Back to the Future: Bringing the Practice of Tuning Historical Temperaments into the 21st century by Returning to True Historical Methodology

Wouldn’t it be a wonderful thing if one could convert a previously realized temperament of an organ into measures and lines, or in reverse, apply the measures and lines to an organ? Wouldn’t the pure harmony be thereby clearly conveyed? Of what use are all the measures and lines if the musical intervals aren’t arranged according to them? Surely they can convince the intellect and the eye as to the necessary conditions, but without strings, pipes, and song, they are of little help.
- G. A. Sorge, Zuverlässige Anweisung, Claviere und Orgeln behörig zu temperiren und zu stimmen, 1758

Tuning a keyboard instrument consists of two steps:

1. Tempering a central octave which serves as a references for all the other notes (historically this was often done in the tenor octave octave beginning either from tenor c or middle c).

2. Tuning all the other notes/registers to the notes of the temperament octave.

Of these two, the second represents the largest amount the work. The good news is that this kind of tuning is very easy to do since it only involves octaves and unisons. The bad news is that there is no way to do this except by ear; no machine or technology of any kind can make this task any easier. The only way to master this task is to practice, practice, practice.

Step 1, however, is another story. Many people consider this to be the most difficult and challenging part of tuning, but this largely due to a stubborn adherence among modern tuners to an anachronistic methodology originally developed during the 19th century to tune equal temperament. When we realize the true nature of historical methodology, there is really only good news; this part of the tuning process is the fastest and easiest to perform, ultimately requiring no skill other than the simplest of the two already needed for accomplishment of Step 2: tuning unisons.

How should we tune the temperament octave?

Many professional tuners and musicians from the “Historically-Informed Performance Practice” movement think that the best way to set a temperament is “by ear”, a concept which almost always means manipulating the sizes of the tempered fifths and thirds by counting the beats they make in a certain amount of time. These beats are then either compared to the beats of other fifths or thirds or are controlled by referring to a list of correct beat rates for each interval for the temperament in question. Most books on the practical application of historical temperaments published in the last 50 years provide either a list of beat speeds or methods for determining the proportional speeds among various intervals. This manner of tempering is often asserted to be the best for two reasons:

1. Ostensibly, this is the way that tuners and musicians worked in during the times of the widespread use of unequal temperaments (approximately from the early 16th century to the end of the 18th century).

2. Ostensibly, it is the best way to become familiar with all the subtle differences between the fifths and thirds in all the different tonalities for any given temperament, which will help the musician decide which temperament is best for any given literature.

Unfortunately, neither of these assertions stands up to close scrutiny. Some years ago, I, too, thought much along the same lines, but the more direct experience I had the original sources, the more I doubted the validity of these modern assumptions. Now that I have read over 140 original works on organ, harpsichord and piano construction and maintenance, tuning and temperament, and musical acoustics written between 1511 and 1890 (mostly in German), I have changed my thinking completely.

While a few sparse references to beat speed or beat proportion between intervals can be found in the historical sources (I know of four cases in the entire body of literature before c.1800), there is no evidence whatsoever to support the idea that musicians or tuners regularly worked in the modern manner until the middle of the 19th century – long after the general abandonment of unequal temperaments! In fact, there is much evidence to the contrary, such as statements from 19th century writers that this method was “new” and that the organ tuners of previous times did not know how to make any practical use of the observation that tempered intervals produced beats. Rather than being the common historical practice for setting unequal temperaments, the method of counting and comparing beats was developed during the first half of the 19th century specifically in order to resolve the difficulty of setting a perfectly equal temperament. Having become the default method for tuning keyboard instruments, naturally when the “early music” movement began in earnest in the middle of the 20th century, tuners automatically applied it to the tuning of historical unequal temperaments as well, completely unawares that this was foreign to the historical situation.

Mersenne mentioned the possibility of using beats to judge the size of tempered intervals, but no one seems to have applied the technique to an entire temperament until Robert Smith published his lengthy and obtuse (Thomas Young’s evaluation!) treatise Harmonics in 1754, in which he gave the beat rates of all fifths for various forms of regular meantone (by the way, Smith’s title should not be misunderstood as referring to harmonics as we understand them today, of which he seems to have been completely unaware; he meant “Harmony”). This work seems to have been completely ignored, however, not only in England, but more importantly, on the continent, especially in Germany, where I have not found a single reference to it. The modern practice of precision beat counting really begins with the works of Heinrich Scheibler, who first published a book in 1834 called Der physikalische und musikalische Tonmesser (The Physical and Musical Measurement of Tone). His theories were then further expounded and somewhat simplified by J. J. Loehr in his Ueber die Scheibler’sche Erfindung überhaupt und dessen Pianoforte- und Orgel-Stimmung insbesondere (On Scheibler’s discovery in general and his pianoforte and organ tuning in particular – 1836), which was also published in translation in England in 1853. More importantly, in 1842, under the tittle Die Scheibler’sche Stimm-Methode leicht faßlich erklärt und auf eine neue Art angewendet (Scheibler’s Tuning Method easily and simply explained and applied in a new manner), the famous theorist of organ design, J. G. Töpfer, published for the first time in history a simple method for calculating the beat rates from the two known frequencies of any kind of tempered fifth, fourth, third or sixth.

