[pianotech] Do fourths beat faster?

[John Delacour]

At 17:49 -0500 8/2/09, BobDavis88 at aol.com wrote:

>That said, the math must itself be based on correct inputs. 
>Calculations based on frequency tables may be correct to six 
>decimals, but are not the information we need for tuning. (Because 
>of inharmonicity, if A4 is 440.00 Hz, D4 will not be 293.664776, but 
>something closer to 293, and their 3:2 coincidence will not be 
>exactly 880 and 880.99xxxx, but something different depending on the 
>inharmonicity of each note). Inharmonicity is exactly what this 
>whole conversation hinges on, being the cause of fourths and fifths 
>staying close to the same up the scale. Fourths will typically, but 
>not necessarily, increase in speed very slightly as we ascend 
>through the temperament area, but in no case will their beat rates 
>come close to doubling each octave, and in most pianos, they stay 
>close to the same above (and below) the temperament. 
>ThisÊisÊcounter-intuitiveÊonly if we don't have a full understanding 
>of the effects of inharmonicity.

Very interesting.  I'm glad I didn't wade into this discussion 
earlier, mainly because I tune but don't sell my services as a tuner, 
being mainly a restorer.

The maths I don't have too much problem with now, but only because 
I've sweated over the years to familiarize myself with the maths that 
I do need for design and especially string design.  And there's 
nothing wrong with the theory or the maths, as you say, provided you 
supply all the necessary data.

One point that Ed Sutton raised is also interesting, and that is, 
that no matter how good the designer of the string scale is, at 
certain points in the scale the gauge is going to have to change, and 
on many pianos we have whole gauge jumps except in the high treble. 
This is going to make a difference to the inharmonicity of adjacent 
notes and is quite unpredictable unless one knows or measures the 
scale, which no sane tuner will do.  The ear is always going to win 
and the Zen tuner is always going to be the best.

As to the "overstretching" of the treble, by which I mean the 
stretching of the scale beyond the requirements of inharmonicity, I 
am sure this would come under the heading of psycho-acoustics.  For 
certain music there is no doubt that a scale stretched to the point 
where the octaves are almost discordant can be very effective and 
exciting, and after all, the reason pitch tends to creep up is that 
the fiddles in the orchestra aim for more brilliance by playing 
sharp, or so I was always told.  I have used two good tuners for most 
of my career and sadly one of them died a couple of years ago. 
Somehow his work was always more exciting than the other's, who tunes 
for the orchestras, because he did stretch the scale more.  The other 
man can do it, but I have to remind him.

JD