Introduction

This page presents source materials of three anonymous 18th-century English manuscript instructions for irregular keyboard tunings, and one comparable anonymous Italian instruction. The sources are G. Sargent, "Eighteenth-century Tuning Directions: Precise Intervallic Determination", in The Music Review (1969) vol.30 no.1, p.27-34, and Mark Lindley, Stimmung und Temperatur (see the reference in Temperament_Ordinaire). I (T.D.) also make brief comments on the possible realization and use of the instructions.

I have not included Sargent's "intervallic determinations" for the simple reason that they do not help in interpreting the 18th-century source material. Their precision is spurious, and in at least one case Sargent's deductions are incorrect.

The 'Newcastle' tuning instruction

This appears in a manuscript, according to Sargent, "connected with Charles Avison" (1709-1790). http://en.wikipedia.org/wiki/Charles_Avison

The instructions can be concisely summarized in a single stave with simple annotations:

"x" with fermata : "as flat as ye Ear will permit"

"x" without fermata : "as sharp as ye Ear will permit"

To interpret this, it is useful to recall that meantone was a very common keyboard tuning in the Baroque period, probably the one most often described in written sources. Quarter-comma meantone is also the simplest historically relevant tuning to set up in practice, due to its pure thirds and regularity. Whatever the exact variety of meantone, there were two more or less equivalent types of bearing plan. If we assume that one starts from C, the first involved tuning four narrowed fifths (or widened fourths) C-G-D-A-E and checking whether the third C-E was pure, or pure enough. The second involved setting the pure (or slightly wide) third C-E at the beginning, then tuning narrowed fifths C-G-D-A and checking on the fifth (or fourth) A-E. If the check gives a satisfactory result, i.e. if all the intervals so far tuned correspond to the instruction and are musically acceptable, one may proceed; if not one or more steps must be re-done.

We can then recognize the first five "bars" of the instruction, concerning the notes C, G, D, E, A, as this second type of bearing: the third C-E is made pure, considering that the E in the first bar (like the C above middle C) has neither a 'flat' nor a 'sharp' sign; while the fifths C-G-D-A are tuned flat. The fifth "bar" concerns the notes A and E which have already been tuned, and is thus the check.

The sixth "bar" similarly contains the note A, which has been previously tuned: it serves as a check on F which is tempered as a narrow fifth from C. (Given the previous tuning steps, F-A is likely to be a pure third, or nearly so.) The seventh "bar" asks for Bb to be tuned a pure fourth above F, then the previously tuned note D is a check on the chord of Bb major. Here Bb-D will not be pure, but the overall sound of the chord should still be acceptable. Similarly, after Eb is tempered as a narrow fifth from Bb, G is played to check the chord of Eb major.

The significant departure from meantone is that E-B and F-Bb are pure fifths. This is consistent with all major thirds from G-B sharpwards to E-G# being slightly sharp. They need not be equally so, but the instruction does not indicate any gradation. Likewise Bb-D and Eb-G are slightly sharp thirds. As a result the "wolf" G#-Eb is likely to be only about a comma sharp; perhaps more importantly, the "wolf" thirds such as B-Eb, F#-Bb and F-G# are also somewhat less violent. In particular B-D# and F#-A# as dominants of E minor and B minor respectively may be half a comma better than in meantone. (T.D.)

Harleian manuscript instruction

The second is an anonymous tuning instruction in a British Museum manuscript (Harl. 4160). This is again summarized on a single stave with annotations:

f : flattish

s : sharpish

p : perfect

We recognise, even more clearly, the basic meantone sequence C-G-D-A-E. Here the two types of meantone bearing plan are combined, in that C-E is tuned at the start in the middle octave, then treble E is tuned via flat fifths C-G-D-A-E, and finally the octave E's are to be played together as the check. If E and B are tuned as major thirds within their common chords, as indicated, it may be more difficult to hear the degree of purity of C-E and G-B respectively: the thirds could turn out slightly wider or even slightly narrower than pure. Then the fifth E-B is another check: players experienced in tuning meantone will know that the more checks one has on tempered fifths the better, since there is some room for error in setting successive notes via thirds, even more so when the thirds are inside common chords. Perhaps also E-B was singled out to be checked because chords of E major and minor occur very often in the most often used keys; B-F#, F#-C# and C#-G# are not checked.

The departure from meantone comes only on the flat side: F-C is pure, Bb-F is narrow but Eb-Bb is wide. Between Eb and G there are two narrow tempered fifths and one wide, meaning that Eb-G is only marginally better than a Pythagorean third. Conversely, B-D# will be only marginally worse, making E minor significantly less dissonant than in plain meantone. Other "wolf intervals" are only marginally affected; G#-Eb may again be 'only' about a comma out of tune. (T.D.)

