By far the most common fault with gramophone records of all eras is eccentricity due to the spindle-hole not being coïncident with the exact centre of the groove spiral. This being a function of a manual step in manufacturing a record.
The WOW! pitch-correction correction algorithm in Stereo Lab is intended to correct this problem. WOW! digital record-centring is scheduled for a near-future version of Stereo Lab.
When WOW! is used as a digital, record-centring algorithm, the needle-drop is processed to discover the frequency and phase of the cyclic speed (and hence pitch) variation and the calibration of the degree of pitch correction is programmed via a slider in the preferences dialogue. This measurement is calibrated in mm of the observed weave or sway of the cartridge as it plays the disc.
Until now, the centring of eccentric records required the rather fraught opening out of the record's centre-hole and then centring the record by hand. Alternatively, one could obtain one of Nakamichi's automatic centring turntables (the rare Dragon CT or the very rare TX-1000).
These turntables incorporate a lower, driven metal plate upon which rests a massive glass platter with centre spindle. The turntable is computer controlled and uses a special sensor tonearm to measure the eccentricity, whereupon a small plunger comes out of a housing next to the platter and gently nudges the glass top-platter until the record turns about the exact centre of the groove spiral.
In Stereo Lab, this centring process is effected in digital signal processing.
The smallest detectable pitch variation for human beings occurs around 500Hz and is measured to be about 1Hz difference at 500Hz. That's to say, a change of 0.2%. Pitch perception deteriorates above and below this frequency¹. So a speed variation (a "wow") of less than ±0.1% represents a performance which is irreproachable. Indeed this is a figure which the best quality record decks regularly achieve². A figure of ±0.2% peak or 0.4% peak-to-peak variation is taken as the lower bound in the Stereo Sauce WOW! correction algorithm. Experiments have shown this is the perceptible lower-bound of wow performance¹.
The RIAA dimensional specification for phonograph records is oddly silent on the tolerance of the position of the centre of the hole from the centre of the Archimedian spiral formed by the recording grooves. An earlier NAB standard required that ..... the disc center hole be concentric with the recorded groove spiral within 0.005 inches (0.127mm)³. But this is a broadcast standard for transcription discs, not for manufactured records. The modern standard is IEC 60098:1987 which says (Section D.12.2.), the distance of the centre of the centre hole from the centre of the groove spiral shall not exceed 0.0082 (0.2mm).7 But the origin of this figure is unclear so it's not obvious how long this figure applied for, or to what territories it applied prior to being integrated into the modern international standard.
When a record exhibits eccentricity, the information spiral is misplaced with respect to the turning centre of the record (the spindle-hole). Thus, the spiral-centre orbits the record-centre.
The simplest way to formalise this is to consider Kepler's 2nd law which prescribes the way the velocity V of an object orbiting a single centre varies around its orbit. In the case of an elliptical orbit, it states that an object's velocity V increases when its distance r decreases, and vice versa.
Kepler says, The rate at which the line to the centre ("radius vector") covers area does not change around the orbit. In other words, the swept area is equal in an equal period.
The law asserts that the ratio of velocities equals the inverse of the ratio of distances. Or,
V1 ⁄ V2 = r2 ⁄ r1
In this application, Kepler’s law conveniently gives us the ratio of peak maximum velocity at the Perihelion and the minimum "slow-point” at the Aphelion and thus gives us directly the peak-to-peak pitch variation.
Notice how, because the offset which respectively adds and subtracts from the value of r2 and r1, that wow due to eccentricity becomes worse the nearer the groove is to the centre of the disc. Also, that rotational speed (33, 45, 78 etc.) plays no part in this expression. Only the geometry affects the percentage speed variation.
The RIAA standard limits of inside and outside groove diameters are:
Plugging-in our IEC-allowed 0.0082" offset (0.2mm), and assuming a inside groove radius of 60.3mm (innermost groove of the record), we get,
(60.3 + 0.2) ⁄ (60.3 - 0.2) = 1.00666 or a 0.67% peak-to-peak speed variation.
Which demonstrates that the IEC standard tolerance is not an especially ambitious figure as this is already above the threshold of perception¹. The NAB standard is better as a allowable tolerance of 0.127mm results in a wow figure of 0.4% pk-pk which is right on the threshold of perception and well judged¹.
If all records were made even to the (not especially rigorous) IEC standard, it would be marvellous. But they're not. It's not uncommon to find examples of the centre-holes of manufactured discs offset by up to a millimetre from the spiral-groove centre8. And values greater then this are relatively common with older, shellac discs.
Substituting in the equation we can see that an centre-hole offset of 1mm would lead to an overall speed variation at the innermost groove of,
(60.3 + 1) ⁄ (60.3 - 1) = 1.034 or a 3.4% peak-to-peak speed variation, which is a totally unacceptable degree of distortion.
No correction is applied in Stereo Lab until we arrive at a spindle-hole offset which produces a frequency change just above the threshold of perception¹. A ¼ mm offset is the lower end of the range of the WOW! correction. Thereby, a disc manufactured at the limit tolerance allowed by the IEC may be corrected by Stereo Lab. The upper limit for WOW! correction is an arbitrary 1mm. Note 4
After all, if record manufacturers can't get this right, how does a record collector measure the degree of eccentricity?
