Yes it would probably sound like an octavia but with 'cleaner' higher frequencies (hopefully).
Tunnel diodes have the very weird property that they conduct most current in the "backwards" region. So where a normal diode blocks current they conduct heavily. Therefore they have to connected in series instead of parallel. In this case back to back means: connected in series with their N side or P side together.
In the forward region they first conduct, then when you increase the voltage the current drops (negative
differential resistance) and when the normal turn on voltage is reached they start to conduct again:

Taken from this site:
http://www.mpoweruk.com/semiconductors.htmIf you connect them back to back you will get this:

Although this looks like an easy circuit it is very difficult to get to work in practice. The problem is to prevent oscillation as the voltage of the tunnel diode is in the negative differential resistance region. I'll have to look at the information from the working circuit again. I haven't looked at it for 3 years as it was a project for undergraduate students to get some insight into electronics. I was the supervisor for three years.
I think the best thing is to add some resistors in parallel so the total IV curve does not have a region that goes down. Basically it's like adding a I=V/R (linear equation) to the curve. Then this resistor has to be connected as closely as possible to avoid RF oscillation. RF oscillation causes a small jump in the IV curve which simply results in a harsher sound. Another issue is current protection. During the 3 years of supervising the tunnel diode setup I lost about 3 units. Mostly due to errors of the students but also possibly due to the fact that they just break down easily. Therefore I connected two normal diodes back to back to avoid too much voltage on the tunnel diodes.
A better design would be something like this:

The normal diodes protect against straining the tunnel diodes too much. The other resistors have to be similar to the ones my test setup. Afterwards it might be needed to remove some of the clean signal which is caused by the extra resistors.
I might just order a few and play a bit with them.