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Precise Calibration of Tuning Forks

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Precise Calibration of Tuning Forks 228 PHILIPS TECHNICAL REVIEW VOL. 12, No. 8 PRECISE CALIBRATION OF TUNING FORKS by C. C. J. ADDINK. 681.831.3 :534.321.71 :534.63 The introduction into the field of music of the new international standard of concert pitch based on a frequency of 440 els for the 110teA3 in the middle octaveinstead of 435 cis still involves difficulties owing to the lack of good standards, the tuning forks used in practice leaving much to be desired. Hence the greater interest now being shown in accurately calibrated tuning forks. An international conference held in London in tuned higher than 435 els but often differ, in the 1939 recommended that such bodies as the "Comité positive or the negative sense, several els from the Consultatif International Téléphonique", the "In- figure of 440 els. Since there was no standard ternational Electrotechnical Commission" and the for the frequency of 440 els in this laboratory a "Union Internationale de Radiodiffusion", as method has been developed, as the first step in also the various national standardisation commit- this direction. for measuring audio frequencies tees, should fix the concert pitch at a frequency of direct (i.e. by counting the number of oscillations 440 els for the note A3 of the middle octave - in- in a time interval) and with extreme accuracy. stead of the 435 els internationally accepted at With the aid of an apparatus working according Vienna in 1885 - and that this should be adhered to this method not only have tuning forks of 440 els to as closely as possible in all musical performancesI). been calibrated but also sets of 13 tuning forks, In practice the usual tuning forks are, it is true, forming a tempered chromatic scale of one octave (fig. I) . The methodreferred to will be described here, but the question to be considered first is the degree 1) See, e.g., Internationale Ncufestsetzung des Stirnmtones, Akustische Zeitschrift 4, 288, 1939. of accuracy to be demanded from a tuning fork. Fig. 1. Set of 13 tuning forks made in the Phi1ips Laboratory. Together they form a tem- pered chromatic scale from Cl to c2, with al = 440 els. The reason for the cylindrical shape is explained in the last paragraph. FEBRUARY 1951 CALIBRATION OF TUNING FORKS 229 Accuracy required of a tuning fork frequency with sufficient accuracy without some The useful decay time of a normal tuning fork other aids. It is true that a tuning fork can be kept is 5 to 15 seconds. When the pitch of a musical in vibration by electrical means, but then, unless instrument is compared with the tuning fork in a great deal of care is taken, the frequency at which the normal way one can usually hear beats. If, it vibrates differs somewhat from the frequency however, the difference in frequency is so small of a fork vibrating freely, and it is just this free that there are no more than two or three beats vibration that has to be measured accurately. during the decay time then they are hardly notice- What is needed for calibrating, therefore, is an able as such and one has reached, the limit of the auxiliary oscillator which, once it has been matched accuracy of the tuning fork. It serves no purpose, with the freely vibrating fork, continues to oscillate therefore, to require any greater precision than in that frequency for an unlimited length of time. 0.2 cIs (one beat in 5 seconds), or in other words An RC oscillator consisting only of resistors, the frequency of the tuning fork has to lie between capacitors and amplifying valves is very suitable the limits of 439.8 and 440.2 cIs 2). (This degree for this purpose. If such an oscillator is properly of accuracy is obviously only required for musical designed, when it has reached temperature equili- instruments with a fixed tuning, such as the organ, brium the relative frequency change in the audio- the piano, the harp, etc.) The frequency, however, frequency range can be kept smaller than 1:1053). has to be determined with greater accuracy, The matching of the frequency of the oscillator because one must be quite sure of the last decimal with that of the tuning fork can be done with suffi- in the said limits. The permissible measuring error cient accuracy if a cathode-ray oscilloscope is therefore 0.05 cle, which at a frequency of 440 cIs is employed, by applying the signal from the RC amounts to a measuring accuracy of about 0.01 %. oscillator to one pair of plates and a signal with the This implies that account must be taken of the frequency of the tuning fork to the other pair. temperature when measuring and when using the The latter signal can be