Source: Outlines of Experiments and Inquiries respecting Sound and Light, from Philosophical Transactions Royal Society of London (London: 1800)
Original text

Young’s temperament is usually considered to be an example of a circulating or “Well” temperament. In the modern literature, it is always forced into the mold of rational circulating logic by describing it as having four fifths tempered by -1/6 of the Pythagorean comma (C-G, G-D, D-A and A-E) and four fifths tempered by -1/12th Pythagorean comma (B-F#, F#-C#, Bb-F and F-C). This ubiquitous modern misrepresentation of its structure is caused by a failure to consult the original source. Young’s original instructions as well as the monocord dimensions he gives prove that this rationalization is incorrect, and is an unfortunate perversion of the historical record which hides the true origins of Young’s logic and methodology: the tradition of mollified meantones. While it would appear that Young was behind his continental colleagues by 50 to 100 years, it must not be forgotten the English musicians apparently clung to regular meantones until almost the end of the 18th century. Thus Young was simply accomplishing a logical step in the organic evolution of temperament structure, evidently unaware that so many had already taken this same step many years before him.

Exactly like those earlier French and German authors, Young begins by defining the first trient by fixing the size of the major third CE and the four fifths it comprises. Young’s solution is a slightly wider-than-pure third, which he defines unequivocally as being too wide by 1/4 of the syntonic coma. While this description has puzzled many a modern writer, it is actually incredibly easy to do by ear (see below). Young says nothing about the sizes of the four fifths encompassed by this third, evidently assuming that one would simply do what was normal in any regular meantone: temper them all by the same amount. His monochord lengths prove this assumption to be valid; each fifth is tempered by 3/16ths of a Syntonic comma.

His next step is to address the traditonal problem of the function of note G#/Ab, thereby defining the widths of the second and third trients. His solution is to divide the minor sixth E-C into two major thirds of the same size (each too wide by a little less than half the Diesis).

Young’s unique contribution to the history of mollified menatones comes in determining the sizes of the remaining fifths. Rather than treating the second and third trients as two individual groups of four fifths, as do the French authors, Young begins by tuning a contiguous chain of four pure fifths centered on the pivotal note G#/Ab. The remaining two fifths at either end of this chain are then simply left to become whatever size is required to fill the spaces between E-F# and Bb-C, approximately the same size as the fifths in Equal Temperament. In this way, the chain of fifths comprising the second and third trients form a palindrome, the one trient being the mirror image of the other.

Young concluded his discourse by briefly mentioning an alternative possibility which he said would work almost as well, which is a symmetrical regular 1/6th Pythagorean comma rational circulating temperament. This alternative is much simpler in its basic structure, and appears to have been offered for those not sophisticated enough to understand either the elegance of the structure nor the obvious easy implementation of his real temperament, a situation which persists to this day.

Disclaimer: the attribution of comma fractions to the tempered fifths is done by an automatic table look-up function. If the exact value is not in the table, the system grabs the nearest lower value. Naturally, my table does not have all possible fractions of both commas for both narrow and wide fifths. Therefore, with all modified meantone temperaments, for those fifths which “close the circle”, i.e. fill in the gap left by the departure from pure meantone logic, the amount of tempering has been somewhat arbitrarily chosen, exactly as one does when tuning an instrument, although in this case, working with decimal values for the proportion of the fifth. Therefore, the final size may not represent any fraction of any given comma, and there is no guarantee that the amount of tempering indicated as a comma fraction in the graphic is precise. The value indicated in cents, however, is derived from the proportion, and is therefore completely trustworthy.

Young's mollified meantone

How to implement Young’s first step by ear

First, one tunes C-E as a pure major third and the first four fifths are tempered alike, as in regular meantone. Next, the note E is raised so as to make a pure fifth with A. This makes the major third C-E too large by 1/4 comma, precisely as Young says. Finally, the notes G, D and A are all raised slightly so as to make all four fifths once again tempered by a common amount, which is 3/4 Sytnonic comma divided by 4, or 3/16ths of a Syntonic comma. Simple!