A good conductor and orchestra does this automatically when they intonate by ear and instruments used have or are made to have nice "harmonics" (the 2nd overtone for example is slightly greater than x2 the frequency of the fundamental by the right amount required by the ear-brain).
How about keyboard instruments?
We can take to our advantage that a correct octave to ear brain system is slightly more than x2 in frequency. This will allow correctly "stretched" octaves (as a good tuner tunes by eliminating beats) which will accommodate slightly "expanded" 5ths and the circle of fifths will close ie Pythagoras's comma will be gone.
In similar words. Instead of trying solving the Pythagoras comma problem we can start with a closed fifth circle (in fact expanded one so that the lowest note will sound in tune to the highest note of the same type to our ear brain). Then built everything around it including specifying and trying by experiment every single note's overtones, for the whole range of the keyboard. Technology makes this now readily possible.
So instead of trying to hit the "target" with the arrow we can throw it where we like (pleases our ear) and then draw a nice target circle around it paraphrasing Brian Eno's words in his interviews.
So how.
We can create notes with slightly more than 2x, 3x overtones, such that they sound correct and pleasing to our ear - brain system.
Then creating a temperament by according (tuning) all notes (everything octaves, 3rds if that can be possible etc) to these notes and their overtones.
It has been tried on the DX7ii and Korg Triton (Pleiades temperament) with very nice results. More work is needed as the DX7ii using algorithm 32 can specify a general overtone structure for all notes but not for every single note. Nevertheless this ahead of its time synthsizer can then be programmed for the frequency of every single note (all note scale). Using contemporary additive synths such as Camelion it should be possible to specify every single note harmonic structure. And perhaps nature which already helps us will help us more and notes and overtones will coincide when we try to tune every single note with the true harmonics of pleading sounding notes.
References:
Discussions with piano tuner Albert Ketenjian
Pleiades tuning for DX7ii and Korg Triton
Various scientific papers found on earlier euroelectron posts such as Octave Strech by Ernst Terharldt.
The perfect fifths tempered scale, a proposal or already a practice? - Klaus Gillessen.
How about keyboard instruments?
We can take to our advantage that a correct octave to ear brain system is slightly more than x2 in frequency. This will allow correctly "stretched" octaves (as a good tuner tunes by eliminating beats) which will accommodate slightly "expanded" 5ths and the circle of fifths will close ie Pythagoras's comma will be gone.
In similar words. Instead of trying solving the Pythagoras comma problem we can start with a closed fifth circle (in fact expanded one so that the lowest note will sound in tune to the highest note of the same type to our ear brain). Then built everything around it including specifying and trying by experiment every single note's overtones, for the whole range of the keyboard. Technology makes this now readily possible.
So instead of trying to hit the "target" with the arrow we can throw it where we like (pleases our ear) and then draw a nice target circle around it paraphrasing Brian Eno's words in his interviews.
So how.
We can create notes with slightly more than 2x, 3x overtones, such that they sound correct and pleasing to our ear - brain system.
Then creating a temperament by according (tuning) all notes (everything octaves, 3rds if that can be possible etc) to these notes and their overtones.
It has been tried on the DX7ii and Korg Triton (Pleiades temperament) with very nice results. More work is needed as the DX7ii using algorithm 32 can specify a general overtone structure for all notes but not for every single note. Nevertheless this ahead of its time synthsizer can then be programmed for the frequency of every single note (all note scale). Using contemporary additive synths such as Camelion it should be possible to specify every single note harmonic structure. And perhaps nature which already helps us will help us more and notes and overtones will coincide when we try to tune every single note with the true harmonics of pleading sounding notes.
References:
Discussions with piano tuner Albert Ketenjian
Pleiades tuning for DX7ii and Korg Triton
Various scientific papers found on earlier euroelectron posts such as Octave Strech by Ernst Terharldt.
The perfect fifths tempered scale, a proposal or already a practice? - Klaus Gillessen.
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