Audio concepts and terms explained.
by Michael Riggs
Cartridge and Arm: Making the Best Match
FOR YEARS WE'VE BEEN SAYING that a proper match between cartridge and tonearm is vital to getting good sound from any system, regardless of price. The arm/cartridge resonance frequency should be high enough that the system will not overreact to record warps, yet not so high as to exaggerate bass response. At the same time, we've been aware that it is far easier to say that this is desirable than to explain how it is to be accomplished. Several variables are involved, and the information necessary for balancing them is seldom all available in usable form.
The resonance data in our cartridge, tonearm, and turntable reports can serve as a guide, if used cautiously, but they are strictly valid only for the reference components that DSL uses for these measurements. For cartridges, this means an SME 3009 Series II Improved tonearm; for tonearms, it is a Shure V-15 Type III cartridge. Although both units are fairly typical, they are not truly representative of every model in their respective component categories.
We are therefore delighted to announce that Diversified Science Laboratories has developed a measurement technique that enables us for the first time to report reliable figures for effective tonearm mass and cartridge compliance. These, together with the nomograph shown here and the cartridge-weight and resonance data we have been publishing all along, will enable you to determine unequivocally the compatibility of any given cartridge we have tested with any given turntable or tonearm we have tested. In the case of cartridges, we will be able to tell you right out the effective tonearm mass that will yield an optimum resonance frequency (10 Hz) and the range of masses that will yield what we consider an acceptable resonance frequency (between 8 and 12 Hz).
The relationship between resonance frequency, cartridge compliance, and tonearm mass is defined by the formula frequency, C is the cartridge's low-frequency dynamic compliance at its recommended tracking force, and M is the total effective mass of the arm/cartridge system. M is equal to the effective mass of the tonearm alone (mT) plus the weight of the pickup (mp), and 2 π is approximately equal to 6.28, so the formula becomes…
f =
Simple algebraic manipulation gives the formulas for dynamic compliance and effective tonearm mass:
C = 1/(m.. + 1 mT = 39.5f^2c mP)
and
mT=1/39.5f^2, respectively.
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By means of this nomograph, you can quickly and easily deter mine the compatibility of any cartridge and tonearm we have tested. The key parameters are: dynamic compliance of the cartridge (vertical axis): total effective mass (horizontal axis): and the arm/cartridge resonance frequency (diagonal lines).
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Although these equations can serve as an aid to understanding, you won't actually have to use them. We've already done the math for you and put the results into the nomograph reproduced here. Cartridge compliance is represented by the vertical axis, total effective mass (tonearm effective mass plus cartridge weight) by the horizontal axis, and resonance frequency by the diagonal lines. If you know any two of these three quantities, you can quickly and easily read off the third value from the nomograph.
Ultimately, you are always going to want to know the vertical resonance frequency for whatever arm/cartridge combi nation you are contemplating. In the simplest case, you can begin by looking up the weight and dynamic compliance shown in the cartridge report and the effective tonearm mass listed in the turntable or tonearm report. Add the weight of the cartridge to the effective mass of the tonearm to get the total effective mass. Then find the point on the graph where the vertical line for the total effective mass intersects the horizontal line for the cartridge's dynamic compliance.
Ideally, this point would fall on the 10-Hz line, but so long as it is in the white band between the 8- and 12-Hz diagonals, the arm and cartridge should work well together. (In fact, it is usually okay to let the resonance rise as high as 15 Hz.)
When necessary, you can also use the nomograph to back-figure compliances and effective masses for cartridges and tonearms tested before we began reporting these quantities directly. For cartridges, look up the vertical resonance frequency and cartridge weight listed in the test report. Add 15 grams (the effective mass of the SME tonearm used for the resonance measurement) to the cartridge weight to get the total effective mass. Then find the intersection of the diagonal line representing the measured resonance frequency with the vertical line representing the total effective mass calculated in the previous step. Now you can read off the cartridge's vertical dynamic compliance from the horizontal line passing through the point of intersection.
To determine an unknown effective tonearm mass, look up the vertical resonance frequency listed in the test report for the tonearm or turntable. Find the intersection of the diagonal line for that frequency with the horizontal line representing a vertical dynamic compliance of 22.5 x 10^-6 cm/dyne (for the Shure V-I5 Type III cartridge used in the resonance measurement). Reading down the vertical line on which the point of intersection falls will give you the total effective mass of the arm with the V-15 Type III mounted in it.
Then subtract the Shure's 6.3-gram weight to get the tonearm's effective mass.
This simple little system should put you well down the road to phonographic bliss. One cautionary note, however: Be cause of differences in measurement technique, manufacturers' specifications for compliance and effective mass often differ from our findings and may yield inconsistent results if used with this graph. So stick with the data in our test reports.
- HF
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