After the turntable was repaired in early August, I was at first not using the "rolled" extra added headshell mass I had been using last year (though the arm and headshell had damping hockey tape) and that was clearly wrong, then I added back in the rolled 6.1g mass I had been using last year--but then decided it was too much, so I replaced it with a "stacked" 4.9g added mass. Comparing all three I guesstimated that I needed to reduce that 4.9 mass to about 2.9g to increase the horizontal resonant frequency (as most easily measured by the Feickert Adjust records) up from 8 Hz to 9 Hz or so.
But yesterday I found it wasn't that simple. With the mass reduced by 2.2g from 4.9g added (therefore about 2.7g "added") the lateral resonance was still clearly loudest at 8 Hz, as if it had barely changed. (It's complicated because the lateral resonance is actually bimodal, with high and low resonant frequencies and a null in between them...the true center of the resonance. So with 4.9g added mass, both of the modes are centered around 8 Hz. With 2.7g added mass, the upper mode is just barely edging up to 9 Hz, but 8 Hz is still by far the loudest.)
Finally with about 3.2g removed from 4.9g and therefore 1.7g "added" headshell mass* I found the resonance was no longer clearly centered at 8 Hz, though it was still noticeable at 8 Hz. 9 Hz was barely different, and now the center of the resonance seemed to be around 10 Hz (often considered optimal) with a bit more at 11 Hz. Because of the bimodality it seemed that the resonance barely moved from 8 Hz until it nearly jumped to 10 Hz. And at 1.7g added mass the bimodality of the resonance is most clear on the Hifi News Test Record. There's a visible null at about 9.5 Hz and nodes at 11 and 8-9 Hz. This is about as low as I want the lateral resonance to go.
(*1.7g "added mass" is an educated guess. I first took off 2.2g from the 4.9g, and then took off another 2g and then added about half of it back in, losing track of the exact changes. The range of possible values is about 1.2g - 2.5g.)
Meanwhile the vertical resonance is higher. With no added mass, the vertical resonance is around 14 Hz or slightly higher (because of low frequency rolloff, the resonance peak is where the graph shows it beginning to trail off). With 1.7 g added mass it's lowered to about 13 Hz, a desirable improvement. With 4g added mass it's lowered to 12 Hz and with 6g to about 11. 6g or more added mass might be preferable with regards to the vertical resonance, but it makes the horizontal resonance go to 8 Hz and below and is therefore undesireable.
There's more horizontal mass because horizontally the base of the tonearm has to move on it's ball bearings. This is a lot more mass than the tonearm itself, but it's centrally located and doesn't increase the effective mass by a lot. But clearly by several grams, just looking at the present measurements.
This means the optimal tuning is going to be a compromise between making the horizontal resonance frequency high enough and the vertical resonance frequency low enough. Exactly as I have now done. And this also means accounting for the lower mode of the bimodal horizontal resonance. I feel that the lower mode should be somewhat above 8 Hz, and it's OK for the vertical resonance to be as high as 13 Hz.
Korf (previously linked) showed that the tonearm/cartridge resonance is not a simple spring/mass resonance because the stylus is actually suspended in a circular donut. That makes the resonances bimodal among other deviations from the simple model, and prone to seeming to change in non-linear jumps because of that bimodality. The only way to get it right is by actual measurement with test records.
It's also desirable to keep the added mass as low as possible to achieve the desired resonance frequencies, because more added mass loads the stylus on warps and warp wow.
So I think I've optimized it now, and it took less added mass than I was thinking it would need.
Antiskate compensation seemed to require 2.5g setting on the Feickert test record. With these settings the Feickert tracking test is clean until the very highest level where it seems to distort somewhat. When I first tried this record a few weeks ago, I was getting some distortion on the preceding two tracks.
In the following graphs made using the Hifi News Test Record 2, the horizontal resonance is on the left, and the vertical resonance is on the right. Each has to be played separately then they are combined in a single track with editing (which is not exactly perfect so things may not line up perfectly among the different mass conditions). The top pair is 4.9g added mass, the middle is 1.7g added mass (the current adjustment) and the bottom is 0g added mass.
In the top set of 6 graphs the marker is placed at 9 Hz in the lateral resonance test. Because of rolloff that is occurring below 20Hz at >6dB/octave, the point where the resonance seems to end on the downside is actually the center of the resonance. With that in mind, you can see in the top pair that the horizontal resonance is clearly at 8 Hz, about 1 Hz lower than the 9 Hz marker. This is more clear on the Feickert test record where it seems like nearly all of the resonance is at 8 Hz with hardly any at 9 Hz or 10 Hz.
In the middle pair, with about 1.7 g added mass, the horizontal resonance has moved upwards and now it looks like the resonance ends pretty much at 9 Hz though it is still fading away down to 8 Hz. There is a null around 9.5 Hz, this is the true center of the resonance, and a upper mode that reaches up to 11 Hz. I am calling this "optimal."
In the bottom pair, with 0g added headshell mass, the horizontal resonance as moved upwards so it's thickest portion is now centered around 11 Hz and reaches up to 13 Hz. This is high enough that it begins interfering with bass response and is undesirable. The horizontal resonance seems larger and lumpier as well. It still doesn't go away completely at 8 Hz despite now being centered at 11 Hz.
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| Marker at 9 Hz in Horizontal sweep for 4.9, 1.7, and 0g added mass |
The next set of 6 graphs has the marker at 12 Hz in the vertical Resonance. With 4.9g added mass on top, it's clear the peak resonance is about 11 Hz. With 1.7g added mass in the middle the peak resonance is now around 12-13 Hz, higher but still acceptable. With 0g added mass, the peak is 14-15 Hz, clearly too high.
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| Marker at 12 Hz in Vertical Resonance for 4.9g, 1.7g, and 0g added mass |
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