Comparison of Scaling
What do we mean by scaling?
As we all know, the longer a flute is the lower the pitch it will play. Comparing the length of bass flutes with standard flutes and piccolos is enough to remind us. The basic relationship is simple - if you want to go up an octave, you halve the length; to go down an octave you double the length. In mathematical terms, the pitch is inversely proportional to the length. In reality, it gets a little more complicated because of end effects, but they needn't concern us here.
So if doubling the length halves the pitch, what does a small increase in length do? Not surprisingly, it drops the pitch a little bit. We also know that - pulling our tuning slides out a little flattens the flute.
So it should come as no surprise that, to be able to play at any particular pitch (e.g. our modern 440Hz), there is only one length of flute that is theoretically suitable. Conversely, flutes of lengths other than that one true length are going to play sharper or flatter than modern pitch; indeed, we should be able to get some impression of how much sharper or flatter by comparing the lengths with our one true length.
And it also means that a clever flute maker can scale a flute up or down in length as required to achieve the pitch desired.
How do we measure scaling?
When we come to comparing the scaling of historical flutes, we strike a dilemma - there is no recognised system other than measuring the sounding length of the flute in question, and this can be very misleading. So, I'm going to rely on my own system, which you can see discussed at C# to Eb - a more useful indicator of flute pitch?. Essentially, I take the distance between the centre of the top hole (C#) and the centre of the Eb key. Reasons for this choice are set out in the article mentioned.
And I'll take the graph from that page to illustrate the scales of flutes throughout the 19th century. And we'll see below if we can find some of our old friends ...
Early English 8-key, exemplified by Richard Potter (post 1785)
Yep, up there in the top block, you'll find Potter, W.H. William Henry was Richard's son and made flutes very similar to Richards. You'll see I've labelled that block as Very Low pitch, less than 430 Hz. You'd find it very hard to play one of these flutes at modern concert pitch.
Nicholson's Improved (post 1816) and the flutes based on it
Two mentions, one near the top of the second block, and a later one near the top of the third block, Low pitched, circa 430 Hz. So, very long, but getting shorter with time. Still very hard to play at modern pitch. If you wanted a new flute based on a Nicholson's Improved, you'd want to make sure the maker rescaled it for modern pitch.
And, in that same block, there's Rudall & Rose, popular heroes of our time. Hey, are you telling me their flutes are hard to play accurately in modern pitch? Yep! Another job for rescaling.
Boehm's Ring Key conical (post 1832)
Not present in the list above, but if I told you I measured one of his at 258mm, you'd see he fits in near that first Prowse Nicholson. The timing is right. A later one made by Rudall & Rose clocks in at 254mm. Again, flutes shortening (getting sharper) with the passage of time.
Siccama (post 1847)
Abel Siccama clocks in just a little below that Rudall & Rose, again logical, the time is right. Still a smidge flat of modern pitch, but at last within lipping-up range.
Pratten's Perfected (post 1852)
Hey, we went right past modern pitch without seeing anyone there! Correct, modern pitch came in after High Pitch - the flutes in the Modern Pitch range are all much later.
We find Pratten's Perfected in the Slightly High Pitch, circa 445Hz, block. Remembering that Pratten redeveloped Siccama's flute (in the low pitched area), but kept the same bore, it's clear that his major contribution was shortening the length to make it easier to play at the higher pitches coming into vogue. If we have some difficulty playing the earlier flutes at modern pitch, imagine what fun professional musicians of the time would have had playing them at high pitch! They must have flocked to Pratten. No wonder Boosey "acquired" him! And, in the context of this page, a hero,The Bold Re-scaler.
Now it's interesting to note that Pratten doesn't appear to have gone the whole hog and rescaled for High Pitch. That would have produced a flute that could only be played for orchestral gigs. He seems to have either presaged the Society of Arts argument or coincidentally arrived at the same conclusion - a compromise is best.
So does that mean we have to scale down Pratten's flutes for modern pitch? Not really, it's so close to our own pitch that a few tweaks to fingerhole positions and/or size is enough. Don't just believe me, look around you. Those with original Prattens flutes find they can play them unmodified without much effort at modern pitch.
Modern Boehm cylindrical flute.
Not included in the chart above and for good reason.
Its cylindrical bore makes direct comparison with conical bored
instruments invalid. A modern pitch cylinder flute is about 255mm C#
So what did we learn by investigating the scaling of our representative shopping basket of old flutes? We found that over the first fifty years of the 19th century, flutes dropped about 8% in scale length. Remembering that pitch and scale length are directly (although inversely) linked, that represents a change of pitch of 1.2 semitones, or 120 cents. Not surprising then that not all of these flutes are comfortable at modern pitch!
We also saw that Pratten might have the distinction of being the only flute designer who dared to make a quantum leap in scaling. Rather overdue by that time!
In practical terms, if you are looking for an old flute to play, you would probably want to avoid flutes with a C# to Eb length exceeding 254mm (10"), or be prepared to have it tweaked.
And when we come to looking at the Tuning of some of these flutes, we'll see that Scaling and Tuning are intrinsically linked.