This is an expanded version of a comment I posted earlier this week on the hpschd-l. Anyone who wants to get into historical harpsichord tuning and never come out again ought to search the archives of that list. There’s several lifetimes worth of tuning wisdom and tuning folly to be found there. In this post, I discuss one randomly picked topic from tuning lore: the so-called inharmonicity of strings and what to do with it.
A very short popularized version of the theory says that in stiff or thick (or both) strings the partials are out of tune; thick, stiff strings act acoustically as a rod. Imagine a 1950s staircase and its iron handrails. The rods that attach them to the ground say (when one tried harping on them, which one wasn’t supposed to do) plink/plank/plaing/plunk/plong, but mostly “ploink”; the “oi” factor in this ploink indicates that something – in terms of a pure sound – isn’t as it ought to be. When tuning very thick foreshortened bass strings or the treble strings in a modern piano, we are facing palpable manifestations of this inharmonicity. Even in the strings of early keyboard instruments there is theoretically some inharmonicity. This wisdom works wonders for the fantasy of some insiders.
1) Stretching the treble. In modern piano tuning, the treble octaves are supposed to be stretched, i.e. tuned somewhat too wide, in order to cope with the string’s inharmonicity. However, this octave-stretching varies mightily, even when we only consider the absolute top level of performance of professional modern piano tuners. If you have access to the following recordings, you can compare how the pianos are tuned:
— Rudolf Serkin’s 1984 recording of Reger’s Bach variatons Op. 81, CBS (the end of the fugue is a good testing point)
— Vladimir Ashkenazy’s 1996-98 recording of Shostakovich’s 24 Preludes & Fugues Op. 87, Decca (the second Prelude and Fugue as an example)
— Claudio Arrau’s mid-1980’s Liszt CD that was issued in 1990, with his second recording of the sonata in B minor and other pieces, Philips (listen a bit into “La Chapelle de Guillaume Tell”)
— Murray Perahia’s 1991 Franck and Liszt CD, CBS (the beginning of the Rhapsodie espagnole)
Two of these are examples of extremely stretched trebles (Perahia, Arrau); in the two other ones the stretch is imperceptible for the listener. All examples lie more or less within the scope of ‘what is done today'; nevertheless they seem to vary strongly in the level of deliberateness with which the octave stretch was applied.
In view of the fact that modern equal temperament makes use of very large major thirds anyway, I believe that treble stretch should be applied with a light hand even, or especially, in modern pianos. Listen again to the Major thirds in the spread-out arpeggios at the beginning of Perahia’s Rhapsodie espaniole: in the upper treble, they are painfully and entirely unnecessarily out of true. (All this has obviously nothing to do with artistry and interpretation. I’m criticizing the piano tuner here).
One would think that all this has nothing to do with historical instruments with their relatively thin and soft strings. However, once after I tuned a Viennese 5-octave fortepiano for a performance, someone came with an electronic tuner (call it a wise-guy-gizmo) and curiously checked what I had done. As it turned out, (and if we can believe the accuracy of that sort of apparatus, which some don’t), I had stretched the octaves slightly, without knowing, or hearing it.
An analysis of this experience should lead to an abrupt conclusion of this chapter: inharmonicity makes one involuntarily compensate in certain ways during tuning. This is something totally different from having to do these things in order to meet the requirements of inharmonicity. In short, inharmonicity does something to us, but we shouldn’t worry too much about doing anything to inharmonicity. Anyone who spends his time doing more than trying to get the octaves subjectively in tune will likely go over the edge and ruin the tuning for the ears of others.
2) Can we actually hear inharmonicity in historical instruments? I have my doubts. True, it always seemed to me that the inharmonicity of certain fortepiano trebles is difficult to cope with. Inharmonicity in a harpsichord, on the other hand, is not something that has ever caused me any trouble – except, I thought, in the most abysmal specimens. But if I re-think this experience, I must admit that I am talking about false strings, which is not the same as inherently inharmonious strings. False strings (strings with kinks, rust, strings that are guided by loose bridge pins, too thin strings that are excited too strongly and so on) are impossible to get fully in tune, so much is true.
3) In conclusion, I believe that the matter of inharmonicity often gets too much attention in harpsichord and early piano tuning discussions. At a recent early keyboard meeting in Edinburgh, there was a doctoral student who discussed the “problem” of tuning the so-called Vis-à-vis by J.A. Stein (1777), a large harpsichord-fortepiano combination instrument, at length and to no avail with a top specialist in the field. This specialist had tuned the recently restored instrument several times, and said that it had been no trouble at all, in spite of the fact that the fortepiano part of the instruments has thicker strings and a shorter scaling (consequently, the fortepiano strings have, in theory, a higher degree of inharmonicity than the harpsichord strings). The man kept asking “but how is this possible considering the difference in inharmonicity between the parts of the instrument?”
The answer is, similar to my reasoning above that, in tuning, everything is possible as long as it is possible, whatever the theory may be. Successful tuning is about whether our ears can cope with a situation or not, and not about whether the theory allows us to cope or not. This realization should help to reduce about half of the woo-woo out there, and leave us more time to keep our 4′ registers in tune, which can be a real pain.