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Constructing a perfect temperament is impossible if you require each logical tone to be mapped to a constant frequency. I've long been curious about what would

by shemol 12y ago

Constructing a perfect temperament is impossible if you require each logical tone to be mapped to a constant frequency. I've long been curious about what would happen if you allowed the specific frequencies to drift in order to keep the ratio between concurrently sounding tones perfect (well, closer to perfect, as you add more tones). No idea whether the shift would be perceptible, or to how many ears.

baddox 12y ago
Do you mean shift the frequencies when the key changes, e.g. between songs or when a song modulates? That certainly works, at least with electronic or continuously variable instruments. But even within one diatonic scale in a single key, it's impossible to have a fixed set of frequencies such that the intervals are correct in all of the diatonic triads. I suppose you could shift individual frequencies based on the chord currently being played, but I'm not sure how that would sound.
- shemol 12y ago
  Per-chord is what I meant, not per-key. 3:2 means you can't have a coherent set for all tones in a key, full stop. But you could slightly shift the frequencies of the notes in a given chord to make that chord perfectly tempered. There'd be a million details; making sure the melodic voice, bass, or both avoided wolf intervals; figuring out what to when some voices are moving over a sustained chord in others; keeping the main anchor frequency from drifting "too far" from the original (and probably determining "too far" in the first place); figuring out whether the resulting sound was going to be anywhere near distinguishable enough to be worth all the effort of hacking through all this rigamarole.
  - baddox 12y ago
    Yeah, it sounds complicated. I wonder what a cappella groups like barbershop quartets do, or if they even think about it.
    - shemol 12y ago
      Complicated, no doubt, but agree it's probably not far from how any non-tempered instrument player harmonizes already, with little or no thought. Thanks for the link to Gary's blog. Good read.
  - baddox 12y ago
    It looks like there's no problem with just swapping frequencies as you change chords. This youtube video is great, as is the guy's blog: http://youtu.be/jA1C9VFqJKo http://youtu.be/jA1C9VFqJKo

by shemol 12y ago

baddox 12y ago

Do you mean shift the frequencies when the key changes, e.g. between songs or when a song modulates? That certainly works, at least with electronic or continuously variable instruments. But even within one diatonic scale in a single key, it's impossible to have a fixed set of frequencies such that the intervals are correct in all of the diatonic triads. I suppose you could shift individual frequencies based on the chord currently being played, but I'm not sure how that would sound.

shemol 12y ago
Per-chord is what I meant, not per-key. 3:2 means you can't have a coherent set for all tones in a key, full stop. But you could slightly shift the frequencies of the notes in a given chord to make that chord perfectly tempered. There'd be a million details; making sure the melodic voice, bass, or both avoided wolf intervals; figuring out what to when some voices are moving over a sustained chord in others; keeping the main anchor frequency from drifting "too far" from the original (and probably determining "too far" in the first place); figuring out whether the resulting sound was going to be anywhere near distinguishable enough to be worth all the effort of hacking through all this rigamarole.
- baddox 12y ago
  Yeah, it sounds complicated. I wonder what a cappella groups like barbershop quartets do, or if they even think about it.
  - shemol 12y ago
    Complicated, no doubt, but agree it's probably not far from how any non-tempered instrument player harmonizes already, with little or no thought. Thanks for the link to Gary's blog. Good read.
- baddox 12y ago
  It looks like there's no problem with just swapping frequencies as you change chords. This youtube video is great, as is the guy's blog: http://youtu.be/jA1C9VFqJKo http://youtu.be/jA1C9VFqJKo