If you want an all-encompassing song, I would use "Joy to the World" because the first eight notes are a descending major scale. One octave. done.

Types of Instruments:

Musical instruments use a few different techniques to resonate.

String instruments amplify the vibration of the string with a resonator box, like the body of a guitar or violin. The physics behind this relates to the mass of the string and the tension in the string. Your physics text probably describes the equations somewhere. Low pitch strings are massier and looser than the high pitch strings. If you are going to make one of this type, you will need to have several string of different tension/mass and some sort of resonator box. This would probably be the easiest way to get a lot of different notes.

Brass instruments themselves are a resonator, amplifying the vibration you create with your lips. To resonate low pitches, you make the horn "longer" by adding tubing. This is most easily pictured on a trombone, where the slide can be seen moving in and out. The physics behind this is that your lips create pressure waves that resonate the air in the horn. When the horn's natural frequency (determined by length) and the pitch you are buzzing match, you achieve resonance. However, you can also achieve resonance on any of the higher modes above the natural frequency of that length. This is what makes a brass instrument "jump" between different pitches at any given horn length. Replicas of brass instruments are easy to make with tubing. The hard part is getting it to resonate on each pitch of a scale, which is unnatural to how the vibration modes work. You must be able to change the length of tubing to achieve resonance at each pitch on a scale.

Reed instruments vibrate one or two reeds and then the horn resonates that sound. These achieve resonance by making the horn the correct length to match the fundamental frequency of the reed vibration. The difference between these and brass, however, is that the horn almost always functions at a given lengths fundamental frequency and does not utilize the higher harmonics as much. By covering holes with your fingers, you lengthen the horn and get a lower pitch. A clarinet is one of the most common examples.

Flutes use the oscillation of air over a hole to create the vibrations that are resonated by the instrument. Jugs work this way, too. The vibration is actually the air switching between going inside the instrument and going outside the instrument. Again you would cover holes to lengthen the instrument and change the fundamental frequency.

Here is a fantastic resource about the basics of many types of instruments.

I'm biased towards brass instruments, as it is what I play. (That's a euphonium.)

As a first step, I would poke around the fantastic resource I mentioned above. Decided which type of instrument you want to tackle, and then we can discuss materials and options. I vote brass, but it may be a good challenge. That would just net you that "A" you want, though. And I would have much more to offer.

Jeez, now you got a ton of ideas floating zipping around my brain. Let's continue this in the forums.

Oh... you might have to join Instructables for that. But you should anyway, since you'll be posting an I'ble of your project ;)