It's actually very simple. Because in an eccentric record, the true centre of the recorded spiral orbits the spindle-centre, the cartridge swings or sways as it plays the eccentric grooves. (See the GIF at the top of this page.) The degree of sway or weave of the cartridge is equal to 2 × the offset. This measurement can be made at any point in the cartridge travel across the disc but it's most conveniently made at the outside edge of the disc as the first few turns are played 5.
Experience has shown that it is quite possible to make measurements of this swing using a simple ruler or set of vernier calipers (like those shown above) to an accuracy of ½mm, meaning that the offset may be easily judged to an accuracy of 0.25mm which is sufficient to correct the pitch variation to the limits of the algorithm.
Needle-drops of speed-varying material must be made at 96kHz or 192kHz sampling rate. The extra bandwidth above the audio information is useful is determining the phase and frequency of the pitch variation, and the finer "structure" of the dual-rate file also enables finer quantisation of the pitch correction6.
Prior to recording, the degree of "sway" or weave of the cartridge as it plays the outer few grooves of the record must be measured. The measurement of weave is programmed via a slider in the PHONO preferences dialogue which runs from ½ mm to 2mm in steps of ½ mm. After that, the processing is entirely automatic.
Here the correction signal derived in Stereo Lab is overlayed on a spectrogram of the original music
1. Sek, A., and Moore. B. C. J. (1995). Frequency discrimination as a function of frequency, measured in several ways. J. Acoust. Soc. Am., 97, 2479-2486.
Sek and Moore's study involved the presentation of two successive steady tones with slightly different frequencies. The subject was asked to judge whether the first or the second had the higher pitch. The order of the tones was varied randomly from trial to trial, and the minimum perceptible change of frequency was taken as that frequency separation between the tones at which the subject achieved a certain percentage of correct responses (75%). This measure is called the difference limen frequency (DLF) Sek and More found it to be 0.2% at 500Hz.
A second measure of threshold change-of-pitch perception invetigated by Sek and Moore was using tones which were frequency modulated (FM) at a low rate to determine the amount of modulation required for detection. This measure is called the frequency modulation detection limen (FMDL). Clearly the FMLD test is closer to the case of pitch perception due to the unsteady speed of a gramophone record. The study showed that FMLDs are always higher than DLFs at all frequencies.
So taking the low limit for DLF (0.2% pk-pk at 500Hz) maybe over-safe as the lower bound for the perceptibility of wow. This is confirmed in an old, but very good, paper by Hisao Sikai of NHK (Perceptibility of Wow and Flutter JAES, June 1970) who determined in extended experiments that the threshold for peception of wow on the most critical music programme reproduction (found to be solo piano music) is 0.14% RMS which is equivalent to ±0.2% peak or 0.4% peak-to-peak variation. So this figure is taken as the lower bound in the Stereo Sauce WOW! correction algorithm.
However, the DLF is worth knowing because it does give an indication of the acceptable quantisation of the correction process. Provided pitch discontinuities are restricted to 0.2% in either direction, the pitch change won't seem to "jump".
2. Turntable speed accuracy is measured using a test disc cut with a 3150Hz steady tone. DIN 45 465 is one such and has the great attribute of a locked outside groove which allows the disc to be carefully and accurately centred, thereby taking disc eccentricity out of the equation. With this done, it is possible to measure down to around 0.06% unweighted wow, sufficient to identify the performance of top quality turntables. The best direct-drives manage this level of performance. Most belt drives are worse with measured wow being about 0.12% pk = 0.24% pk-pk.
3. NAB AUDIO RECORDING AND REPRODUCING STANDARDS FOR DISC RECORDING AND REPRODUCING. Engineering Department, National Association of Broadcasters, 1964
4. It's worth putting this into a musical context. Although a speed (and therefore pitch) variation of ±1% is enough to leave you feeling pretty queasy as the music sways like a drunk, it's still only a fraction of a musical interval. A well-tempered semitone interval represents a 6% frequency change relative to its nearest neighbours.
5. In making the weave measurement, it's important not to take too much time and accidentally include the lateral movement of the cartridge due to the spiral groove in the overall weave figure. The technically correct place to make this measurement is with the stylus locked into the circular, "locked groove" at the end of the side. When tracing this perfectly circular groove, the lateral "weave" of the cartridge is solely due to the eccentricity of the spindle-hole in relation to the groove. The only disadvantage of this approach is the awkwardness in leaning over the playing surface to take the measurement and accidentally touching the disc surface or bumping the tonearm.
An ingenious solution which entirely sidesteps these difficulties and also greatly enhances the accuracy of the measurement is described by S.E. Grimm (https://xyplo.blogspot.com/2016/10/b-centring-records.html). By the simple means of attaching a small laser pen/pointer to the tonearm, the moving laser spot, due lateral movement of the tonearm, may be projected onto a nearby wall. Provided the distance of the tonearm pivot to the stylus is known and a multiple of this distance is arranged in the distance of the pivot to the wall, the movement of the spot on the wall may be measured as a multiple of the movement of the stylus thereby increasing the accuracy of the measurement.
6. New Algorithms for Wow and Flutter Detection and Compensation in Audio. Czyzewski A. et al. Paper given at AES 118th Convention, Barcelona, Spain, 2005 May 28–31. This paper has a good set of references to previous studies and methods.
7. IEC 60098:1987 Analogue audio disk records and reproducing equipment. Available at: https://webstore.iec.ch/publication/734
8. Novel Wow and Flutter Meter, Ockleshaw, R., Wireless World, December 1971. Ockleshaw referes to a letter in Hi-fi News Sept 1971
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