As reference I have chosen to have maximum flexibility, therefore I have chosen LM431 which is easy obtainable. Virtual any reference will fit as long as the voltage is above the common mode limit for the used opamp. 2.5-7 V will work and in some cases also 1.2 V. At the moment I have tested 1.55 V from a red LED with perfect results. I have used LM431 and this very cheap reference is rather, no, very good, although not as nearly as good as LM329 but much, much better than a regular zener diode (which also can used). R3 is carefully selected and may be changed if especially lower voltages are to be chosen.
The reference voltage is filtered by R7, C7 and C8 in order to remove the noise and as a side effect you will get a smooth startup. R7 should optimally be R8 and R9 in parallel. You can either choose 499 ohms or simply solder two 1 kohms on top of each other. If you have matched input impedance's you will minimize the input offset and also the drift with temperature (not very important in audio applications). It may also be good when it comes to common mode rejection. Since the whole design is placed on a groundplane I'll gather that high frequency problems are not so big so you must take this into account. R10 and C9 are parts for "just in case", to tailoring the frequency properties. Normally R10 is only a wire jumper and C9 is omitted.
For low voltages it becomes rather complicated to calculate the resistor for the reference if it is a LM431 and similar with feedback. It's easy to get a hang-up at a voltage lower than the reference. The reason for this is that the feedback of the reference serves as a plain voltage divider so in order to get it working properly you must choose the resistors with taste. In the partslist there will be a couple of tested combinations with parts and output voltages.
The opamp can be almost any type (DIL08 holemounted or SO08 surface mounted) as long it's not too fast, faster than the output stage. The maximum speed of the opamp at unity gain is around 30-40 MHz. The AD825 has the bandwidth of 34-37 MHz at unity gain and the AD797 has unity gain bandwidth of approx. 30 MHz. If extremely low noise is important AD797 might be suitable but if "low" noise is sufficient I think any good audio opamp will do, like AD8610, OPA134 etc. Even good old NE5534 may work but I haven't tested this opamp. The only thing you must think of is the common mode limits for the inputs of the opamp. At start-up it's important that the opamp has a predictable behaviour, especially sensitive is this for a negative regulator.
At the moment only AD797 and AD825 are tested for 5-24 volts, both positive and negative (in the JSR05) output voltages.
Power for the opamp
You can either take the power from the output or before the pass transistor T3 (T4). What you choose is dependent of used opamp and how low the minimum supply voltage is (see the datasheet for this parameter). Minimum voltage for AD797 is 10 volts so if you want to be really sure you must feed it from the unregulated side if you want less than 10 volts out. Parts which are involved in this are R11 and R12.
AD825 has 6 volts as minimum but I have tested down to 3.1 volts with good results. This was valid for the tested regulator and the used AD825 but I'm not sure every AD825 will work.
Positive regulator, power from the output
R11 = used
R12 = not used
Positive regulator, power from the unregulated side
R11 = not used
R12 = used
The feedback network
The feedback network is very simple, only R8 and R9. C6 reduces the output impedance half of it's the value. This capacitor is hardly necessary in real life but if you want lower output impedance you should use it. The values of the feedback resistors should be a low as possible considering the max power dissipation. It serves to purposes. The first is to create a voltage divider with good high frequency properties (avoiding unstability) and also to draw current out of the pass transistor, T3 (T4). If current flows all the time also the output impedance can be kept low. It's also important for stability reasons.
The output voltage is determined by the reference voltage * (R8/R9 + 1)
The output stage
The output stage is rather unusual. Normally you have only one emitter follower, maybe together with a driver transistor forming a Darlington transistor. This type of output stage is rather slow, too slow here. To speed up things the driver transistor is changed to a class A emitter follower as the driver for the pass transistor. The load of the emitter follower (T5/T6) is a current source formed by a reference voltage, the LED H1 (makes a nice glow) and R13 together with T1/T2. The current through the LED should be 1-3 mA. If you want very low voltages you must change the value of R13.
The current through T1(T2) is set to 10 mA and this is determined by R14 and used reference voltage, used LED. This current times the current gain of the output transistor T3(T4) will set the limit of possible output current which is 600 mA to over 1 A.
The current through T1(T2) can be set lower and the max is set by max power dissipation of T1(T2) and T5(T6). Up to 25-30 mA is "normal" I think. Remeber that SOT23 is rated for less than TO92 transistors.
Worth noticing is also that using two silicone diodes (=1.3-1.4 V) will decrease possible losses and use of nicer colours than red, especially blue and white will increase the minimum input voltage and also increase losses in the T3 (T4). In the schematic you have formulas for calculating for different colours of the LED. You can't simply change the LED I'm afraid.
The driver is also a bit backwards. This creates a very special and also very important feature, the possibility to a safe power up of the opamp. The output stage deliver max output voltage when the opamp is inactive. This makes the opamp come alive. The zener DZ1 increases the startup voltage and creates also a necessary DC shift so the output of the opamp works at ideally at half the output voltage. This zener voltage must be decreased when lower output voltages are wanted. For 5 volts it's sufficient with a diode in the forward direction, creating only 0.7 volts. T5/T6 is added compared to Walt Jung's original (but Mr. Kaneda had it) and unloads the opamp from the drive currents. C11 takes down the impedance of the zener.
If you are interested in low voltages you must see to that the current through the LED H1 is sufficient. Strive to have as much current so you will see some light from the LED which is 0.5-2 mA. R13 is 10k for over 10 volts out but for low voltages you may decrease R13 down to 1k.
For low voltages you must also change the DZ1. The value of this zener should be half of the output voltage. 5 volts out requires 1.6 volt at least which is a LED in forward direction.
No short circuit limiting
I have increased the current of the driver T1/T2, for higher speed but this makes also the regulator more vulnerable against short circuit so I suggest you are careful when you are connecting. The LM317 has current limiting so you will have to trust this IC. I recommend careful handling though.
Capacitive load and C12
The faster opamps you have, the more sensitive against capacitive load the regulator will get, meaning low loss capacitive load. The regulator has a minimum load of 0.3-0.5 ohms and if you have a 100 nF connected very close to the output transistor you can get an impedance lower than 0.5 ohms. This frequency will be at 3 MHz. Therefore the C12 must not be too "good". In fact a "normal" cap is sufficient and if you choose a low impedance cap you may experience unstability. If you use a fast opamp, it simulates a cap rather high up in frequency so serious decoupling this close to the output transistor isn't necessary but if you only have 30 mm wire the regulator can take 100 nF or more. The short wire creates a small inductance which is sufficient in order to limit the lowest impedance.
Choice of resistors
I recommend plain 0.6 W 1% metal film resistors as a good start. It's up to you to test other types. MK2 Caddock resistors have been used with good results altought they don't fit perfectly, the wires are more narrow than plain resistors.
The tolerance is not either very important but in case you wonder R8 and R9 in parallel should be close to the value of R7.
Choice of non-electrolythic caps
I recommend small polyester types but any good capacitor with good HF-properties will do. Even good ceramics will work. Tolerance is unimportant, only HF-properties.
Choice of electrolythic caps
I recommend any type, from general purpose to low impedance types. I have used Sanyo MV-AX, low impedance.
Tolerance is unimportant but check voltage rating.