This train of thought is heading towards major surgery on my bass amplifier, which may not be appropriate. I am beginning to realize that it is really set up to look after a bass guitar, rather than an upright bass.
My Hartke HA7000 amp is very versatile head. It has so much headroom for most gigs, the single valve in the preamp sounds sweeter than the solid state option, the crossover offers great potential, and the graphic eq is a bonus... sometimes. Since I moved to upright bass I've started noticing the graphic equalizer more, because I'm trying to shape the fundamental end of my sound, only to find it appears to place more control above 1kHz than below; apparently strict octave intervals up to to 2kHz, then random but finer intervals.
After finding a schematic on the web, I started investigating inside.
Graphic scenes follow...
So there are two 5-band graphic eq chips fitted on the Hartke, the Mitsubishi M5227P, and from what I've been hearing from my amp over the past 10 years, they seem ok for the job, on bass guitar. Any product offering 5 bands of eq is likely to be enjoying the convenience of this type of chip, which helps keep the component count down.
Below shows the graphic panel, with its nominal band intervals, and below it is the chart of capacitors responsible for each band, and its "Q" value.
It would appear that the desired frequencies on the front panel are a little irregular, but to be fair, in a production environment there are inevitably other constraints on preferred capacitor values, which may well dictate a substitution or two, to avoid stocking reels of a new value which isn't used anywhere else in the range.
The data sheet gives the method for calculating frequency band and Q, which I plonked into Excel and dragged out into a matrix for E12 capacitor values, then chopped out the numbers which were out of the range.
When visualizing frequency range of audio, the bode plot is the standard graph used. The horizontal axis is logarithmic and segmented in decades, 10Hz, 100Hz, 1000Hz, etc. It should be familiar to DAW users recording at home, when adjusting eq, and is recognized everywhere. The graphic eq, however, is traditionally divided by octave, rather than by decade. In a full-blown 1/3 octave, 31 band graphic, there are three sliders per octave, though this can also be described as roughly 10 sliders per decade, which is tidy. Therefore, on a simpler eq:
1/2 octave intervals correspond to 6.67 bands per decade,
2/3 octave, 5 bands per decade, and
1 octave, 3.33 bands per decade, covering the audio range with fewer sliders.
Picking from E12 capacitor values, that's 12 nicely spaced values per decade, matching to any of the above specs will require some compromise, either on actual frequency, or component count. Working with fractions of an octave simply does not "fit" with twelfths of a decade. So instead, I can choose to base a design on:
slightly broader than 1/2 octave intervals, 6 bands per decade,
slightly broader than 2/3 octave intervals, 4 bands per decade, or
slightly broader than 1 octave intervals, 3 bands per decade.
The coloured cells are examples. Ticking every third cap from the top with every third cap down the left, I get a sequence such as 44.5, 80.1, 144.8, 249, 445, and 801Hz, (shaded blue), with Q keeping a very consistent 2.37 to 2.43. The logs (1.65, 1.90, 2.16, 2.40, 2.65, 2.90) suggest very even spacing of frequencies.
Watch this space for further developments....
I have often wondered why graphic equalizers are based on musical intervals at all. Perhaps the intervals should be as unrelated to the octave as possible, especially when applied to harmonically dependent string instruments. Or maybe there is scope for picking out odd harmonics, which always seem to get guitarists excited. Using the traditional multiplier of two:
f0 passes through 2f, 4f, 8f, 16f, 32f, 64f, 128f...
Using instead, a multiplier of three:
f0 passes through 3f, 9f, 27f, 81f, etc.,
and for finer intervals, use √3,
f0 passes through 1.73f, 3f, 5.2f, 9f, 15.6f, 27f, 46.7f, 81f, etc.