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 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"

In order to make sense of this instruction, it is useful to recall that the common keyboard tunings in the Baroque period were based on regularly-sized fifths. The typical tempering in a fifth ranged from 1/4 comma to about 1/6 comma, to taste. Lindley in his "Temperaments" article (New Grove) suggested that the most commonly used size of fifth in the 17th century was probably about 1/5 comma. All of these "regular" or "meantone" temperaments are easy to set up in practice, due to the consistent sizing of their fifths and the resulting consistent quality of their major thirds. In a fifth, the amount of narrowness that "ye Ear will permit" can vary from one instrument to the next, due to differences in overtone structure.

There were two more or less equivalent types of bearing plan. The first, starting from C, involved tuning four narrowed fifths (or widened fourths) C-G-D-A-E and checking whether the third C-E was "good" enough. The second involved setting the tastefully sized third C-E at the beginning, then tuning narrowed fifths C-G-D-A and checking on the fifth (or fourth) A-E.

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 "good", then 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. If this succeeds, i.e. if the tempering of A-E is not too large, then one may proceed.

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 similar in quality to C-E, or perhaps to G-B.) 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 be wider than F-A, 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 "regular" 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 sharper than C-E. They need not be equally so, but the instruction does not indicate any gradation. Likewise Bb-D and Eb-G are slightly sharper thirds than C-E or F-A. 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 1/4 comma meantone.

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 (presumably pure or slightly wide) in the middle octave, then treble E is tuned flat fifths C-G-D-A-E, and finally the octave E's are to be played together as the check. The fifth E-B also seems to be a check, since these notes were previously tuned as thirds from C and G respectively. Players experienced in tuning meantone will know that the more checks one has on the tempered fifths the better, since there is some room for error in setting successive notes via major thirds.

The departure from regular 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. Other "wolf" intervals" are only marginally affected; G#-Eb may again be 'only' about a comma out of tune.

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 also 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 of F-C-G and D-A-E 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.

Padua manuscript instruction

This anonymous Italian instruction comes from a manuscript (18th-century)? in the University of Padua. Like the third English source, it is a simple list of tuning steps, which I will summarize in English.

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

Then C-F-Bb are tuned via sharp fourths.

The notes Bb-Eb-Ab are tuned by flat fourths.

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.)

Again we have the initial sequence of meantone flat fifths. Since there is no check of C-E, we cannot assume that this third was pure. However, the tuning cannot actually have succeeded if C-E was much different from a pure third, i.e. if the tempering of the fifths was much 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. practically pure.

The simplest way to deal successfully with the instructions is then to use steps of approximately 1/4 or 1/5 comma tempered fifths. This is consistent with the assumption that this range of meantone was the most widely known and practised tuning in the Baroque period, at least in Italian-speaking areas: players would be accustomed to tempering fifths by this amount, not only on keyboard instruments but perhaps also on the open strings of violins.

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