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For practical performance of alternate intonations, you can tune a guitar so that a particular chord shape presents perfect roots and 5ths, while arranging for

For practical performance of alternate intonations, you can tune a guitar so that a particular chord shape presents perfect roots and 5ths, while arranging for a single string to be a perfect third (e.g, a few cents "flat" compared to equal temperament.) When playing this same chord shape (or an appropriate derivative) up the neck, the relative intervals is maintained for other chords, allowing perfect intonation not just of the root chord but of other chords in the key family. For chord shapes where a flatted string cannot be used as a 2nd or 3rd, it will sound objectionably flat, but for many chord shapes it's possible to fret the flat string with additional pressure to bring it back into tolerance. Mastering this technique makes the guitar sound much more in tune with itself which is a wonderful sensation as a player.

cscheid 2y ago
(In case you didn’t know, it’s fun that) Jacob Collier plays a 5-string guitar in a tuning that takes advantage of this trick exactly. IIRC, from lowest to highest he tunes them a fifth, a fifth, a fourth and a fourth apart. By flatting the middle string a dozen cents or so, you can get a root-fifth-perfect tenth voicing of a major chord. Neat trick.
- wrs 2y ago
  Speaking of Jacob Collier, this is a good time to mention the song where he “hacks” equal temperament to modulate to G-half-sharp without anyone noticing. https://www.youtube.com/watch?v=Xd54l8gfi7M&t=3m17s https://www.youtube.com/watch?v=Xd54l8gfi7M&t=3m17s
  - cjbprime 2y ago
    One more Jacob Collier mention: also generally releases albums using just intonation, I think, and especially does hand-tuning of thirds etc. I like his description of having to "monkey swing" when an e.g. flattened third needs to become a new root note.
bwanab 2y ago
Aren't you still fighting the fact that the frets themselves are tuned as 12TET?
- elevation 2y ago
  The fight increases the faster/further you jump around the circle of 5ths. The 12TET fret spacing aligns octaves and 5ths with JI, so if you tune for a JI `I` chord, your other chords will be internally JI but only your `V` chord will be spaced perfectly from the `I` chord. The other chords will be closer to perfect JI the closer they are to `I` on the circle of fifths. This microtuning isn't perfect in theory, but it's a favorable compromise for a lot of western music, especially for legato strumming where the inter-string intervals are heard more often than the inter-fret intervals.
kazinator 2y ago
Most guitars are not properly in equal temperament intonation, because that requires compensation at the nut. In particular, an unwound G string can be off. I got sick of three decades of listening to that out of my main guitar, and earlier this year finally did something out of it with satisfactory results: https://mstdn.ca/@Kazinator/112332540341043265 https://mstdn.ca/@Kazinator/112332540341043265 Without this string, I cannot get these G and D power chords to be in tune simultaneously: G: E |---|---|-*-| B |---|---|-*-| G o|---|---|---| D o|---|---|---| D: E x|---|---|---| B |---|---|-*-| G |---|-*-|---| D o|---|---|---| If you tune the latter D, then the open G is too flat in the former G. If you sharpen the open G, the latter D is out of tune. The problem is that when we fret the A note on the G string near the nut, it stretches; the string goes sharp. So the interval between the nut and that fret is wider than a tone, without the compensation that shrinks it. The other strings have the problem, but the unwound G has it worse due to lower tension relative to mass. I'm so happy with the G compensation on that guitar, that it needs nothing else. Anyways, there are videos out there which do A/B comparisons between ordinary guitars and just intonation. They feature uncompensated guitars, so they perpetrate a fallacy. The guitarist must experience a properly intonated guitar with nut compensation first, then decide whether going to exotic intonations is worth it.

cscheid 2y ago

(In case you didn’t know, it’s fun that) Jacob Collier plays a 5-string guitar in a tuning that takes advantage of this trick exactly. IIRC, from lowest to highest he tunes them a fifth, a fifth, a fourth and a fourth apart. By flatting the middle string a dozen cents or so, you can get a root-fifth-perfect tenth voicing of a major chord. Neat trick.

wrs 2y ago
Speaking of Jacob Collier, this is a good time to mention the song where he “hacks” equal temperament to modulate to G-half-sharp without anyone noticing. https://www.youtube.com/watch?v=Xd54l8gfi7M&t=3m17s https://www.youtube.com/watch?v=Xd54l8gfi7M&t=3m17s
- cjbprime 2y ago
  One more Jacob Collier mention: also generally releases albums using just intonation, I think, and especially does hand-tuning of thirds etc. I like his description of having to "monkey swing" when an e.g. flattened third needs to become a new root note.

bwanab 2y ago

Aren't you still fighting the fact that the frets themselves are tuned as 12TET?

elevation 2y ago
The fight increases the faster/further you jump around the circle of 5ths. The 12TET fret spacing aligns octaves and 5ths with JI, so if you tune for a JI `I` chord, your other chords will be internally JI but only your `V` chord will be spaced perfectly from the `I` chord. The other chords will be closer to perfect JI the closer they are to `I` on the circle of fifths. This microtuning isn't perfect in theory, but it's a favorable compromise for a lot of western music, especially for legato strumming where the inter-string intervals are heard more often than the inter-fret intervals.

kazinator 2y ago

Most guitars are not properly in equal temperament intonation, because that requires compensation at the nut. In particular, an unwound G string can be off. I got sick of three decades of listening to that out of my main guitar, and earlier this year finally did something out of it with satisfactory results: https://mstdn.ca/@Kazinator/112332540341043265 https://mstdn.ca/@Kazinator/112332540341043265 Without this string, I cannot get these G and D power chords to be in tune simultaneously: G: E |---|---|-*-| B |---|---|-*-| G o|---|---|---| D o|---|---|---| D: E x|---|---|---| B |---|---|-*-| G |---|-*-|---| D o|---|---|---| If you tune the latter D, then the open G is too flat in the former G. If you sharpen the open G, the latter D is out of tune. The problem is that when we fret the A note on the G string near the nut, it stretches; the string goes sharp. So the interval between the nut and that fret is wider than a tone, without the compensation that shrinks it. The other strings have the problem, but the unwound G has it worse due to lower tension relative to mass. I'm so happy with the G compensation on that guitar, that it needs nothing else. Anyways, there are videos out there which do A/B comparisons between ordinary guitars and just intonation. They feature uncompensated guitars, so they perpetrate a fallacy. The guitarist must experience a properly intonated guitar with nut compensation first, then decide whether going to exotic intonations is worth it.