There's a new tool on the site. Pick your cartridge from a list of 66, or type two numbers off its spec sheet, and it tells you where the cartridge resonates on the Clear Wave, or on any arm whose effective mass you know. It shows the working as well as the answer. You'll find it at boolaudio.com/tools/resonance, and there's a permanent link in the footer under Tools.
What the number means
A cartridge suspension is the spring. The arm and cartridge riding on it are the mass. Put a mass on a spring and it resonates at one frequency, whether you want it to or not. The only choice you get is where.
You want that frequency between 8 and 12 Hz. Record warps and footfalls put their energy in below that band; music starts above it, at 20 Hz. Land inside the band and neither can excite the resonance. Fall below 8 Hz and a warped record or a heavy footstep sets the arm bouncing until the stylus loses its grip on the groove. Go above 12 Hz and the resonance sits close enough to the audible range to colour the deepest bass.
The frequency comes from three numbers: the arm's effective mass, the cartridge's weight, and the cartridge's compliance, which is how soft its suspension is. The calculator does the arithmetic and plots the result on a bar running 4 to 16 Hz, so you can see not only whether the pairing lands in the band but how much margin it has.
Why you can't take the spec sheet at face value
Here's the part that catches people out, and the reason we built a database instead of a bare formula.
Compliance figures are published three different ways. Some makers measure the suspension moving at 10 Hz, which is what the resonance formula wants. Japanese makers usually measure at 100 Hz, which gives a number about 40 percent smaller for the same suspension. Others publish a static figure, measured with the suspension held still, which reads about twice the 10 Hz value.
The units are identical in all three cases. Nothing on most spec sheets tells you which one you're holding.
The database holds two good examples. Goldring's pages quote 24 cu for the 1042; their own specification labels it a static figure, so the 10 Hz value is nearer 12. Denon quote 5 cu for the DL-103, measured at 100 Hz; at 10 Hz it's nearer 8.5. Feed either raw number into a calculator that assumes 10 Hz and the frequency comes out about 30 percent wrong, in opposite directions: the Goldring reads low, the Denon reads high.
Our database records which standard each maker uses and converts to the 10 Hz basis the formula needs. Any result that went through a conversion is marked as an estimate, so you can tell a maker's own figure from a rule of thumb.
Where the figures come from
Each of the 66 cartridges carries the source of its figures: the manufacturer's product page, their specification PDF, or their official distributor where the maker's own site omits the number. Pick a cartridge and the result names its source, with a link, so you can check the figures against the maker's page yourself. Where the only source we could find was a forum thread or a retailer listing, the cartridge stayed out.
Two absences are deliberate. Linn publish no compliance figure for their current cartridges, and neither do Rega. We looked hard, and the honest position is to leave them out rather than guess. If you have a figure for one from elsewhere, the manual fields take it.
One caution that applies to every row: published compliance is optimistic more often than not, makers measure differently even within a standard, and suspensions soften as they age. The calculator tells you where a pairing should sit; a test record with a resonance sweep tells you where it actually does.
Two pairings, worked
The Denon DL-103 weighs 8.5 g with a converted compliance around 8.5 cu. On the Clear Wave that lands at 12.2 Hz, the top edge of the band. The DL-103 has been in production since 1962, the received wisdom that it wants a heavy arm is nearly as old, and the arithmetic agrees with it.
Ortofon's Quintet Blue, 9 g and 15 cu measured at 10 Hz, lands at 9.1 Hz, the middle of the band with margin on both sides.
Those links are live results, not screenshots. Every calculation has its own address, so if a pairing question comes up in a forum thread you can answer it with a link to the working.
The practical details
The calculator works with JavaScript switched off; with it on, the result updates as you type. There's no signup. If you want to see where the Clear Wave's own 11 grams comes from, weighed part by part, that's a post of its own coming shortly.