Thank you David and William,
It's true that each piano is different but what I have done is identify the "ideal" piano, for lack of a better term, and with that comes some choices.
I would like to discuss this from the point of view of how many intervals we can get to be pure.
But to do that, we need a definition of what pure is.
For this discussion, we will say that "pure" (with quotes) is defined as an interval whose check intervals "sound" the same speed. I have shown that all humans, regardless of tuning or musical experience, can identify non-equal beat rates only after they are more than about 3% different. Each person may be higher or lower, but every person has a limit! "Pure" intervals are tuned within that limit.
Try it yourself:
https://howtotunepianos.com/ear-training-for-piano-tuners-beat-speed-difference-sensitivity-test/How to Get Pure Intervals in the PianoThe pianos inharmonicity will allow some intervals to be tuned "pure", but after that, we must make choices if we want more "pure" intervals.
For example, on many well-scaled pianos, it is possible to tune a mid-range "pure" 4:2 and a "pure" 6:3, at the same time, where M3=M10 and m3=M6,
as far as we can tell. (i.e. "pure" with quotes) if the piano will let us.
I call these Small Scale Octaves since the distance between the 4:2 and 6:3 is small.
In Figure 13 we see that this "pure" 6:3 is actually narrow but it has the m3 and the M6 existing in each other's 3% bubble. That's why we can't tell it's narrow; why it "sounds" pure to us.
In this way the piano
allows us to tune a "pure" 6:3 and a "pure" 4:2 at the same time.
But it is what
we do with the M17 that allows us to have a "pure" P12 and a "pure" P19 at the same time.
For mid-range octaves where "pure" 4:2 and "pure" 6:3 are
not possible, I used to say that the "pure" P12 and "pure" P19 were not possible either, but that is not entirely true, as shown in figure 19.
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Mark Cerisano, RPT
B.Sc.(Mech.Eng.), Dip.Ed.
https://howtotunepianos.comhttp://mrtuner.com1-866-678-8637
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Original Message:
Sent: 06-23-2020 10:06
From: David Pinnegar
Subject: Tuning Stretch. Is there a better way?
It was a very interesting seminar, although I came in only in the last half hour with computer not equipped with video or microphone.
Thanks so much for organising it.
I tune pure 12ths in the bass, but find that no one solution fits all instruments.
Best wishes
David P
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David Pinnegar, B.Sc., A.R.C.S.
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+44 1342 850594
Original Message:
Sent: 6/23/2020 9:01:00 AM
From: William Ballard
Subject: RE: Tuning Stretch. Is there a better way?
Greetings, Mark,
Missed the zoom explanation,but thought I'd add a comment.
"Pure P12, pure P19, AND pure P22? Now that sounds like a very accurate and precise stretch. No guessing and I can explain how it works."
The P12 is a 3:1, the P19 in a 6:1, and a P22 is an 8:1. In his book "The Craft of Tuning", Dan Levitan has shown that any of these coinciding harmonic relationships inherently produce their own stretch, depending on how far away each harmonic is from from its 1st partial. The actual stretch of these intervals on any given piano is the product of the inherent stretch at each of the notes in the interval and that note's inharmonicity.
Yes the above intervals can be tuned, but the choice of a "default" interval for any region of the piano has its implication for the width (or narrowness) of the intervals above (or below) it.
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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: 06-19-2020 17:13
From: Mark Cerisano
Subject: Tuning Stretch. Is there a better way?
There are two types of technicians and both can do high level work. It's just that the ones who know why their tunings work, can teach others.
Case in point. Tuning the stretch. The accepted method is to "stretch the octaves". Just what does that mean anyway? Guess!?
I get it. After 10 or 20 years of guessing, you get good at guessing.
But what I have found is that if the mid-range octaves are tuned as pure 6:3 which is the best size for a piano where the 4:2 and 6:3 are close to each other (I call this a Small Scale), then we can tune pure P12 AND pure P19, at the same time.
AND, if the mid-range 8:4 works out to be as narrow as the P4 is wide, you can tune pure P12 AND pure P22, all at the same time.
Pure P12, pure P19, AND pure P22? Now that sounds like a very accurate and precise stretch. No guessing and I can explain how it works.
Join me for a FREE Zoom meeting this Monday at 12:00pm Eastern.
https://zoom.us/meeting/register/tJwtcuiuqD0tGtVYYEwBEmZytJFPQo-c5EHd
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Mark Cerisano, RPT
B.Sc.(Mech.Eng.), Dip.Ed.
https://howtotunepianos.com
http://mrtuner.com
1-866-678-8637
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