Cooper's Scale Revisited

by Trevor Wye with William Bennett and Eldred Spell.         

Albert Cooper's Scale revolutionized our flutes, serving us well for more than 30 years. It remains considerably better than the non-Cooper variety, but needed updating.

    For those readers unfamiliar with flute scales there is much to absorb in this article. To make this easier, after an Introduction, it has been divided into six sections:

1. Why a Revision of Cooper's Scale is Necessary. The history behind the formation and calculation of the first Cooper Scales and concludes with how the Revised Cooper Scale was arrived at, together with notes on retuning flutes.

2. Intonation Control by Flutists which may help illuminate some of the problems of performers and their flutes.

3. Twelve Popular Misconceptions about Flutes and Intonation.

4. Is Your Flute in Tune? A simple process using a flute and a tuning machine, by which a player  can find out whether their flute has a good scale. Includes advice on buying a flute.

5. A Plea to Teachers, Players and Makers.

6. The Revised Cooper Scale: the figures. 

Introduction: To understand a flute scale, the tone-hole positions are best seen as related to the layout of the guitar fingerboard, an idea suggested by the brilliant Theobald Boehm and referred to as his "Schema.":-

    The placement of tone holes follows a simple mathematical layout, but with certain allowances added for tone hole size, open/closed keys, key height, and a few more subtle compromises. Until the 1960s, the traditional high-quality flutes, such as those by the two famous US makers, and many European instruments too, were built to between A=435hz and A= 438hz, the performer being expected to play them at A=440hz or higher. As the orchestral pitch rose in the 1930s, makers appear to have shortened the head joint, but also as time passed, made alterations to the scale by moving a few holes. Perhaps the reason why a complete revision of the scale was thought unnecessary was that the rise in pitch was too small, or perhaps the knowledge of how to achieve this was wanting. Makers ought to have calculated a new scale, but the method of calculation seems to have died with Boehm.

When the scale is poor, the player needs to develop special intonation control skills to overcome the faulty workmanship of the maker. Some have managed to do this with great dexterity in the same way that a fine violinist might still manage to play a badly tuned violin in tune. But why should they? The remedy is easy. Older flutes may be well loved and cherished, but today, it is relatively easy to buy both a first rate flute and separate head joint which would satisfy the most discerning player who has an open mind.

1. History of the Cooper Scale.

    In 1945, Albert Cooper returned from military service back to Rudall Carte & Co, the London flute makers, where he was formerly apprenticed. There he repaired and overhauled numerous makes of flutes, becoming  interested in the difference in scales between them. In 1959 he left Rudall & Carte to set up a repair service, but soon began making flutes. He devised an initial scale, based on what he saw as the 'faults and virtues' of those flutes he had measured at R&C and his own reasoning and experience. In 1955, William Bennett was playing a Louis Lot flute rebuilt by Charles W. Morley, probably to a Rudall & Carte scale.* In 1956, whilst in the USA, he tried Haynes and Powell flutes but was dissatisfied both with the scales of  the US flutes and of his rebuilt Lot, and began changing the scale according to his ears and performing experience. To do this, he devised a method of removing the tone holes, hard soldering them onto a piece of scrap tube which were then cut out to leave enough remaining material to allow them to be replaced in the new position, a technique known as 'patching.' This ability to adjust one or more tone holes  still remains an essential tool in the search for a perfect scale. 


    A talented and intelligent London orchestral principal, Elmer Cole, calculated the tone hole positions according to Boehm's Schema. The resulting scale was based on tone holes of an equal diameter, 15.6mm. For tonal reasons, flutes require graduated tone holes, becoming smaller as the scale ascends. Cole devised a 'correction graph' to enable the position for smaller diameter tone holes to be calculated, but found that even further adjustments were required for serious performing.  Richard Lee, another London player, was also involved in retuning his flute and, along with Bennett, was in frequent consultation with Cole. All were in regular touch with Albert Cooper, whose home became a clearing house for information on 'the scales.'

Meanwhile, the Taylor brothers, Christopher and Richard together with Alexander Murray, at that time all London Symphony Orchestra players, made  their own contributions, based on the Cooper flutes they owned and played and their criticisms of the scale. One of these was that both the top four left-hand notes  A#, B, C and C#- and the last three right-hand notes - F, F# and G - were too flat. Cole changed his Correction Graph to put this right, curving his graph at each end in order to sharpen the left hand notes, and sharpen the foot joint notes too. (C, C# and D). Cooper's pragmatic solution was to use Boehm's Schema but split into two, using a sharper version for the right hand and the usual one for the left, though he too sharpened the A#1, B2 C2 and C#2. These were really variants of the same idea.

