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6. The Revised Scale 2012. A=441       Updated June 2015
This is based on an octave scale length from C1- C2 of 324.1mm.  This is adequate for playing at 440-442cps.
Instructions:- To check a flute or to mark up a stick:- measure your tone hole diameters to see if they are close to, or the same as those in the first column.  Read the figures in the column which describes your flute, A, B or C. The large C# (B/C# trill) has also been shown. On a C foot, the end of the flute is C natural and on a B foot, the end of the flute is B or 0.00. The key cup rise should be 3.8mm in the foot and right hand; 3.4mm in the left. This is larger than customary but important for both pitch and tone.
Since the calculation of this scale, we have corrected some notes slightly after performing trials. These notes are now incorporated into the figures set out below.  A recent correction to Csharp2 is shown in red.

The Figures
                                                       A                             B                                    C
                    Tone hole               C Foot                            C Foot                                    Low B foot
                    Diameter                (Closed hole)                 Open hole)                             (Open hole)

Low B           15.6                        ---                                 ---                                                0.00
 
Low C                                                        0.00                                           0.00                                                             45.5

C#                                                                43.35                                         43.35                                                            81.85       

D                                                                   77.7                                           77.7                                                             116.2
   
Eb                                                                 110.1                                        110.1                                                            148.6
........................................................................................................................................................................................................................................
E                      14.2                                    141.8                                         140.1                                                            178.6
  
F                                                                   169.3                                          168.05                                                         206.55
 
F#                                                                 197.7                                         196.45                                                         234.95

G                                                                   224.3                                          224.3                                                          262.8   
........................................................................................................................................................................................................................................
G#                   13.5                                   248.2  (if 12.8 then 248.65)       248.2  (if 12.8, then 248.65)                       286.7  (If 12.8: 287.15)

A                                                                 270.6                                            269. 45                                                       307.95
     
Bb                                                               293.15                                          292.15                                                        330.75

B                                                                 314.0                                           314.0                                                          352.5

C                                                                333.15   (if 12.8, then 333.55)    333.15  (if 12.8, then 333.6)                     371.65 (if 12.8, then 372.05)               Please note: After a good deal of testing, we are now of the opinion that C2 would be better if placed 0.3mm flatter than shown above. June 2015.

C# large trill                                        352.4   (if 12.8  then 352.85)       352.4   (if 12.8, then 352.85)                    390.9  (12.8: 391.35)
........................................................................................................................................................................................................................................
C#  normal        6.7                                    364.3                                             364.3                                                          402.8
              (This hole position has  been revised (sharpened  by 0.5mm) after a lot of testing and experiments, to address the slightly flat octave. The new figures are in red. The tone hole should also be undercut all round, but the diameter of the top of the hole should remain at 6.7mm)
(This tone hole should be deeper than the others by 0.5mm and the key opened to 3.5mm above the tone hole)  This is important.
........................................................................................................................................................................................................................................
D (trill)           7.5                                    382.8                                             382.8                                                           421.3

D#                                                               398.7                                              398.7                                                          437.2
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The ‘End Correction’ (the distance from the end of the flute to the centre of the low C# hole): 7mm. This figure has already been added to the final figures.
The open hole corrections (Eldred Spell, March 2011)  E: 1.7; F: 1.25; F#: 1.25; A: 1.12; A#: 1.1.
To check your flute against the figures above: Use large size Vernier calipers and sharpen, by filing, the fixed inside edge so as to make a sharp edge for an accurate reading against the inside face of each tone hole.  Measure the diameter of each tone hole north to south and east to west (this is to check if they are identical). If the tone hole diameters differ from those given above, a correction should be made, though most flutes will correspond. (A tiny difference is not important). Now measure each tone hole from the end of the foot to the inside (south) edge of each hole. Add the radius (half the diameter) to this figure. This gives the distance from the end of the foot to the centre of each hole. Compare with the figures above.

                  William Bennett, Eldred Spell and Trevor Wye . January 2014

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           A Quick Check for your flute
This process may take a little time and is best done where there is quiet. Allow at least 30 minutes to make these checks and may need to be repeated on successive days.
1) Warm up the flute thoroughly. Then play low C, C1.  Overblow to the second harmonic, C2. Now take your fingers off the keys to compare the second harmonic to the natural note, the octave above, C2. . Do not move your lips or attempt to make any alteration to the intonation. If it is not exactly an octave, adjust the headjoint by moving it in or out until the two Cs, C1 and C2 are as near as possible at the same pitch.
2) Repeat this for low C# and compare it with the octave above. Usually, the two C# are not in tune, even though the two C naturals are. This is common and obviously they should be the same. Don't move the headjoiunt to tune them. Let it remain in tune for the two Cs.  Now check the pitch of C1 and C2 with your tuning machine.  This should tell you the pitch at which your flute was made.
Now you are going to use 3rd harmonics of lower register notes to check the pitch of the second octave. Unlike 2nd harmonics (octaves), 3rd harmonics (12ths) are sharper than the natural note. What you have to do is determine the degree of difference between these two notes.
4) Play C1 once again, this time overblowing it until it produces the 12th above, G2. Compare this harmonic with the natural G2 . There should be a difference, but note how large the difference is is.
c) Change to C#1 and then compare it to G#2. Observe the difference. Now try D1 and compare it with A2. Continue through Eb1 comparing it with Bb2; E1 comparing it with B2 and then F1 comparing it with C3. You can make a ‘double check’ here: between the 4th harmonic of C1 (C3), and the 3rd harmonic of F1, also C3.
You will have to be patient, always making a note of how large the gap is between the natural middle register note and its fundamental (the low note) There should be a small difference: the harmonic being sharper. It’s the degree of sharpness you are checking. The swing of your tuning machine needle between the two notes, may be helpful. Remember not to assist the difference with your lips!
You may find that there are some notes which are flatter than the harmonic indicating a problem.
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