[CAUT] Measuring FAC (was Re: Re. Link to Young Paper)

[Fred Sturm]

On 1/19/07 8:30 PM, "Jim Busby" <jim_busby at byu.edu> wrote:

> Hi Fred,
> 
>  
> 
> At a convention someone mentioned this as ³the² way one should take the FAC
> measurements. Wasn¹t this in the journal once too? I¹m still unclear as to the
> ³step by step² instructions. (1, 2, 3Š) For the gadget impaired, (me) would
> you give those instructions???
> 
>  
> 
> Thanks,
> 
> Jim Busby
Hi Jim,
    I am not aware of anyone teaching this particular method. I have heard
of a couple of different variants, at least one of which was published in
the Journal, but they were substantially different and for different
purposes.
    Here are step by step instructions:
1) Turn on SAT, press tune button. You are at A4, 0.0 cents. Tune the string
and stop the lights. (Side effect: WOW! You have tuned a string to the pitch
where you want to leave it).
2) Octave up to A6. Play A4 holding the measure button to stop the lights
(or do cents up, whichever you prefer, and whichever produces more accuracy
­ maybe a combination).
3) Take that number and multiply it by 0.8. (Eg, 10.0 x 0.8 = 8.0). Using
the cents down button, move the display number to the resulting number (Eg,
from 10.0 to 8.0). Enter that number (Shift/Stretch) and the display will
now move to C6, 0.0 cents.
    (For ease in doing this in my head, I prefer to think of it as reducing
the number by 1/5. Divide the number by 5 and subtract that from the total.
And, hoping not to confuse the issue, an additional mathematical trick to
accomplish this is to multiply by 2 and then divide by 10. So, eg, 11.7 x 2
= 23.4 / 10 = 2.3. 11.7 ­ 2.3 = 9.4. If this seems like gibberish, ignore
it. If it makes sense, use it.).

4) Now you are on C6 at 0.0. Tune C6 to stop the lights.
5) Octave up to C8. Measure. I find it helpful to do cents up with the cents
up button to about 30 cents, then use the measure button (makes it easier
for the SAT to find the pitch).
6) Take this result and divide it by 5. (Eg, 35.0 / 5 = 7.0). Octave down to
C7. Cents down to the resulting number. Enter that number (shift/stretch).
The display moves to F5, 0.0 cents.

7) Do F as usual. 
    But I¹ll comment a little on the F number, which, it seems to me, is the
weakest link in the FAC system. I find that it doesn¹t really serve well for
pianos that have high inharmonicity for F3. The major effect of a high F
number is seen in the bass, from A0 to B2, and high F numbers will produce
octaves that are too wide (IMO), especially for those spinets to studios
which have the highest numbers.
    And, of course, it all depends whether F3 is wound or plain wire. The
scaling of a Hamilton is very close to that of an Acrosonic, except the
Hamilton has a plain F3 while Acrosonic has a wound F3. So the Acrosonic¹s F
number is a lot lower. There are lots of other similar examples.
    Bottom line, I reduce high F numbers, usually to a nominal 10.0

8) ³Across the break.² As long as I¹ve gone into this much detail, I¹ll
mention a bit about tuning across the break, meaning in pianos with a big
jump in inharmonicity between plain and wound strings. Sanderson provides an
article or two (or they did ten years ago) suggesting the use of two tuning
pages to smooth the tuning across the break. One tuning uses the measured F
number, the other uses a lower number derived by measuring the top wound
string, as I recall. The instructions are to use the page with the higher F
number for the plain wires, the lower number for the wound strings. This
does make for better octaves in the tenor and bass (as I described above, in
advocating for a lower F number), but it does nothing to smooth the
transition across the break, defined as making the M3, M6, M10 beat rates
progress more evenly. In fact, the two tuning pages will have numbers that
are identical in the area across the break (or, at most, varying by 0.1 to
0.2 cents, basically insignificant).
    Bottom line, I¹d advise not bothering. If you want to smooth the break,
I can give you a way to do it with a SAT. I¹m not convinced anyone but a
tuner would notice. People notice the break, but not because the M3s don¹t
progress or have a little jog in beat rate. It¹s because the inharmonicity
changes, so the sound of the notes themselves, and especially the sound of
octaves and 5ths changes. And there is nothing we can do about it in tuning
the piano. The partial ladders line up differently, and they are going to no
matter what. Better to ³let the numbers fall where they may² and focus
instead on unisons in that area, IMO.

I hope this is helpful.
Regards,
Fred Sturm
University of New Mexico


> 
>  
> 
> 
> From: caut-bounces at ptg.org [mailto:caut-bounces at ptg.org] On Behalf Of Fred
> Sturm
> Sent: Friday, January 19, 2007 4:47 PM
> To: caut
> Subject: Re: [CAUT] Re. Link to Young Paper
> 
>  
> 
> On 1/19/07 3:29 PM, "David Brown" <David.C.Brown.2 at asu.edu> wrote:
> 
> Dear Fred-
> 
> I wonder if you could expand on this a bit more. I attempted to calculate FAC
> this way after reading your post but I must have done something wrong. The
> difference between the first and fourth partial of A4 seemed to yield a wider
> octave ( larger A number, to be expected I suppose) than the normal reading,
> but the difference between the first and fourth partial of C 6 yielded numbers
> well into the 20¹s or 30¹s! I tried the the difference between the first and
> second partial of C7 as well and still no real usable numbers for me. There
> must be a way to enlighten me!
> 
> 
> Hope all is well in New Mexico.
> 
> Regards-
> 
> David
> 
> 
> Hi David,
>     The A4/A6 difference needs to be multiplied by 0.8, to factor out the
> difference between 1st and 2nd partial and leave the difference between 2nd
> and 4th partial. The C6/C8 difference needs to be multiplied by 0.2 to factor
> out the difference between 2nd and 4th partial and leave the difference
> between 1st and 2nd partial. The difference between 1st and second partial is
> 1/4 the difference between 2nd and 4th partial (it¹s a logarithmic scale,
> based on a square of the difference between partial numbers, kind of).
>     So, if you read A4/A6 as 10 (zero A4 and read its 4th partial at A6 as
> plus 10 cents), you enter 8 as the A number. When you have calculated the
> tuning, the number for A4 (the tuning offset, tuning it¹s 4th partial) will be
> 10. For C6/C8, if the number is 35 (C6 zeroed, its 4th partial at C8 read as
> plus 35 cents), you enter 7. (Obviously when you enter the number, you have to
> go to the right note name and octave, and scroll cents up or down).
>     Is this clearer?
>     (BTW, David is referring, I believe, to some posts I sent to pianotech
> around ten years ago, when I was coming to terms with my SAT).
> 
> Regards,
> Fred Sturm
> University of New Mexico
> 
>   
> 


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