lowest overtone scale?

Starting with points that you all know better than I:

The lowest overtone of an acoustic instrument depends on the class of instrument. For many, perhaps most, it's the 2/1 "octave" interval. For some it's the lowest odd harmonic, namely the 3/1 "twelfth" interval.

Transverse vibrations in percussion instruments having rods or bars that are free at both ends as resonators produce a lowest overtone one octave above an interval that ideally tends toward the otonal harmonic 11287/8192, almost exactly 62/45, or about 3 cents away from 11/8. However, slight variations in material or geometric properties of the resonator cause noticeable departures from the mathematical ideal. To keep the lowest overtone close to its ideal, each rod or bar must be tuned by the instrument maker.

(In practice, makers of these instruments often tune such overtones away from their mathematical ideal and toward the more diatonically familiar octave or twelfth instead. But they could tune those overtones toward the ideal.)

Lamellaphones like tongue drums, kalimbas or mbiras having resonators fixed at one end produce a lowest overtone two octaves above an interval that ideally tends toward the otonal harmonic 51341/32768, almost exactly 47/30, or about 5 cents away from 11/7. Again, in actual instruments the lowest overtone frequency is highly sensitive to slight variations in resonator materials and geometries. Each tongue or tine must be tuned carefully or its lowest overtone will depart from its mathematical ideal value.

(Again, in practice, lamellaphone makers often tune their overtones toward the 6/1 harmonic, an octave above the twelfth, but they could tune them toward the ideal.)

Now to my question:

Can we imagine a prehistory in which some culture produced musical instruments in each of those classes, tuning their lowest overtones close to the ideal values 2/1, 124/45, 3/1 and 94/15, and then chose a musical scale transposing them into the octave?

Such a "lowest overtone scale" would have sounded best for ensemble music in which the ensemble included an instrument in every class. Gradually, as our imaginary culture acquired its musical idiom, the ensemble could have been reduced, class by class, until music for solo performances became acceptable, as the listeners' familiarity with the idiom grew able to supply the "missing" overtones.

What scale would this culture have chosen?

Several 13-tone JI scales are among the possibilities, notably:

0: 1/ 1
1: 22/21
2: 12/11
3: 8/ 7
4: 14/11
5: 4/ 3
6: 11/ 8
7: 16/11
8: 3/ 2
9: 11/ 7
10: 7/ 4
11: 11/ 6
12: 21/11
13: 2/ 1

However, instrument makers might have found overtone tuning easier if their scale divided the octave equally. Here, 17EDO would be the obvious choice, with under 4 cents average harmonic error compared to the ideal values for the lowest overtone in each class.

Something analogous to a 17-tone well temperament, optimizing minimal and/or proportional beating for every overtone class in a small number of keys from a chain of fifths, might also have developed ... eventually.

Now for my consequence:

If our hypothetical culture selected 17EDO as their "lowest overtone scale" their instrument makers would tune their lowest freebar overtone to the 8th degree and their lowest lamella overtone to the 11th degree of 17EDO. Of course, the 3/2 "perfect fifth" (an octave below the lowest odd harmonic) would have the 10th degree.

When combined with the root pitch or 0th degree, the 8th degree would sound best on a freebar instrument, the 10th degree on an integer harmonic or odd harmonic instrument, and the 11th degree on a lamellaphone. This would establish, or define as consonant, three different dyads but no single instrument would make all three sound great. Only the whole ensemble could make that happen. Or could it?

Would 17EDO music from this prehistory that we've imagined, played by a properly tuned acoustic ensemble or digital simulation, be worth composing and hearing?

Just curious!
==
Manu

The alternate musical heritage I've outlined here stretches back to a prehistory in which some culture divided up their musical instruments according to overtone class and based their harmonic system on one dyad from each class, each dyad consisting of the root or fundamental tone and the lowest loudest overtone in its class. This imaginary heritage leads to one or more scales in which all those dyads can be played. I listed only four overtone classes (arbitrarily omitting others) and showed how they could have pointed this hypothetical culture toward any of several 13-tone just intonation scales or a 17-tone tempered scale with either well or equal temperament.

As noted, one problem with such a narrative is that it requires ensemble music to precede solo performance. Otherwise, if only one instrument class is audible, some dyads from other overtone classes will not match any timbre in the performance. Only as history unfolded, and audiences became habituated enough to this musical heritage, could listeners' memories have come to furnish the missing timbres when classes were dropped from the ensemble, finally making solo music acceptable.

As a development from prehistory to history, my narrative suffers from other plausibility problems too. For one thing, the ideal values of the lowest overtones in some instrument classes cannot be calculated without fairly advanced mathematics, geometry and physics. I've been presuming that an attentive ear could substitute for calculation but the wide variance in overtone frequency among actual real-world instruments makes that presumption problematic.

I guess it's easier to imagine prehistoric people whittling their xylophone bars to modify their overtone frequencies than it is to imagine them comparing the overtones of unmodified bars and identifying the attractor frequency that those overtones approach. Ditto for them crimping their kalimba tines, et cetera.

Okay, so my narrative isn't totally plausible. Nevertheless, in our own ongoing history, I personally remain fascinated by the possibilities of ensemble music where certain dyads are defined as consonant but where a given dyad may need to be played on an instrument of the proper class before it can sound consonant. And I'm intrigued by the happenstance that 17-tone temperaments seems tailor-made to accommodate these possibilities.

I mentioned that some 13-tone JI scales can do so too. I forgot to add that several 25-tone JI scales are also among the potential realizations; I'll post one when I get the chance.

Cheers!
==
Manu