In the RCA datasheet 12ax7 filament voltage is claimed must be within + or - 20%
(for 12.6v = 10.08v till 15.12v / for 6.3v = 5.04v till 7.56)
http://www.tubebooks.org/tubedata/HB-3/Receiving-Type_Industrial_Tubes/6681_12AX7.PDFin the GE datasheet 6au6 filament voltage is claimed must be within + or - 10%
(for 6.3v = 5.67v till 6.93v)
http://www.mif.pg.gda.pl/homepages/frank/sheets/093/6/6AU6A.pdfthe minimum voltage requirement are 5.04v for the 12ax7 and 5.67v for the 6au6, total minimum voltage required 10.71v
so as you have a 12v heater supply you are in the ballpark
Quote from Merlin's web page
Series and parallel: Valves which are normally designed to be run in parallel can be run in series provided you ensure their current demands are met correctly, althopugh series heater chains are not recommeded for audio. For example, an EL84 and ECC83 could be run in series from a 12V supply. The EL84 is rated at 0.76A while the ECC83 is rated at 0.3A, therefore a resistor must be placed in parallel with the ECC83 to pass the additional current without damaging the valve. We want to pass 0.76 - 0.3 = 0.43A through the resistor, and we want the voltage across the resistor to be 6V. Use Ohm's law to calculate its value:
6 / 0.43 = 14 ohms.

The power dissipated will be:
(0.43 * 0.43) * 14 = 2.6W
So we would probably use a 15R, 5W resistor.
All sorts of heater chain combinations can be created in this way.
Series AC heater chains will not benifit from a grounded centre tap [see below], but will benifit from an elevated centre tap, to reduce noise.(note this ! - K add on)
Because the heaters are in series it doesn't matter in which order the valves are wired. However, if one end of the heater chain is to be grounded, then the most sensitive preamp valves should be closest to the grounded end of the chain.
Since the different heaters will often have different warm up times that could put stress on the other valves, a thermistor can be placed in series with the chain, or a resistor switched in and out by a standby switch
as your tubes are both indicated to have a consumption of 0.3A you must do some test and try to find the real current each tube draw, than you can apply the formula to calculate the value of the "balancing" resistor
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in your schematic your PS is draw as it has a 15v winding, if you want to increase the voltage of the heater may be you can try to use that winding with an in series resistor
K