obtained by setting up the tuning fork in practice. The temperature coefficient tuning fork in front of a microphone. There then of the frequency in the case of a steel tuning fork appears on the screen of the oscilloscope a changing is in the order of -1 X 10-4per oe, while for the forks Lissajous figure which, when the frequencies are made of a hard aluminium alloy îllustrated in fig. 1 equal, becomes a stationary ellipse 4). it is about -2.5 X 10-4 per oe. There is, however, a drawback to this method. The Lissajous figure cannot demonstrate whether Method of measuring the frequency deviation is positive or negative, As is evident from the foregoing, for calibrating hence the operator does not know in. which direc- a tuning fork a more accurate method is needed tion to turn the oscillator tuning knob. If this is than that where the tuning fork is compared with turned in the wrong direction the consequent time a standard frequency byear. Furthermore, with loss results in the tuning fork signal having decayed frequency differences less than 0.1% the sign of too far, and the fork has to be struck again. the error can no longer be determined by car. To obviate this, the following method is adopted. The method of calibrating worked out by us The signal from an RC oscillator is applied direct briefly amounts to the following. The frequency of to one pair of input terminals of the oscilloscope an auxiliary oscillator is matched with that of the and also,. after having been shifted 90° in phase tuning fork to be calibrated and then a synchronous in a network of resistors and capacitors, to the clock is connected to the oscillator and the oscilla- other pair of terminals (fig. 2). Given the right tions made by the auxiliary oscillator in a certain proportions of amplitude of the two signals, a interval of time are counted. This time interval is circle is then produced on the screen of the oscillo- measured with the aid of a calibrated pendulum scope. timepiece. The tuning fork to be calibrated is set up front in of a microp~one, the amplified signal from which Matching the auxiliary oscillator '. 3) See, e.g., E. L. Ginzton and L. M. Hollingworth Owing to the damped character of the vibration Phase-shift oscillators, Proc. Inst. Rad. Engrs 29, 43-49: a tuning fork is not suitable for measuring the 1941; K. Bucher, Re-Generatoren, Telegr. Fernsprech- Techn. 31, 307-313, 1942. 4) For this and the other method to he described later it 2) Other authors arrive at the same tolerance another way: is an advantage to use an oscilloscope with two amplifiers H. J. von Braunmühl and O. Schubert Ein neuer one for each pair of plates, such as type GM 3159 0; elektrischer Stimmtongeher für 440 Hz' Akustische GM 5655 (Philips Techn. Rev. 9, 202-210, 1947, and n, Zeitschrift 6, 299-303, 1941. ' 111-115, 1949 (No. 4». 230 PHILIPS TECHNICAL REVIEW VOL. 12, No. 8 is used for modulating the beam current of the If a voltage source with the standard frequency is available cathode-ray tube, such that the beam current is (e.g. an electrically driven tuning fork, or the 440 cis signal allowed to pass only during the positive half cycles as regularly transmitted by the B.B.C. for tuning purposes), then the tuning-fork frequency that is to be determined can of the microphone signal. Thus only half a circle be compared directly with the standard frequency by means is seen on the screen (fig. 2). When the oscillator of the set-up shown in fig. 2, replacing tile RC oscillator by the frequency is exactly equal to the frequency of the standard frequency signal. When this method is followed a tuning fork this half circle is stationary, but when rotating half-circle is again seen, and from the number of there is a difference in frequency it rotates. The revolutions it makes in a certain time it is easy to derive the difference in frequency (the sign is indicated by the direction best method is to arrange the apparatus so that of rotation), Thus one measures, as it were, a fraction of a the tuning knob of the oscillator has to be turned beat. The accuracy is proportional to thc duration of the clockwise to increase the frequency and that the observation, being already very great at the duration of the half circle rotates clockwise if the oscillator fre- decay time..If, for instance, the half cirele makes 114 revolution quency is too high and anti-clockwise if it is too in 12.5 seconds then the frequency differenceis 0.02 cis. low. Matching is then. done very quickly, the vernier control of the oscillator being turned in Measuring the oscillator frequency with the aid of a the direction opposite to that in which the half clock circle is moving, until the latter is stationary 5).
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