Originally posted by Brian W.
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It's long been known that a less electrically conductive pole magnet will give a higher Q factor, meaning more treble at peak resonance, and more permeability will give you more inductance, meaning a lower peak frequency, meaning less treble, and more recently established that the stronger magnetic field does in fact result in more treble.
The question then is, what effect will more cobalt have on those different parameters? It's complicated by the fact that the final properties of the AlNiCo have partly to do with the composition, but also how it's annealed or otherwise made. Cobalt is more conductive than iron, that should mean a lower Q factor, less treble at resonance. But this is a small difference you'd probably never hear, because this change in Q factor can be seen in bode plot tests, and while it's there, it's a very small difference.
Cobalt is less permeable than iron, so the inductance will drop by some amount, that will increase the treble. In the case of a Fender style single coil, the permeability of the pole piece can swing the over inductance of the pickup enough to move the resonant peak quite a bit. The degree of change will depend on how much cobalt is added. For reference, a few years ago I measured the inductance of a Strat pickup with different grades of AlNiCo:
Steel - 3.975H
AlNiCo 2 - 2.203H (13 parts cobalt, says wikipedia)
AlNiCo 3 - 2.244H (no cobalt)
AlNiCo 4 - 2.184H
AlNiCo 5 - 1.882H (24 parts cobalt, says wikipedia)
Air - 1.493H
And I didn't test AlNiCo 8, but wikipedia says it's 35 parts cobalt, it's especially strong (and brittle) . From these data points, you can get an idea for how permeability / inductance drops, and strength rises in proportion to cobalt.
Cobalt apparently makes the magnetic field stronger, or the "residual magnetic flux", and that increases the treble in how it both causes higher harmonics to be created due to string pull, and received by the pickup when the guitar string is magnetically saturated.
Subjectively when guitarists will say that pickups with AlNiCo 5 sound brighter than AlNiCo 2, even across a variety of pickups with difference inductances. Raising the pickup closer to the strings also creates a stronger magnetic coupling between the pickup and the strings, and is also said to bring out more treble, so I think the evidence is there to say that the increased treble from stronger magnetism is audible by itself.
In summary, cobalt increases the treble for three different reasons, with how it effects the magnetic strength and the inductance being the most prominent.
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