Wouter's page : matching your cartridge and tone arm

From www.datateam.hu/pages/sme/:
The effective mass of an arm and cartridge resists motion least at low frequencies but increasingly as frequency rises. It is this resisting force which makes the operation of a cartridge possible. At subsonic frequencies the armature and stator move as one allowing the slow movements needed to negotiate the record surface without generating a signal. At audio frequencies however the increased resisting force causes the armature to move relative to the stator and a signal is produced. The transition point between these two conditions is important for a clean low frequency response and is established by the compliance of the cartridge and the total effective mass of the arm and cartridge body.

If this doesn't make much sense to you, the rule of thumb, as given by JohnAFR in this rec.audio.high-end posting (Thanks Google), is to keep the resonance between 8 and 13 Hz. Also, Galen Carol Audio says "The goal in matching a specific cartridge and arm is to achieve a resonance in the 10 to 14Hz range. Some feel that limiting this range even further, to 9 to 11hZ, is best."

So that gives us a target.

From the Sound digest (hosted at lists.io.com, speak to majordomo@lists.io.com) volume 2, Number 287 of 1999-09-27:
Resonant freq = 1/(2*pi*sqrt(M*C))
Where M is the sum of the effective mass of the arm and the cartridge weight, and
C is the (dynamic) compliance of the cartridge (at 100Hz)

From a usenet article in r.a.he, citing a review of the SME 3009 III This has resulted in an effective mass, for the tone arm alone, of about 5 grams. When a cartridge weighing about 6.5 grams is mounted in the tone arm, nearly all of its mass is seen by the stylus, so the effective mass would be about 11.5 grams. This is still an extremely low total effective mass. Note that the SME 3009 Series II has an effective mass of 12.5 grams (9.5 grams for the non-detachable headshell).

Now for a few examples

Ortofon Super OM10 (MM)

Compliance 25um/mN, cartridge weight 5g.

Ortofon 310 Universal(MM)

Compliance 20um/mN, cartridge weight 5g.

Ortofon SPU (MC)

The Ortofon SPU is regarded as "stiff" at 8um/mN compliance, weight is around 30g.

Ortofon MC10S / MC10 Super (MC)

Compliance 14um/mN, cartridge weight 7g.

Ortofon MC25FL (MC)

Compliance 16um/mN, cartridge weight 10,5g.

From this, we can see that moving coil cartridges have a lower compliance than moving magnet cartriges.

So, assuming an arm effective mass of 5g (SME 3009 Series III),
fo = 1/(2*pi*sqrt((5+[5 | 5 | 7 | 10.5])*[25 | 20 | 14 | 16]e-6))
= 10.1 Hz (OM10) / 11.3 Hz (310) / 12.3 Hz (MC10S) / 10.1 Hz (MC25)

Assuming an arm effective mass of 12.5g (SME 3009 Series II),
fo = 1/(2*pi*sqrt((12,5+[5 | 5 | 7 | 10.5])*[25 | 20 | 14 | 16]e-6)
= 7.6 Hz (OM10) / 8.5 Hz (310) / 9.6Hz (MC10) / 8.3 Hz (MC25)

The lower compliance raises the resonant frequency (remember to compare cartridges of the same mass, i.e. OM10 vs 310), alternatively, higher compliance lowers the resonant frequency.

What is important here is that the resonant frequency should be above 5-8 Hz, since this is the frequency generated by record warp, and below 15 Hz, or whatever the lowest frequency is that you expect to find on the record.

From this it is clear that the MC10 is a very good match for the SME 3009 Series II, while the OM10 isn't.

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