial of the measured note to be zero beats does that you were expanding a normally contracted interval? I just checked this on my piano and I definitely hear the beats you mention. Very cool test. Thanks.
Narrow and wide intervals are not involved in this situation. These are created by the Comma of Pythagoras. What Carl is doing is tuning a 9:1 "triple octave", similar to using a P12 (3:1) to "tune an octave". (I once got into trouble in the PTJ, calling the P12 and octave. NO, it most certainly is not an octave relationship, but if it's used to transfer the temperament to the outer octaves, it doing octave duty. I remarked at the time that if Reagan's Dept. of Agriculture deemed ketchup a vegetable, then school hot lunch programs could put bottles of ketchup on the tables and thus be delivering a vegetable.)
What's behind Karl's use of this is the stretching of all the other intervals below the 9:1 (i.e., 2:1, 3:1, 4:1, 5:1 6:1, on up). Dan Levitan has a wonderful metric for determining the inherent stretch of any interval, before the inharmonicity of the notes in the interval is ever applied.
That is:
[(partial# on lower note)^2] — [(partial# on upper)^2]
This is because of the way inharmonicity for each note in the interval is entered as a factor in the stretch of an interval (on a particular piano, for 2 given notes). The stretch from the mathematically pure partial, due to a note's inharmonicity, equals:
[(inharmonicity coefficient of that note)]*[(the partial #)^2]
To simplify the comparison of the inherent stretch in intervals, Dan simply lets the inharmonicity coefficient = 1 . Actual coefficients can be plugged in anytime you want, but they are a complication to this comparison. Dan calls these Expansion Units. They are explained on p.73 of "The Craft of Piano Tuning", along with a table of EU's for common intervals used in tuning
So the stretch of a 2:1 single octave is 2^2 - 1^2, or 4-1, or 3.
The double octave is 15; the P12, 8; and the 6:3 octave is 27. Karl's 9:1 "octave" is a whopping 80.
So that's what Karl is doing, inducing a stretch on the 6th and 7th octaves of the piano, by basing them on the high partials of notes 3 octaves below.
But in satisfying this customer, it might have been possible to find the stretch of this 9:1 "triple octave" compared to his SAT octave settings and used that stretch for the rest of the notes above that.
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William Ballard RPT
WBPS
Saxtons River VT
802-869-9107
"Our lives contain a thousand springs
and dies if one be gone
Strange that a harp of a thousand strings
should keep in tune so long."
...........Dr. Watts, "The Continental Harmony,1774
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Original Message:
Sent: 11-02-2017 23:28
From: Geoff Sykes
Subject: Thank you Dan Levitan?
Am I correct that when you set the 9th partial of the measured note to be zero beats does that you were expanding a normally contracted interval? I just checked this on my piano and I definitely hear the beats you mention. Very cool test. Thanks.
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Geoff Sykes, RPT
Los Angeles CA
Original Message:
Sent: 11-02-2017 22:20
From: Karl Roeder
Subject: Thank you Dan Levitan?
I had an interesting experience today with an elderly client with a S&S model L. My client is 92 and her piano has been her faithful and treasured companion since the 1970's. Our own Rick Butler put hammers and shanks on it in the early 90's before the piano and the family moved to South Florida around the turn of the century. After my last visit she called to say that the treble had gone out of tune very quickly. I went by today to see what I could see and found the instrument pretty well in tune and entirely consistent with the way I have tuned it for the past 10 years or more. Mrs.W said that it was all perfectly fine except that the top two octaves sounded flat. I did all my interval checks and it was if anything a bit sharper that I would normally leave it. This was bad news. I've had a number of clients all serious musicians who suddenly after the age of 85 or more lose the ability to discern pitch above F6 or so. The first client I had with this problem heard the notes 100 cent flat of where they actually were. Today's client wasn't that far off. Still, I needed to come up with a solution that would let her hear the music the way she expected to hear it and yet still sound musical to anyone she might play for. Hence the title for this thread. Dan Levitan has been teaching a class on the indispensable 9th partial and though I couldn't make it to his class in St Louis I have been playing around with using the ninth partial as an aural check in the 6th and 7th octaves ever since the convention. From what I understand his approach is to listen to contiguous 23rds ( triple octave plus a whole tone ) which normally beat 4-5 times a second in that range to check for even progression. In my case I needed to tune really sharp but wanted to have some objective standard for the area I was stretching. So I fired up the trusty Sanderson tool and starting at C6 I set the note to measure the fundamental of the note I was tuning and then measured the ninth partial of the note a M23rd below. I then tuned the note in question to be pure with the ninth partial. It ended up 10 -20 cents north of what I would usually do. The octaves were beating 5-8 time per second but when actually playing the piano it really wasn't that noticeable. Mrs. W sat down and played a Grieg Nocturno ( at 92!) that had been really bothering her and in seconds her face lit up and she said "now it sounds right". She then confessed that she hadn't held much hope that I could do anything about it once she realized that her hearing had changed. And she would have been right if not for this little organization of ours and it's ability to transmit an idea from a person in New York to another person in Florida. An idea that even when used not as intended could help someone continue to experience the joy of music. So thanks Mr. Levitan and I hope you'll pardon the mis-use. Has anyone else had elderly clients suddenly start hearing the top octaves wildly flat?
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Karl Roeder
Pompano Beach FL
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