So, I've noticed these ratios of range in the modern orchestra, which is primarily strings:
- Soprano:Alto - Factor of 4 or 5 more soprano than alto
- Tenor:Bass - About twice as much tenor as bass
- Alto:Low range - About the same amount of Alto as Tenor + Bass
This clearly shows an exponential decay curve as the range gets lower, similar to this curve:
Thus the Violin:Viola:Cello:Double Bass ratio in an orchestra could easily be this:
60:15:8:6 (in fact, I often see ratios similar to this in say a recording of Beethoven's symphonies, but over time, every part of this ratio becomes bigger, yet the ratio in simplest form is almost the same as in Beethoven's symphonies)
Now in this question about a possible woodwind predecessor to an orchestra, Ceremonial flute choirs as a predecessor to the orchestra, how plausible is this? I mentioned in the comments and in the main body of the question these same ratios that I listed above and somebody mentioned that this exponential curve is not ideal, that it would lead to too little bass and too much soprano. Which is why I'm asking this question.
Why is the exponential curve a default for the orchestra if in an entirely woodwind ensemble, it would be unbalanced? What is it about the timbre of multiple string instruments that leads to this exponential curve? I know that the difference between 1 and 3 of the same string instruments is staggering(1 gives you a solo timbre that can be more nerve-wracking, almost painful at high pitches(in the case of the violin and viola), soulful(in the case of the cello and to some extent the high range of the double bass), or intensely deep(in the case of the double bass), 3 gives you a more orchestral-type sound)
But in small string ensembles, the ratio is almost 1:1 and is 1:1 in the case of the Trio and Sextet(that is if the Sextet does not include the Double Bass, which some do). Yet as it gets larger and approaches the 60:15:8:6 ratio of Beethoven symphonies, it goes from this 1:1 or almost 1:1 to an exponential curve.
Why is that? Why is it that the orchestra follows an exponential curve with pitch range and small ensembles have an almost 1:1 ratio for all the ranges?