Loudness determination

I am seeking help with a maintenance issue.

With advancing age it seems to become more important to be wary of loudness issues when regulating a harpsichord. I have listened to quite a few performances on the internet (but did not keep a record of which) where some recordings seem to be very strong in the base. While it is not clear whether that impression is “merely” a matter of a regulating process or the natural response of the particular instrument, the internet has not offered much in quantitative terms of regulating, other than admonishment to adhere to “equal loudness” uniformly over the whole compass. In his kit-construction notes Frank Hubbard admonishes, without further quantitative advice that

“ Each note should be equal in loudness to its neighbor and the bass and treble should balance as well.”

That uniformity may become somewhat of a problem with older players (“technicians”), as it requires a rather subjective interpretation. On the other hand, if I am way off, I’d like to know about that, too (kindly).

Not having access to what I would consider a first-rate instrument for emulating (I own —a well and carefully self-built— Hubbard Kit # 625, but nothing to learn from) makes regulating rather difficult with advanced age (pushing 90). We have a senior individual in the Los Angeles area who is called on for all the important baroque music events when one or more harpsichords are required, but his plectrum treatment is rather harsh whenever I was able to experience it. He is a very kind and helpful individual, but on one occasion, when I needed help, he judged me to be too particular.

The human ear is a highly nonlinear sound transducer which responds to sound level (volume) with a strong dependence on frequency (see, e.g., Suzuki et al: http://www.mp3-tech.org/programmer/docs/IS-01Y-E.pdf ); important names associated with these developments are Fletcher-Munson (1933) and Robinson-Dadson (1956). My concept of “equal loudness” for all keys is thus based on the assertion that achieving equal loudness for all keys requires that the correction for the nonlinear hearing response encompassed, e.g., by curves like those in Figure 5 of Suzuki et al., one should obtain the same value of loudness for each key, and thus when plotting loudness against key number (or frequency) all sound values should — in the best of worlds—fall around a line parallel to the key-number axis, with a scatter of about +/- 2 or 1.5 dBs. I had my feelers out to a group of acousticians, to make sure I am not way-off. I also tried to consult with the leadership of the American Acoustic society for support or a reference, but never received a response. Maybe they were turned off by my special reference to “Harpsichords”?

Six years ago I had the opportunity to measure the loudness of a register on a tracker organ in our town, because I knew the organist; I thought, certainly, a professional organ technician knows how to adjust the loudness of an instrument professionally. I use(d) a TENMA 72-947 Sound Level Meter, which proclaims to contain the adjustment for the nonlinear hearing of loudness for the human ear; I was totally surprised by how non-uniform the key-to-key loudness was (11 dB for a next neighbor and about 17dB for the C2#-to-D2# keys) and how nonuniform and “no-equal” across the span of C2 to C6 (for only one register tested). This record exceeds the expected scatter of 3 to 4 dBs (+/- 1.5 to 2 dB).

I would like to know what “Equal Loudness” means objectively (measurably) for a harpsichord, by looking for a result similar to the figure above, but obtained from a well recognized and maintained instrument. Or, are all (good) instruments (like Gustav Leonhardt’s. e.g. at the extreme) really regulated on a totally subjective basis? That is what I seem to encounter.

Where can I get reliable information on that question? Is there any data that records sound level measurements for a high quality harpsichord that are accepted by a number of reputable harpsichordists or builders? Perhaps our colleagues from an academic institution have something like that in their archives?

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Before I add my comments on the topic, here is a very nice hearing test that will generate your personal equal loudness curve, or frequency response.

I went to university with Professor Joe Wolfe some hundreds of years ago, so I trust his work. That site has a lot of valuable information on acoustics. University of New South Wales, here down under!


As to Frank Hubbard’s quote, much as I admire his work, he quite frequently wrote some incorrect ideas or things that are outright wrong. I find this statement to be absurd - it’s self contradictory. If all notes are to be equal loudness, then what does it mean to make bass and treble balance? To balance would imply the notes have different volume, contradicting the initial instruction. It’s hard to take this exhortation seriously. The only way I could understand it is that he may have meant you have to find an absolute loudness level for the whole instrument range such that the bass balances the treble. But I am dubious. If he meant the latter, he could have written as much.

I do not agree with this concept of ‘equal loudness’. It seems very arbitrary to me. And reminds me of the nonsense propagated about equal string tensions in violins and other similar instruments. I’m not sure what sort of Platonic ideal drives people’s desire for equality in all things technical. Maybe it goes along with the mindset of equal temperament. Some desire for symmetry, totally misplaced.

