I’ve been doing some empirical work to figure out what the FRQ parameter actually means in Hz for the Equalizer’s shelf filters. Both follow an approximately exponential frequency mapping — about 10 parameter units per octave across most of the range, with some nonlinearity at the extremes.
A couple of things worth noting: the Q parameter has no effect on shelf filter response. And the default value of 63 corresponds to ~80 Hz on the high shelf and ~1200 Hz on the low shelf.
Lookup tables below, computed from fits to the measured data. Use them as a starting point — ears still win. Full methodology and plots in the attached writeup.
High shelf
| Hz (approx) |
FRQ |
| 20 |
43 |
| 25 |
46 |
| 31.5 |
49 |
| 40 |
52 |
| 50 |
55 |
| 63 |
58 |
| 80 |
62 |
| 100 |
66 |
| 125 |
70 |
| 160 |
74 |
| 200 |
78 |
| 250 |
82 |
| 315 |
86 |
| 400 |
89 |
| 500 |
93 |
| 630 |
96 |
| 800 |
100 |
| 1k |
102 |
| 1.25k |
105 |
| 1.6k |
108 |
| 2k |
110 |
| 2.5k |
113 |
| 3.15k |
115 |
| 4k |
117 |
| 5k |
119 |
| 6.3k |
121 |
| 8k |
123 |
| 10k |
125 |
| 12.5k |
126 |
Values above 5k are less reliable.
Low shelf
| Hz (approx) |
FRQ |
| 25 |
4 |
| 31.5 |
8 |
| 40 |
12 |
| 50 |
15 |
| 63 |
19 |
| 80 |
23 |
| 100 |
26 |
| 125 |
29 |
| 160 |
33 |
| 200 |
36 |
| 250 |
40 |
| 315 |
43 |
| 400 |
46 |
| 500 |
50 |
| 630 |
53 |
| 800 |
57 |
| 1k |
60 |
| 1.25k |
63 |
| 1.6k |
67 |
| 2k |
71 |
| 2.5k |
74 |
| 3.15k |
78 |
| 4k |
82 |
| 5k |
86 |
| 6.3k |
90 |
| 8k |
95 |
| 10k |
99 |
| 12.5k |
104 |
| 16k |
111 |
| 20k |
117 |
OT_EQ_Frequency_Mapping.docx (66.9 KB)
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Following up on the shelf filter measurements, I’ve done the same characterization for the parametric mid EQ.
FRQ mapping
Clean exponential (linear in log space) across the full range:
Hz = 2^(2.3866 + 0.0933 × FRQ)
R² = 0.9996. About 10.7 FRQ units per octave throughout. The default FRQ = 63 lands at ~310 Hz, and the model predicts FRQ = 127 reaches ~19,300 Hz — consistent with the range being designed to top out at 20 kHz. Simpler than the shelf filters, which needed cubic fits.
Q mapping
Also a clean exponential:
Q = 2.0 × 13.0^(param / 127)
Q = 2.0 at param 0, Q = 7.3 at the default (param 63), Q = 26.0 at param 127. Verified at five points with residuals under 0.1 throughout.
Lookup table
| Hz |
FRQ |
Hz (predicted) |
| 20 |
21 |
20.3 |
| 25 |
24 |
24.7 |
| 31.5 |
28 |
32.0 |
| 40 |
31 |
38.8 |
| 50 |
35 |
50.3 |
| 63 |
38 |
61.0 |
| 80 |
42 |
79.0 |
| 100 |
46 |
102.3 |
| 125 |
49 |
124.2 |
| 160 |
53 |
160.9 |
| 200 |
56 |
195.3 |
| 250 |
60 |
253.0 |
| 315 |
63 |
307.1 |
| 400 |
67 |
397.7 |
| 500 |
71 |
515.1 |
| 630 |
74 |
625.4 |
| 800 |
78 |
809.9 |
| 1000 |
81 |
983.3 |
| 1250 |
85 |
1273.5 |
| 1600 |
89 |
1649.3 |
| 2000 |
92 |
2002.3 |
| 2500 |
95 |
2430.8 |
| 3150 |
99 |
3148.2 |
| 4000 |
103 |
4077.3 |
| 5000 |
106 |
4949.9 |
| 6300 |
110 |
6410.7 |
| 8000 |
113 |
7782.8 |
| 10000 |
117 |
10079.6 |
| 12500 |
120 |
12237.0 |
| 20000 |
127 |
19291.8 |
Full writeup with methods and figure attached.
OT_Mid_EQ_Mapping.docx (71.1 KB)
7 Likes
Thanks @Bryan_T !
Would be great if you could do it for Filter FX and with tuning and fine tuning like for Lofi AMF. The idea would be to use it as a tuned band pass resonator…
How do you reverse engineered formulas ?
I’ll tackle the Filter next. These examples were to work out a method without adding the additional fine-tuning parameter. Now that I have a pretty quick method, the Filter isn’t too daunting. As long as Logic has a filter with similar behavior.
The formulas are a regression model that I have Claude run. Basically, I had my fifteen data points that phase cancelled really well, plotted the relationship, noted it was basically linear if I transformed the data (not a surprise for an EQ), then asked Claude to run the regression.
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Famous last words! The approach I used for the Equalizer does not nearly as well for the Filter. I’ve got some other ideas to explore.
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