David,
Here's the theory in writing:
Facts we already know:
Pianos with higher inharmonicity will have a much more aggressive change in beat
Pianos with low inharmonicity will have a closer compatibility in beat comparisons
My findings:
There's a definite reinforced audible partial with a very distinguishable pitch when intervals like a Maj 3rds and Maj 10ths are played.
The Maj 3rd ( say using F3-A3) will isolate and promote the 4th partial of A3 ( A5).
The Maj 10th ( say using F3-A4) will isolate and promote the 2nd partial of A4 ( A5) 4:2
Could this be why these 2 intervals are used to determine an octave?
I say they have nothing to do with the beat comparisons and have everything to do the about the audible partial they isolate and promote.
Exercise: Play the Maj 3rd and listen carefully to the position of the A5 pitch. Adjust F3 flatter to increase the beats, notice that the pitch remains the same. Thus, raise F3 sharper to decrease the beats, and the pitch still remains the same. In other words, the role of the lower note of the Maj 3rd only acts as catalyst to extrapolate 4th partial of the high note. Interesting.
However if you raise or lower A3 the beat not only changes, but most importantly, so does the pitch of the beat.
The converse behavior occurs when play a minor 3rd/ Maj 6th check for the base.
Say we use C2- Eb 2 / Eb2 and C3 to do a bass note check. The reverse effect occurs. The high note ( Eb 2) plays the role of the F3 in the Maj 3rd check. They work in opposite fashions as the 4:2 check
Things the tuning community doesn't agree upon:
Beats are simply bi-products of interval and only illustrate a beat tendency and act solely as a comparison factor.
Beats don't reinforce any auditory pitch;
Things in which I'm trying to prove:
Beats, in fact are way of extrapolating partials which lie within a given note.
There's a need of doing arpegiated checks which needs to be a part of every tuner's bag of tricks in determining the accuracy of these checks.
Experiment:
Listen carefully when playing F3- A3
the reinforced pitch of the beats of F3 will sound a very definite double octave. Thus the A5 is very audible- the 4th partial of A3
Listen carefully to the Maj.10th with F3-A4, you'll get the a very audible 2nd partial on A5.
The hard part in this listening exercise is not to listen to the tempo of the beats but rather the pitch of the beat. One of the tricks I do (in order to zero in on that partial) is to lightly play the A5 as I'm doing the Maj 3rd test. This will help direct your ears to that partial. Once you've recognized it, it becomes abundantly obvious.
Do the same with the Maj 10th.
I have a feeling that way back when, when temperaments were being devised, that the early theorist used the Maj 3 and Maj 10th specifically because those intervals isolated the very partials which needed tuning to. My theory is that through the years, tuning has been taught in a very mechanical form, basically by counting beats. It's a very easy way to teach temperament development. The easy way of showing a form of an octave is to make the Maj 3rd and Maj 10th have equal beat speeds.
I think where the issue needs exploring is that when we define a 4:2 octave it is when the Maj 3rd and Maj 10th have even beat rates. If we expand to a wider rate, we commonly refer that to a 4:2+.
But is it? What do experienced tuners intuitively do, they stretch the octave beyond the normal 4:2 size, because why... because it sound better. Many will say it sounds better for a variety of reasons, but not attributing to this little recognized phenomenon.
Part of my theory is questioning the definition of a 4:2 or 4:2 + octave. Of course this depends upon the amount of inharmoncity. Pianos with higher inharmonicity will end up with a much more aggressive change in beat speeds. Pianos with lower inharmonicity will be closer to being the same. Again, these are things that we already know and have proved.
Here's the interesting part of this finding: If you can acknowledge this secondary audible phenomena as another thing which we must satisfy, you've now entered another realm of tuning plausibility.
I can tell you that when I started to really listen in this manner, my tunings entered a more true level of satisfying the piano's needs. There is a sweetness and completeness to the tuning which is noticeably better.
I think that experienced tuners achieve at this very point but without the recognition of this neat little phenomenon. I truly think that there's been a lot of bad explaining about this affect by the likes of Virgil Smith. He has been stumbling trying to explain something on some esoteric level, but this little affect I'm trying advocate, might be the final straw which connects the notes to the puzzle.
His explanation of what's actually doing is very difficult to follow, let alone explain. I have a feeling that we, as experience tuners, essentially arrive at the same point, but without knowing what we've actually been doing.
So why does all of this matter. For those who have discovered ( and accepted) the affects of single mute tuning, those techs have discovered some very interesting qualities to their tunings. Why, because you are taking more phenomena's into account, thus the tuning lands on an entirely different plane. You and I have experienced this first hand. It's unquestionably a more complete tuning.
My added theory will only add more bags of tricks to our process. Most importantly, by recognizing these affects, the element should go down dramatically as it cuts to the chase .
The hard part of this theory is that you have to accept some criteria which has been poo-pooed for many years. That is, beats only act as a comparison counter and only give some background vibrato. Beyond that, they have no more use.
But clearly, and I says this as a pianist, many pianists listen to the piano in much different ways then most tuners. Exercises in arpeggios will clearly demonstrate the need to satisfy the piano on a much more broad platform.
By be able to zero in on the pitch of the beats, and tuning the octave as those it was a unison ( and essentially tuning the partials to a beatless rate) we are aurally solving the issue of how much stretch needs to accommodate the inharmonicity factory. The piano will clearly demonstrate where the stretch much be.
This same approach to tuning can be applied the whole way up the tuning scale. I use this right up to C8 and have been amazed how clearly those higher partials present themselves.
Anyhow, I hope I haven't been to long-winded in this explanation. I would love for you to play around with these affects and see if you see this as a plausible explanation to some new and interesting perspectives in tuning.
Tom Servinsky
----- Original Message -----
From: Ryan Sowers
To: pianotech at ptg.org
Sent: Friday, March 20, 2009 9:08 PM
Subject: Re: [pianotech] Tuning in a down economy
Postage on 250 cards is around 60 bucks if you generated 5 responses you probably generated around $500 worth of work - That's NOT lousy, its not bad. You have to keep expectations realistic with this kind of marketing. Professional sales people know this well don't see it is 245 negatives but focus on the 5 positives. Think of what those telemarketers have to put up with. But the reason companies keep using this method is that it actually can work!
I also am a believer in making sure you're business stays in the public consciousness. Even though you only received 5 appointments you also injected the idea of piano servicing into the public mind. Keep it up! It will eventually pay off more than you realize.
On Fri, Mar 20, 2009 at 12:17 PM, Daniel Carlton <carltonpiano at sbcglobal.net> wrote:
sent out about 250 postcards last summer, received maybe 5 responses. LOUSY!
Daniel Carlton
This message was NOT sent from my iPhone, because I don't have one
--
Ryan Sowers, RPT
Puget Sound Chapter
Olympia, WA
www.pianova.net
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