Society of Arts Pitch

Part IV - The Outcome

Summary

If you've got this far, your head is probably still spinning from all those amendments!  So let's summarise what it was all about ...

The meeting had come about because of growing unease about the pitch being used in professional musical circles in Britain, which had risen as high as A455.  The attendance list (see Part I) is certainly impressive, but it would have to be conceded that it was a list of the village elders.  Perhaps not surprisingly they would have liked most to return to the pitch of their youth - variously called theoretical pitch, philosophical pitch, natural pitch, C256, or by its octave frequency, C512.  We would call it today A430, the pitch forte-pianists still use.

But, being practical people, the meeting recognised that this was not likely to get up, and so cast around for a compromise.  They didn't seem moved to consider the French Diapason Normal, possibly because of the old French-English rivalry, or perhaps because at A435 it wasn't much of a compromise.  They were taken though by the recently mandated Stuttgart Congress pitch at A440.  At almost halfway between 430 and 455, it would make an attractive compromise, with the added advantage of international agreement.  It would also not make so many existing instruments obsolete as would a lower pitch.

Whoops?

Perhaps because they were "of the older school", they preferred to think in terms of C rather than A as a pitch standard, even though others around them had shifted to A.  And when called upon to translate pitch to or from A, they employed Just Intonation, rather than Equal Temperament, even though Equal Temperament was now the norm.  So, they framed their resolution:

“That the pitch of 528 vibrations for C be recommended for universal adoption in this country.”

It is clear from the explanation in Part II that they intended C528 to imply A440 (528/2 = 264, 264 x 5/3 = 440).  Indeed they show the mathematical working from Stuttgart Pitch. 

But when anybody else did the conversion back to A using Equal Temperament, they got A444 (528/2 = 264, 264 x 2^(9/12) = 444).  So this has come to be known as Society of Arts Pitch, even though clearly not the intent of the Society.

It might seem surprising that the two methods of conversion yield such differing results, but that's because the interval C to A is a 6th.  The 6ths and the 3rds are the points of the scale at which Equal Temperament differs the most from pure harmony.  In many ways, the Society method was more meaningful.  If you strike forks at 440 and 528 simultaneously, they will be found to be harmonious (5th harmonic of 528 and the 6th harmonic of 440 are both 2,640Hz).  Strike forks at 444 and 528 and the harmonics come in at 2664 and 2640, destroying that consonance.  Still, them's the rules we now live by!

Now this apparent misinterpretation seems to have gone unnoticed, probably largely because the Society's attempted change to pitch fell largely on deaf ears.  Two writers seemed to have covered the Society's meeting, the 19th century acoustician Ellis, and Rockstro.  Rockstro's table is given in his book as an extract from Ellis, so they should be the same.  It seems to be clearer, so let's start with some extracts from there:

We can see that Rockstro employed Equal Temperament to equate the Society's C528 to give A444, not A440 as they had intended.  Indeed he mentions that he used ET in setting up the table.

More oops!?

But note that last entry.  Something else seemed to go wrong with the Society's other resolution, to have a fork made to reify their standard.  It gets a bit hard to follow exactly what happened, but let's try.  According to Rockstro, when Mr Griesbach actually made up a fork for the Society, it ended up sharper again - the original A440 now represented as A445.7!

Ellis paints a slightly more complex picture.  He also gives A444 as the

"Intended but unexecuted standard of the Society of arts to c" 528." 

So, like Rockstro, he had not noticed or had chosen to ignore the use of Just Intonation and not Equal Temperament in the conversion. But Ellis measures the Griesbach fork as A449.4:

"London, from Griesbach's c"534.5, tuned for the Society of Arts as c"528; he tuned a' as 445.7".

We seem to have incurred a second ET conversion here!  If so, the whole story would seem to go like this:

• Society of Arts adopts Stuttgart Congress A440
• Society uses Just Intonation to equate it to C528
• Others convert back to A using Equal Temperament and get A444
• Griesbach makes his fork a little sharp,  at A445.7
• Ellis reconverts A445.7, using Equal Temperament, to get C534.5

We could keep this up all day folks!

Rockstro seems to have chosen to ignore Ellis' C534.5 figure, perhaps believing that Ellis had made a mistake here - one conversion too many.  I'm inclined to do the same until we can prove otherwise.  It certainly amply illustrates the danger of using different standards and methods of calculating between them!

Outcome

I think we'd have to concede that the outcome was not what the committee had hoped for.  The Philharmonic Society remained at high pitch until sometime around 1895, and Kneller Hall, the headquarters for the military band movement, continued with it until the 1926 or so.

So what went wrong?  Perhaps a number of things, and these need researching further.

One worrisome thought is that perhaps the committee was not that representative.  We never heard any voice in the account above that seemed in favour of continuing at high pitch.  Perhaps "those sorts of people" just hadn't been invited?

Secondly, as pointed out by Dr Blood of Dolmetsch Musical Instruments:

Thirdly, we know there were other meetings where the matters raised here were gone over again - Rockstro refers to a meeting at St James's Hall in 1885 where a committee (of which he was a member) concluded that it was impractical to lower the current pitch.  Rockstro's glee is palpable:  "We may therefore reasonably hope that we shall hear no more of the last new craze".  Looking closer into that though, we might just be falling victim once more of Rockstro's outstanding capacity for brazen misrepresentation.  According to Ellis, this meeting also resolved to lower the pitch, a fact Rockstro didn't mention.  We'll delve further into that as time permits.

The pitch did come down, in 1895, just 5 years after the publication of Rockstro's book, and finally settled on the very pitch the Society committee had been attracted to, A440.  So perhaps theirs was the last laugh, even if musicians in England had to wait another 35 years to enjoy it.
 

Acknowledgements

Special thank you to the Archives section of the RSA for making the article available, and to Dr Brian Blood of Dolmetsch Musical Instruments for his help in identifying the attendees of the meeting.