As to the assertion that learning the complex and difficult skill of perceiving, counting and comparing the beats of specific fifths or thirds played in isolation has anything to do with learning the musical characteristics of the various temperaments, this has always been highly debatable. In real music, individual fifths or thirds almost never sound in isolation and in close position. The actual overall musical effect of any tempered interval depends upon the distribution of all of the notes of the harmony in which it occurs, the registers in which they are played, the sound of the instrument, the registration (especially important on the organ), the musical context and the amount of time the ear has to evaluate the quality of the harmony. This complex process simply cannot be equated with counting the number of beats made by two isolated notes on a single 8′ stop in the middle register.

A true appreciation for the advantages and disadvantages of any given temperament can only be learned through broad experience with many different musical works on an instrument correctly and precisely tuned in the different temperaments. The best way to prepare oneself for this long journey of musical exploration is to understand both the theoretical foundations of temperaments and the true historical development of different approaches at different times and in different places.

True historical tuning methodology

…hierzu aber gehöret Cirkel und Maasstab, denn mit dem Stimmhammer allein würde es schwer halten, solche accurat heraus zu bringen, denn das Gehör kan leicht betrügen, und betrogen werden.

[in regards to adjusting the sizes of the fifths on a monochord for a near-equal circulating temperament]…for this it is proper [to use] a compass and a ruler [i.e. the tools for calculating monochord lengths with geometry], for with a tuning hammer alone, it is difficult to achieve the required accuracy, since the ear can so easily mislead, and itself be mislead.
- G. A. Sorge, Zuverlässige Anweisung, Claviere und Orgeln behörig zu temperiren und zu stimmen, 1758

If musicians of the past did not tune the temperament by counting beats, how then did they do it? The evidence from the historical literature indicates three methods:

1. By ear, but only more or less. Many original tuning instruction merely state that the fifths or thirds should be modified by vague amounts: “as much as the ear will bear”, “a little sharp”, “rather piquant”, “almost pure”, “slightly larger than pure”, etc etc.

2. Using a monochord. From the end of the 17th century onwards, texts on the topic of temperaments inevitably included a list of lengths which could be marked upon a monochord, and the use of a monochord during the actual process of tuning a stringed keyboard is mentioned in a number of texts.

3. Using a “tuning pipe”, an organ pipe with a sliding stopper with the position of each note marked upon the slider (Sorge says this is better than a monochord for tuning an organ, and Adlung claims such a pipe was recommended to him by J. S. Bach!).

In other words, two out of three of the true historical methods involve the application of technological devices which produce each note of the temperament octave with its correct tuning, notes which the tuner then copies onto the instrument by tuning unisons (examples here and here). Thus…

If the use of an external “tone generator” represents the actual historical method which was considered as being the most accurate, the most trustworthy and the easiest in the 17th and 18th centuries, why on earth should we reject it in favor of a difficult anachronistic practice from the middle of the 19th century?!!

Nowadays it easier and cheaper than ever before to acquire and employ a technological device. Applications can be purchased for less than 3€ for both the Apple iPhone and Android mobile phones which can be used as tone generators for the twelve notes in place of the historic solutions of a monochord or a tuning flute. These applications can be programmed with whatever temperaments one wishes to use and then adjusted to any pitch level. They allow the musician to quickly and correctly tune the temperament in the same time it takes to tune twelve unisons, a fraction of the time required to perform the same task by the laborious and difficult task of counting and comparing beats, even for an experienced professional tuner. Secondly, they allow the instrument to be tuned perfectly and consistently time after time, a critical consideration for recording sessions. Another very important advantage is that small deviations in the general pitch level can be easily realized (a few cents higher or lower) in order to find the most comfortable pitch for the wind instruments, or to employ various “tricks of the trade”, such as tuning the organ a few Hz too low and the harpsichord a few Hz too high, knowing that during the concert, with the heat generated by the stage lights and the audience, the pitch of the organ will rise and that of the harpsichord will fall. Finally, and perhaps most importantly, the student can easily experiment with a large number of real historical temperaments. Even professional tuners who work by ear usually limit themselves to only 3 or 4 temperaments they have learned to tune, and they are often loath to try others simply because of the effort required in learning a new series of beat speeds/proportions. Additonally, far too often the temperaments they know are those which have the simplest structures, such as Werckmeister III or Vallotti, temperaments which were most likely used very little if at all in ancient times. In fact, I would dare to say that this dogmatic adherence to the false notion that counting beats is somehow historical has probably done more harm than good to the early music movement by propagating the use of a very small number of simplistic temperaments of little or no real historical value! Luckily, for the young generation of musicians, a simple and economic alternative is readily available!