Exactly. I would like to see this done using integer ratios to define the frequency intervals. You can still use the octave as a 'start' and 'end' point for th

Exactly. I would like to see this done using integer ratios to define the frequency intervals. You can still use the octave as a 'start' and 'end' point for the scale to make things simple (although there's no axiom anywhere that says this has to be the case, it's just a good candidate because it's the simplest and most easily recognizable interval, aside from the unison). Since you'd be dealing with a potentially infinite number of intervals, you can start with the 'simplest' 20 or so (using lowest possible integer values to create the distinct ratios). Some would argue that the simplest 40 can be considered musical although that would get you into some seriously dissonant territory, not to mention the amount of possibilities you would have available at that point.