Quasi-Pythagorean tuning instruction

The third instruction was written down on a copy of Rameau's Traité de l'Harmonie (first published in 1722) and is a simple, but rather vague, list of tuning steps. It can be summarized as follows.

The pitch is set to F (presumably in the tenor octave).

The octave F - FF (downwards) is then tuned.

The fifths FF - C and C - G are "as flat as the ear will bear".

G - D is "perfect"

D - A and A - E are "very little flat"

Then "all the rest of the fifths perfect".

I have called it "quasi-Pythagorean" because it proceeds only by fifths, without checking any thirds or chords, and because most notes end up being tuned by pure fifths. Note that there is no requirement (unlike in Temperament_Ordinaire) for the circle of fifths to close. The instructions do not specify any checks that would ensure there was no leftover tempering around the circle after F-C-G-D-A-E are tuned. The final part of the instruction could only be satisfied exactly if the tempering at F-C-G and D-A-E combined adds up to the Pythagorean comma; but the bearing plan, and the vague description of the tempered fifths, make this unlikely in practice. Depending on the order in which the remaining notes were tuned, there could easily be a wide or narrow fifth left somewhere among the accidentals.

The absence of any checks on thirds also suggests that the anonymous scribe was not particularly concerned with their musical qualities: the sizes of the thirds are by-products of the vaguely-described sequence of fifths, which lead you, more or less decently, round the circle. (T.D.)

Padua manuscript instruction

This anonymous Italian instruction comes from a manuscript (18th-century)? in the University of Padua, reproduced as an illustration in Mark Lindley's Stimmung und Temperatur. Like the third English source, it is a simple list of tuning steps, which I will summarize in English, apart from the last part which is difficult to read.

The notes C-G-D-A-E are to be tuned via flat fifths.

Then C-F-Bb are tuned via sharp fourths [equivalent to flat fifths].

The notes Bb-Eb-Ab are tuned by flat fourths [equivalent to sharp fifths].

Returning to the sharp side, E-B-F#-C# are to be tuned as pure fifths.

Then C#-G# is the check : "Prova perche riesce Quinta giusta". (Roughly: Check because a pure fifth succeeds.)

After this apparently complete sequence of steps a remark is written "In questa partecipazione le terze mag[g]iori vengono un puoco alterate non [or ne] piu a le 5.e ma non nel meno". This may be translated tentatively as: "In this temperament the major thirds will come [will be] a little altered [impure] no more than the 5ths but no less."

Again we have the initial sequence of meantone flat fifths. Since there is no initial check of C-E, we cannot assume that this third was pure. However, the tuning is unlikely to have succeeded if C-E was much different from a pure third, i.e. if the tempering of the fifths was very different from 1/4 comma. To see this, consider the thirds E-G# and Ab-C. The first of these is tuned via three pure fifths E-B-F#-C# and the check C#-G#, which cannot be much different from a pure fifth. Thus E-G# is practically a Pythagorean third. Now Ab-C is tuned via two flat and two sharp fifths (or indeed fourths), so it too is likely to be about Pythagorean. Thus C-E is about a comma smaller than Pythagorean, i.e. close to pure.

Note though that the instructions do not say that the sharp or flat fifths and fourths should be the same size or have the same amount of temperament (perhaps the most obvious way to interpret them). The remark at the end appears to be comparing the degree of tempering of major thirds and fifths, an essential step in checking a meantone temperament, whether quarter-comma or another variety. However the instruction as a whole is not meantone and results in a very wide range of sizes of major third - which cannot all be "no more nor less" tempered than the fifths. If the remark is applied to the first four fifths and the third C-E, it implies 1/5 comma tempering, where the fifths and major thirds are equally out-of-tune. Then the circle will not quite close, unless the two sharp fifths are made somewhat less impure than the flat ones (C#-G# might also be very slightly flat) - which may give a quite acceptable musical result.

The treatments of the fifths, taken as a whole, is reminiscent of Rameau's (Rameau_Ordinaire from 1726). His last remark on harpsichord tuning there, about transposition of his temperament instructions. implies that taking flat fifths from Bb round to B, then gradually widening them in the "sharpward" direction to close the circle (the widest fifths being then around Eb), will give the purest intonation to the "most used" harmonies.

The Padua instruction is also interesting in that it shows a closed circle of fifths with an explicit check, unlike the instructions of English origin. This may be a general difference between English and Italian expectations for keyboard tuning in the Baroque period, a subject also touched on by Cavallo in his discussion of the wide modulatory range of the "old" (meaning early 18th-century) Italian composers. (T.D.)