Piano tuning and pitch stretching

[BjornGrohn]

I live in Sweden and have a Ralins piano from 1943, built in Sweden. However I have been in to piano tuning for some years - just as a hobby. Before I often used a self recorded CD with all tuning frequencies instead of a tuning fork, but I always had to adjust the bass and the treble pitch to get it to sound correctly. As you professionals already know, we humans do not have linear frequency perception. An octave is not really an octave when it comes to the lower bass or the higher treble.

Recently I have bought a tuning program where you can tune each note by looking at a spectrum where you can see the frequency peak together with figures of how many cent away you are from the target. The program has some pitch stretching possibilities, but there is no total stretched scale to use for the whole piano. You have to decide your own pitch stretching for each octave.

My question is: Is there a rule of thumb of how much the octaves are to be stretched. Has anyone published tables of frequency deviations from the mathematically calculated frequencies? (I refer to the frequencies based on A=440Hz and each half tone is derived by multiplying 440 by the 12th square root of 2, and so on)

I presume that people's ears are rather individual, so maybe different piano tuners would choose different stretching. But at least it would be interested to get some advice.

[Barrie Heaton]

My question is: Is there a rule of thumb of how much the octaves are to be stretched. Has anyone published tables of frequency deviations from the mathematically calculated frequencies? (I refer to the frequencies based on A=440Hz and each half tone is derived by multiplying 440 by the 12th square root of 2, and so on)

I presume that people's ears are rather individual, so maybe different piano tuners would choose different stretching. But at least it would be interested to get some advice.

First of all your ears calculate the stretch naturally so it would be a big advantage for you to learn to do it with your ears ALL the makers tell you that ETD are only a guide and it is down to the tuner to make the final decision. ETD are only there as an aid to the ear not to replace it.

As to stretch tables yes there are quite a few out there for the common models of piano However, each piano is different and some time you have to modify the stretch the best place to read up on this is on piano tech there are a lot of tuners in the US who use ETD and have published stretch tables for the common makes and models of pianos. The pianotech Archives are here
http://www.ptg.org/pipermail/pianotech/

Barrie,

[classic-keyboard]

It's been a while since I really put my foot in it so...

Shuurly stretch tuning isn't a matter of taste or style, it's to do with inharmonicity and the fact that (in the bass, say) the partials of the strings are sharp because of the increased stiffness of the segment and therefore beat against the fundemental (or some lower partial) of a higher string... and therefore a basic ETD (like a Conn) will aid the tuner if it's 'listening' to the right partial of the string concerned instead of its fundemental. In principle it should be possible to compute the stretch for a given piano if one knew the exact specs of the strings but the windings on a bass string make it a NASA-level calculation. In any case, as I understand it the tuner person has to make compromises that can't be predicted in advance to get the most melodious whole with some degree of beating. Stretching to compensate for human perception is something else; it's about forcing the high treble even sharper than inharmonicity requires, isn't it? (Or perhaps I should stick to talking about Hammonds.)

[BjornGrohn]

I think you are quiet right about this, because I tend to listen more to the harmnonics than I try to measure the fundamentals when it comes to the lower bass of the piano tuning. But even if the tones were pure sine waves, the octaves would probably be sounding bad if they were exactly half or double the frequency. So I think it is a compromise between both strong harmonics produced mainly because of the windings, and the fact that the human ear has stretched frequency linearity.

I have made experiments with sine waves in the treble trying to figure out if different persons have different taste when it comes to stretching. Unfortunately I did not have the chance to ask musicians or piano tuners. The audience where some twenty engineers at the company where I used to work. I held a lecture about sound and hearing, and this was one of the experiments that we made. The result was not clear, but I think that there might be small differences from individual to individual.

Fortunately we tend to focus on the music instead of these esoteric "malfunctions" of our ears when listening to piano music.

By the way; I have a Hammond H-113 as well.
It would be very interesting to know how the Hammond tuning is built up. But this is maybe not the right place.

[Barrie Heaton]

Shuurly stretch tuning isn't a matter of taste or style, it's to do with inharmonicity and the fact that (in the bass, say) the partials of the strings are sharp because of the increased stiffness of the segment and therefore beat against the fundemental (or some lower partial) of a higher string... and therefore a basic ETD (like a Conn) will aid the tuner if it's 'listening' to the right partial of the string concerned instead of its fundemental.

But that the problem even the Vgood ones have problems in the bass on grand’s, small uprights they are pretty hopeless at unisons and not much cop at octaves most of the guys who I know that use them on a daily bases use their ears for the bass they are great for scales and that is where taste is creping in, as quite a few tuners in the US let the pianos stretch too much and you do get comments from visiting pianists both ways and some like Elton John Takes their own tuner to the US but don’t bother for the UK or Europe

In principle it should be possible to compute the stretch for a given piano if one knew the exact specs of the strings but the windings on a bass string make it a NASA-level calculation.

To many variables on Bass strings that is why ETA suffer

Barrie,