Working with a High 4th A4 Number Piano
I’ve measured the 4th A4 Number on one piano to be as high as 4.2 c.. That means when A3 was tuned as a pure 4:2, the A3/A4 2:1 was 4.2 c. wide. A 2:1 octave there, at that width, will be beating too much.
That 4:2 c. wide 2:1 was found on a Baldwin Hamilton S#. 193416.
Here are the A4 numbers for that piano:
4th P of A4: 6.4
8th P of A4: 29.2
2nd P of A4: .6
4th A4 Number: 4.2 c. (When A3 was tuned as a pure 4:2 and then measured it as a 2:1,
the width of the 2:1 was 4.2 c. wide.
All of these A4 numbers are relatively low compared to most other pianos – especially the 2nd P number.
On this Baldwin Hamilton the 4th P of A4 @ 6.4.
To put those numbers in perspective, I have over 800 templates I used for mapping the midrange. The lowest A4 number in all those templates is 4:2. But it is really rare I ever use those because pianos with that low of an A4 number are really really rare. But I have templates down in that are for just those rare occasions. (More on templates later.)
And since those low A4 number pianos are so rare, I just don’t have that many in that ultra low range. I have only 10 templates in the 4.0 – 4.9 range, only about 19 templates in the 5.0 – 5.9 range, and about 30 in the 6.0 – 6.9 range, with 20 of them being 6.5 or above.
So, out of my 800 templates, 740 or so of them are higher than this Baldwin Hamilton’s 4th P number of 6.4.
The next number to look at here is the 2nd P number of .6 c. The iH here is so low that the 2nd P of A4 is only .6 c. sharp.
What makes this 2nd P. number so important is that it is used to tune the pure A3/A4 4:2 octave.
You might think this Baldwin Hamilton’s low A4 numbers are a good thing, you know, because low iH is good isn’t it? Well, not necessarily. And definitely not here.
There just aren’t many absolutes in tuning. At least not that I’m aware of. But I think it can be said that both the A3/A4 2:1 and the A4/A5 2:1 octaves should always be tuned wide.
What is not absolute however is the width of those 2 – 2:1 octaves. But we do know that both of them do need to be wide, we just don’t know how much.
In addition to a good sounding octave, the A3/A4 2:1 also needs to accommodate a good sounding pair of balanced prime 5ths and a pair of good sounding ‘resultant’ prime 4ths (A3/D4 and E4/A4).
The reason the 4th A4 Number was so high (4.2 c.) was because the iH on A3 was much higher than the iH on A4. So when we tune A3 so that it’s 4th P is tuned to the low 2nd P of A4, A3 was tuned lower than usual.
A 4th A4 number of 4.2 tells us immediately that a pure A3/A4 4:2 will be beating too much at the 2:1. We know now too that the A3/A4 4:2 will end up being narrow.
In a nutshell, I say it could be described as this piano having a fairly normal iH on A3, but unusually low iH on A4. That is what caused that wide 2:1 when the 4:2 was tuned pure. In fact we know we will need to contract the A3/A4 octave by about 1.2 c. just to get it around 3 c. wide, which is on the edge of intolerance on most pianos.
For starters, knowing the 4th A4 Number (4.2), we know we will need to contract the octave by about 1.2 c. to get it to the 3.0 c. width.
Instead of absolutes, there is a ‘relationship’ between the prime octave width and the widths of the prime 5ths.
The widths of both the prime octave and the prime 5ths are not absolute.
On most pianos we can end up with a prime 2:1 octave less than 3.0 c. wide, and, that octave ‘size’ can contain a pair of good sounding balanced prime 5ths that are both around -1.5 c. narrow.
But some pianos need something different.
I keep using the word balanced when talking about the prime 5ths. Balancing the Prime 5ths is particularly important when working with a scale such as this.
Using the Baldwin Hamilton as the example, if I contract the octave down to the 3.0 c. wide 2:1 width, I have contracted everything within the octave as well.
On such a scale as this, when using a smooth template with a reasonable ‘piano-shape curve’ for the notes going from A3 up to A4, and the prime 5ths are tuned and then measured, their widths are usually quite different one from the other.
After contracting the prime octave so it is close to 3.0 wide, one of the 5ths was -3.0 c. and the other only -1.0 c. The combined width is -4.0 and the prime octave’s 2:1 is around 3.0 c.
If we balance those prime 5ths so that they are both -2.0 c. narrow, they will both beat equally and actually sound pretty good.
It is at that point – with balanced 5ths – when we can decide if we can stand a little more beating in the 5ths, to quiet down the octave a little more.
Since there are two prime 5ths and only one prime octave, when we alter the width of the octave by .6 c, the width of each 5th will only be effected by .3 c. So in this case if the octave is still too noisy, we can shrink it from 3.0 down to 2.8 (.2 c. in the octave), that change will only effect the widths of the prime 5ths by .1 c..
If we wanted to shrink the octave by .4 c., each 5th would be effected by .2 c.
When working with a piano like this the final determination is an aural decision. We must decide which of our options is the least bad sounding one. But being acutely aware of the specific compromises being made, is a great help in making one of these pianos sound as good as it can.