Here is the practice we follow with our instruments, and the rationale. It’s not just a single note sounding that matters, but the totality of the notes being played. Yes, notes next ot each each other should have a very smooth loudness transition with no sudden bumps, but that does not imply equal loudness. So considering the way most 17-18C onward music is written, most of the action occurs roughly around Middle C. Obviously this is not strictly correct, but it gives a starting point. So to avoid the ear being bashed by clusters and chords of loud notes it is better to voice down the area around Middle C to prevent ear fatigue. Then we use a smooth gentle upward parabolic curve. The reason for a slight increase in loudness in the high treble and low bass is a pragmatic one - the treble way up high has hardly any wood to sound off and you tend to get poppy sounding notes with very little ‘wood’ and they need some boost. The same applies in the low bass where the bridge has started to run out of ample soundboard to work well, so the lowest notes need a boost also. Imagine a loudness curve something like this:


The inflection point being Middle C or thereabouts.

You could say then why not just boost extreme bass and treble to equality. I feel that practice shows this type of shaping gives the best musical result overall.

Obviously this depends on many factors of the build of the instrument, plectrum shaping, soundboard response and wire, and so on and so forth, but I have set out what we do. To my knowledge customers and players have never complained, and while they generally do not know the fine details of this practice, they usually praise the quality and smoothness of the voicing.

Like Wolfgang I also have an expensive, calibrated SPL meter. I have never run it across a harpsichord of ours, but if I get the opportunity I shall do so.

In short, I do not know where the ideal of ‘equal loudness’ came from and I don’t think there is any solid historical evidence that such an idea circulated, and I think it is entirely unnecessary, and besides it ignores the science on equal loudness contours and frequency response in any case.

I don’t believe piano makers such as Steinway or Bosendorfer or Fazioli attempt equal loudness in voicing either. As for organs, they are wayward beasts and all individuals, so I cannot possibly comment.

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Fully agree with Andrew that equal loudness is a poor goal. May I add a few considerations?

An instrument should be considered as a whole entity. The designer and builder gave it a certain character and style, which could be adapted only partly by changing strings, voicing plectra or other measures (eg ravalement). When voicing an instrument one should have a sound ideal for the whole instrument in mind. This ideal is a cultural choice and has a personal component.

The idea of a homogeneous character from bass to treble was abundant in the Renaissance period. Homogeneous consorts of recorders or gambas were built and used in the 16th century. In Baroque and classical styles another ideal became more important: each register should have its own, well recognizable character. A tenor voice should be clearly discerned from a top voice for example. This fits the rhetoric ideal of clear speech. The idea of homogeneous sound over the full range of the keyboard came back again in the course of the 19th century, where pianos were constructed on a large industry scale with a sound ideal of equal quality from bottom to top.

Assuming the ideal for voicing is chosen, even when one will find it difficult or impossible to describe it in words, measuring and controlling loudness will not do. The character and impact of a tone is not only made by its loudness. The attack, or beginning of the note, the development during the sounding of the tone and even the feel on the key adds to it. A short attack will give a harsh and strong impact, a longer one a more sweet one, even if loudness is equal. When, after the attack, a tone develops richly because other strings start to work, or the soundboard starts working, a tone will have more impact than a tone which resonates less. And brass strings will have a different set of overtones than steel ones. Loudness, overtones and spacial distribution over the instrument (and the room it is in!) change over time. The maximum loudness comes at a moment that sound quality is not yet well defined and frequency not yet audible.

When voicing your own instrument, your own ear and sound ideal, even when it is not a perfect as it was, should be the only criterium. Let’s think of Beethoven who had his piano equiped with a large installation of hearing devices to make the sound accessible to him.

I hesitate to say it, but being Dutch and direct, I would suggest to Wolfgang that an attempt to replace one’s own ageing ear with technical means will not lead to a satisfying end result. Why not voice your own instrument to your own perceived sound ideal? Age comes with fantastic new qualities not accessible to younger people. Enjoying and accepting it is a true art.

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In all this discussion I miss something.
I agree that absolutely equal human-ear-perceived loudness is a wrong goal: we have to accept that antique harpsichords tend to sound louder below F and much louder below C (the so-called Flemish bass boom). To try to mitigate this, especially in an instrument with a largely inexpressive keyboard such as a harpsichord, is reasonable, but to try to voice-down the extreme bass so that it sounds as loud as the tenor is a ridiculous goal. So far we seem to agree.

What I find very important, however, is that the loudness curve of an instrument stop, from bass to treble, should be smooth, with no note sounding louder than its neighbours. [This was what I interpreted always from Hubbard’s views, by the way, whether he wrote it down correctly or not.] I have found often instruments where this is not the case (in the case of Delrin, which changes very little over the years, this is inexcusable). I even voice (and string) carefully so that no visitor can tell by ear the transition points from the different string alloys.

(Note: who knows why my spelling “neighbours” is marked as erroneous? AFAIK it is the correct British-English spelling!)

Well said Pieter.
Unless the instrument is being prepared for someone else, make it sound to you like no other harpsichord out there. (Says me with gradually failing hearing).

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Dear Wolfgang

I can refer you to the brief discussion of loudness in the book chapter cited as Fletcher, NH & Beebe, C 2010, ‘Harpsichord and Clavichord’ in Thomas D Rossing [ed], The Science of String Instruments, Springer, New York, pp123–143.



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Thank you Carey for providing a download of a very interesting work of yours.