I've not found anything that exactly matches a 12AY7, even the 12AV7.
Amplification Factor (Mu) is only one of the 3 main triode characteristics; the other two are Transconductance (Gm; plate current change per unit of grid voltage change) and internal Plate Resistance (rp).
You could relate the three as:
Mu = Gm * rp, not unlike
Voltage = Current * Resistance
To truly evaluate the tubes' characteristics directly, we need to check them at the same operating point (plate voltage, plate current, etc) which sometimes doesn't happen with the conditions listed on the data sheets.
From a
12AY7 data sheet,
Mu = 44
Gm = 1.75mA/v (= 1750 µmhos)
rp = 25kΩ
From a
12AV7 data sheet,
Mu = 41
Gm = 8.5mA/v (= 8500 µmhos)
rp = 4.8kΩ
You'll see Mu is similar, but Gm went way up and internal plate resistance went way down. To be fair, the 12AV7 data sheet condition was at an operating point with silly-high plate current which skews Gm up and rp down.
But look at the plate curves for each tube, specifically the -2v gridline. If you follow the 150v plate voltage line straight up to its intersection with the -2v gridline, the 12AY7's plate current is 2.5mA at that operating point while the 12AV7's is 10mA.
So it looks like the 12AV7 will have ~1/5th the internal plate resistance and pass about 5 times the current. This ratio will be different at different operating points, but the 12AV7 will always be a higher-current, lower-rp tube than the 12AY7. Without doing a proper design-check, I'd expect the 12AV7 to exhibit slightly more gain when plugged in the same socket, albeit with the possibility of being biased to a poor operating point for the tube.
Maybe it's worth asking why you need a 12AY7?
If you are replicating an old design to the last detail, or using the tube in an old amp, maybe you really need a 12AY7. Seems like the 12AY7 (or 6072) is your only viable option.
If you wanted a 12AY7 because it is to be used in a new design (maybe the amp in
your other thread?), you may want to ask yourself if you simply need the approximate gain the 12AY7 would provide. It would be a lot easier to take the cheap 12AT7 or the omnipresent 12AX7 and knock their gain down to what a 12AY7 would give.
The tradeoff is generally that the lower-Mu tubes (12AU7, 12AY7) accept larger input signals before overload than the higher-Mu tubes (12AT7, 12AX7), along with having lower gain. Their internal plate resistance can also dictate appropriate circuit resistances, with low rp tubes leading to lower output impedance. That may matter in some applications.