* Rudall Carte had a tradition of altering the pitch of flutes by modifying and fitting old keywork to new bodies, a practice going back for many years but alien to the US makers; it may account for the reluctance of US makers to change the scale.

The London players decided that the new Cooper scale was easier to play in tune and as well as ordering a new Cooper flute, asked Cooper to retune their favourite flutes such as Louis Lot, Bonneville, Haynes and Powell, to his scale. Cooper obliged when he had the time and after removing the tone holes, used both Bennett's 'patches' method and also 'swaging' or pushing and persuading the softened silver tube to partially refill the hole, which allowed the tone hole to be repositioned.

During the 1970's, Trevor Wye began retuning his own flute and was later asked to retune many British orchestral player's flutes to Cooper's Scale using a mixture of Bennett's 'patching' and Cooper's swaging method. During this time, Bennett, Cole and Cooper continued suggesting small amendments to the Scale in the light of criticism and performing experience. Wye incorporated these amendments in his retuning. He also built what became known as an 'Automatic Trevor', a tube with movable tone holes and a powered blowing apparatus. This experiment was conducted to confirm that the Cooper Scale was indeed correct and although several interesting assumptions were confirmed, the device seemed unable to play octaves accurately and was abandoned. 

The correct position of the C#2 hole has been one of the major contentions amongst makers who have struggled over the years with its exact placement. This small tone hole must fulfil seven functions* and needs special management to play it in tune. Its diameter and height also play an important role, the latter not being widely appreciated. Players recommend a variety of ways to control the pitch and colour of C#, but none of these replaces having the tone hole in the correct place.

Working at first independently in the US, Eldred Spell joined in after meeting William Bennett in 1976. Initially skeptical of altering old flutes, he eventually retuned instruments for many of the English principals, including Bennett, Wye, and Geoffrey Gilbert. Being of a scientific/analytical bent, he was particularly bothered by the need to falsify the numbers in order to get a workable scale and has devised many experiments to get at the truth.  Most recently, his apparatus which simulates the blowing of the flute, photographed below, is an attempt to refine some of the less well-known aspects of flute making and scales - such as the displacement graph and the difference in tone hole positions between open and closed flutes. He is hoping too, to establish more exactly the correct 'scale length;' that is the total length of the flute from C1 to C2.

Meantime, William Bennett's continuous experiments with flute scales and the diameter and height of the tone holes, resulted in several important changes to Cooper's original Scale. His dogged persistence in seeking perfection has been largely responsible for this revision of Cooper's Scale. Bennett's Scale, which he has already given to several makers, is similar to Cooper's but with minor personal alterations.

As 'the Scale' developed and players offered their opinions, Cooper updated his figures and gave the latest revision to anyone who asked for it. Over time, he gave the latest scale to different makers. Just a few years ago, he said: 'Cooper's Scale? What's that? There isn't 'a'  Scale. There is a constant revision taking place so that, at any one time, there is a set of figures which you can use to design your flute, but these will change in the light of experience. I altered the scale a little as the years went by, mostly according to certain criticisms levelled at it. I now feel that I have more or less reached the end of the road scale-wise.'

Several versions of Cooper's Scale appear to be used by makers, perhaps passing on the figures to each other, or measuring sample flutes, but the translation from one maker to another has resulted in inaccuracies. In the past few years, we three have questioned the most commonly used set of figures of the original Cooper's Scale supplied by Cooper as manufactured by leading flute makers. These were the general observations: middle D seemed to be a little flat; the left hand Bb and B are too flat; both C2 and C#2 sharp are too high - perhaps because the open hole correction had not been correctly calculated.

The three of us have been in contact over the years regarding changes and improvements, but recently more often because of our common agreement that Cooper's scale is no longer fit for purpose. Although not absolutely satisfied, we agree that we have progressed far enough to publicly declare our findings and make this new scale available for use by makers if they wish. In fact, we urge them to do so. The RCS is free to use as required. 

* It is open for C#2; D2; Eb2; C#3; D3; Ab3; A3

Below is an example of the kind of discussion that used to take place about flute scales:-

* A note from Cooper  to Bennett, c.1986:- ‘Dear Wibb, I wish I had paid more attention to the calculations of the R.H. holes of the Jack Moore flute. Enclosed are my original calculations of which there are 2 errors. Firstly - the F# was wrongly placed, see red ink correction. Secondly - having done the F# correction, all the RH holes should be sharpened .2mm. Take notice of the green ink figures. The odd peculiar R.H. hole size threw me. I hope you can alter the stick as indicated, or let me alter it. I still think the R.H. holes I indicated as flat, are still a bit flat, but not as bad as first indicated.’ A.C.

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