The geometric considerations with regard to vinyl disk recording and reproduction are plenty and can get quite complex. In fact, the entire first section of the Disk Recording Anthology Volume 1: Groove Geometry and the Recording Process published by the Audio Engineering Society is dedicated to groove geometry, with this topic attracting the interest of both engineers professionally involved in this field, and academics approaching the subject from a theoretical perspective.
One of the most widely discussed and even more widely misunderstood topics is vertical tracking angle (VTA) and its relationship to the stylus rake angle (SRA). Misunderstood equally as much by home listeners and mastering engineers, a lot has been said and published about VTA, much less about SRA, and close to nothing about how these two are related.
The origins of the stylus rake angle have absolutely nothing to do with audio. The rake angle is one of the geometric parameters of a cutting tool, as used in mechanical machining operations.
Since all grooved media (disk records and phonograph cylinders) are recorded by means of a mechanical machining operation, on a specialized machine tool called a disk recording lathe (see Copper Issue 95 for a description of the evolution of the disk recording lathe from the screw-cutting lathe), a specially designed miniature cutting tool is required for the removal of material necessary to form a groove. This cutting tool is called a “cutting stylus” or a “recording stylus.”
C. F. Wiebusch, L. Vieth, and G. R. Yenzer, “Vibratory System,” United States Patent Office (1939 Jun.), USP 2,161,489. https://patents.google.com/patent/US2161489
While the ASA (American Standards Association, now ANSI, the American National Standards Institute) standards commonly used in other sectors of industry were never really used to describe disk recording styli, the same geometric parameter descriptions and nomenclature could easily be applied there too. Mechanical sound recording was the earliest form of micromachining, done at such a small scale that it took several decades for other sectors to even attempt any form of micro-machining approaching such minute dimensions.
The rake angle is, therefore, the angle by which the cutting face of a tool is offset from normal to the workpiece (the blank record in our case).
If the tool face is set exactly normal to the workpiece, it is said to have a rake angle of 0 degrees. This applies to all machining operations, including all mechanical forms of sound recording. If the tool appears to be digging into the workpiece, it is said to have a positive rake angle, written as just the number of degrees off from normal, e.g. 5 degrees rake angle.
0° rake angle.
Positive rake angle.
If the tool appears to be stroking the workpiece, it is said to have a negative rake angle, e.g. -5 degrees.
The rake angle can be set in two ways: either we use a cutting tool with a different geometry formed into it, and hold it in the same manner, or we lean the cutting tool to the desired angle.
Whether we’re turning a piece of steel on a metalworking lathe or cutting a record, the principle is exactly the same.
Depending on the workpiece material, the cutting speed, the cutting depth, the other aspects of tool geometry, the material the tool is made of and the required surface finish, a different value of rake angle will be required.
When machining metal, which is not usually meant for subsequent reproduction on a turntable, the most suitable value of rake angle can be selected for the job. As long as the material removal rate is within the economical range and the surface finish is acceptable, it is fine.
Records, on the other hand, need to be played back. But, the grooves still need to be machined in a manner which can achieve the required surface finish in a single pass. You cannot go back there and polish out the imperfections, as done with metal parts, which are often made in multiple passes of different tools, at different speeds.
Fortunately, there is not much diversity in the workpiece materials used in cutting records. Unfortunately, anything more than just one material leaves us with the need for more than one value of rake angle. To further complicate matters, groove depth can vary over a wide range, even within one side of one record. Even though records spin at a constant rpm (angular velocity), the linear velocity (the speed with which the surface of the record moves past the stylus) varies with diameter. Not only that, but there are more than one constant RPM values at which a record may spin, typically 33-1/3, 45 or 78 RPM. The cutting speed is essentially the linear velocity, constantly varying throughout the side – not the RPM. Things can be further complicated by the use of different cutting tool materials, which can be made from steel, tungsten, sapphire, ruby or diamond.
Nevertheless, due to the difficulty of producing complex geometries on such a small cutting tool, all disk recording styli are made with a flat cutting face. As such, the only way to set the rake angle at the time of cutting a record is to tilt the cutter head, or to design this into the head by having the cutting stylus held at an angle.
It may be tempting to think that if all recording styli share the same basic geometry, then surely all cutter head designers will have made sure that the styli are all mounted to the head at the same angle and that all cutter heads would be set for the same tilt, but the truth is far from this.
Depending on when a record was cut, stylus rake angles ranging from -10 degrees to +20 degrees can be encountered. In the stereophonic era, many records were cut with a stylus rake of 0 to +1 degrees, but not all!
If we were only to consider silent grooves, then this would not matter much. But as the stylus-groove interface during playback is very three-dimensional, and especially so when using line contact reproducing styli, accurate reproduction can only be achieved if the stylus rake angle of your phono cartridge is the same value as the rake angle of the disk recording stylus at the time the record was cut.
Two similar cutting tools, one with a flat face and one with an inclined cutting face to give it a more aggressive rake angle.
Sounds sort of similar to what you’ve been told about VTA, doesn’t it? Well, similar idea, but very different effect, which produces a different and perhaps more severe type of distortion than VTA errors of the same magnitude.
The SRA of your playback cartridge depends on how the jewel stylus was lapped and at what angle it was glued to the cantilever. Spherical styli do not have an easily-defined SRA, but line contact types, including elliptical styli, most certainly do. In theory, you can change the SRA value by finding a way to tilt the entire phono cartridge. In practice, however, this will simultaneously change the VTA of the cartridge.
The relationship between SRA and VTA is therefore fixed by the manufacturer of the cartridge. If a user tweaks one of these parameters, it will also affect the other.
Regardless of the actual value of the stylus rake angle when cutting a record, when a cutter head is recording (cutting) vertical information on the groove, it does so in a certain “plane of modulation.” Imagine a cutter head pushing and pulling the cutting stylus straight in and out of the record exactly normal to its surface. This would be exactly on the vertical plane. But if the head is pushing the cutting stylus at any other angle, or in an arc, as is often the case, then the vertical plane of modulation, or in other words, the vertical modulation angle, is offset from the true vertical. This is measured in degrees. Any information recorded in a certain plane of modulation can only be extracted accurately if the tracking angle of the playback setup is equal to the angle of the plane of modulation. The tracking angle must be equal to the modulation angle. So, the vertical tracking angle must be equal to the vertical modulation angle, as this was set at the time of cutting the record.
Inclined plane of modulation.
Vertical plane of modulation.
The vertical modulation angle can only be adjusted at the time of cutting the record by tilting the entire cutter head. This, however, will also change the stylus rake angle, since the recording stylus will be tilted along with the cutter head, changing the angle of its cutting face to the surface of the record. Once again, we see that the relationship between the vertical modulation angle and the stylus rake angle is fixed by the manufacturer of the cutter head. One cannot be changed without changing the other. Just as in the playback side.
In Part Two we will examine the playback side of things in greater detail and relate the significance of VTA and SRA with respect to recording and playback.
A Transco disk recording stylus package. Apollo-Transco was one of the last two remaining lacquer disk and styli manufacturers in the world, until their facilities were completely destroyed in a catastrophic fire earlier in 2020.
Header image of Clearaudio Stradivari phono cartridge courtesy of Wikimedia Commons/Dieter Kamer.
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