Wavelength loss is a combination of two effects. The first of these is scanning-loss which is due to the physical fact that a sharp chisel is used in recording and a rounded stylus is used in reproduction. The sharp chisel is capable of cutting "sharper corners" than the stylus can read and this results in high-frequency loss when the recorded wavelengths approach the dimension of the stylus as illustrated. The stylus acts as a physical low-pass filter.
Wavelength on a record is a function of both recorded frequency and groove radius, so scanning loss becomes more of a problem towards the centre of the record.
The second effect is sometimes called translation-loss and results from yield in the relatively soft plastic record material as the very hard diamond stylus passes over it. This too is wavelength sensitive and thus combines with scanning-loss to be more of a problem at the innermost grooves.
Both scanning-loss and translation-loss effects were investigated and mathematically modelled by Miller1 and this early work was confirmed as equally relevant to stereo records by a team at CBS ten years later2. The CBS version of Miller's model is given in full below.
It all looks pretty complicated, but the details obscure the general form of the wavelength loss mechanisms.
The first point to make is that the second (bracketed) term is irrelevant to wavelength loss. This term models the dynamics of the stylus-disc resonant system3.
This dynamic system operates in the same way at the outside edge of the record as it does on the inside groove. So, in considering wavelength loss, we can ignore the second term and assume it's unity at all frequencies. We can see this in the maths when we note that there is no term equivalent to wavelength (that's to say involving D and N) in the derivation of f0.
This leaves us with a much simpler looking expression,
H( f ) = 1 - ( f / fc ) 2
which describes a response like the parabolic path of a ball, thrown from a height and falling to earth at the point f = fc; known - for obvious reasons - as the cutoff frequency.
The all-important parameter is thus the value of fc. The more this value descends towards and into the audible frequency range, the more the wavelength loss at any particular frequency.
Insight into the physical parameters affecting fc comes from recasting the expression for this term so as to express rotation speed and recorded diameter in terms of wavelength (λ) and in mopping-up all the physical constants as k. Thus,
fc = k . λ . ( E / (R × F) )⅓
fc is thus directly proportional to recorded wavelength. As the diameter of the groove of an LP shrinks from 11.5" at the outermost edge to the 4.75" near the label, the velocity falls to 41% (4.75 ÷ 11.5) of its original value and so does fc.
fc is also affected by both stylus radius (R) and by tracking-force (F) to a a similar - but lesser - extent. Reduce either of these and the value of fc rises. But not in direct proportion due to the fractional (⅓) exponent. The change in fc is related to the cube-root of a change in these parameters.
(Remember, the modulus of elasticity of vinyl or E is a constant, so this doesn't change.)
This may be something of a shock: it isn't widely appreciated that tracking-force (usually, though technically incorrectly, called tracking weight) has the same degree of effect on high-frequency response as the dimension of the stylus. Halving the tracking weight will liberate the HF response from a cartridge every bit as effectively as halving the stylus radius.4 The graph is derived from this model and illustrates the loss at the outer and inner groove for an elliptical stylus (10µm inferior radius) at different tracking weights.
Of course, tracking force isn't usually available to us as a parameter to adjust frequency response as its value is optimised to ensure... well, tracking!
| This feature is due for release in Version 3.n of Stereo Lab |
The existence of Miller's mathematical model makes it possible for very accurate compensation for wavelength-loss to be applied to needle-drop recordings in Stereo Lab.
The critical amount - and form - of treble lift is determined by the difference in wavelength loss at the inner and outer edges of the disc. The algorithm applies this lift gradually - inching up the treble over the duration of a needle-drop. The terminal correction value is dependent on the stylus dimension slider in the Phono EQ tab of the Stereo Lab GUI. (We apply less EQ when the stylus is small - according to the Miller model). The slider allows settings for stylus radii from 2µm to 18µm in 2µm steps. Selection for wavelength-loss compensation is via the check box above the slider as illustrated.
The method assumes that you are recording a needle-drop of a full single-side of an LP. It shouldn't be applied to short files, or indeed to longer files as it will raise the treble incorrectly. For example, it should not be applied across a recording of both sides of an LP with the recorder held in pause as the record was flipped.
1. Stylus Groove Relations in Phonograph Records, Acoustics Research Laboratories Frank G. Miller, Harvard University (Office of Naval Research TM 20: March 1950)
2. Stereophonic frequency test record for automatic pickup testing A. Schwartz et al. CBS Laboratories, Stamford, Conn. IRE Transactions on Audio (Volume: 10, Issue: 4, July-August 1962)
3. Essentially, the effective-mass of the stylus, cantilever and generator assembly resonates (or bounces) on the record-material compliance. The damping of this dynamic system is encapsuled by the epsilon (ϵ) term which holds the balance between the first part of the denominator and which → 0 as f → f0 (and thus sends the overall expression to infinity at f0) and the second part which → 1 as f → f0 and thus causes the response to fall at high-frequencies.
4. The model is limited in that it is only considering spherical stylus forms: the dimensions of fine profile styli also change the area of contact between the stylus and groove. So this statement is a simplification. Nonetheless, it is valid for conic and elliptical styli.
Pspatial Audio Home page
For all support issues, go here.
For Pspatial Audio sales, email: sales@pspatialaudio.com
Apple Certified Developer. Stereo Lab, Aria 51, Aria 20, Head Space, Groove Sleuth, iLOOP and FRANCINSTIEN T-Sym are trademarks of Pspatial Audio. FRANCINSTIEN and Bride of FRANCINSTIEN (BoF) are trademarks of Phaedrus Audio. Macintosh and the Mac logo are trademarks of Apple Computer, Inc.