Recently exhumed from my bedroom closet (along with a really nice tuner I didn't even know was in there) is an old electric guitar that has certainly seen better days. I don't believe it would be worth the cost to restore, but it's still basically functional. This makes it a prime candidate for some, shall we say, unorthodox modifications.
I want to rip out all the frets, refinish the neck, and install new frets with 19 to the octave instead of 12.
Why 19? Well, it's the next equally divided octave (EDO) up from 12 (the standard tuning of modern Western music) that works well for triadic harmony (the most basic chords). Not only does it sound good, it's actually better than normal tuning at approximating 5-limit just intonation. Any piece written for standard tuning can actually sound a little bit purer if it's played in 19-EDO. For example, in 12-EDO a major third is 13.7 cents sharp from the "sweet spot" of the just major third (5:4), but in 19-EDO it's only 7.4 cents flat. Even better, the 12-EDO minor third is 15.6 cents flat from just (6:5), but in 19-EDO it's less than 0.15 cents sharp! Also, as inversions of the thirds, these benefits apply to the major and minor sixths as well.
Of course, there's still more to gain: 19-EDO offers 7 more pitches per octave than standard tuning. The main benefit here is the introduction of some extremely useful new intervals: the traditional second, third, sixth, and seventh are all available in not only two varieties (major and minor) but four each: supermajor, major, minor, and subminor. Additionally, the tritone of 12-EDO is split into two distinct intervals, one for the augmented fourth (the real tritone, a stack of three whole tones) and the other for the diminished fifth. Utilizing these extra intervals opens up broad new expressive possibilities, both melodically and harmonically.
Now, given this list, it's clear that the minor second and its inversion, the major seventh, deviate from 12-EDO by 26.3 cents, which is significant enough they could be considered "neutral" (halfway) intervals. Fortunately, they both fare better as approximations of their respective just intervals (16:15 and 15:8), deviating only 14.6 cents; this is still a distinct difference, though it's slightly less terrible than the 15.6-cent deviations from just that the minor third and major sixth exhibit in 12-EDO. If those intervals are tolerated, certainly these can be as well.
With such a different system, you might think I'd need to relearn how to play every scale and every chord. In fact, the new frets that correspond to the equivalent old frets won't have moved far, so the same hand positions will sound the same scales and the same chords. Effectively, the standard frets will only have shifted up or down the neck a little to make room for the new arrivals. They will be different enough that they will sound "out of tune" if played alongside a 12-EDO instrument; however, 19-EDO is actually more "in tune" to pure intervals than the current standard!
I want to rip out all the frets, refinish the neck, and install new frets with 19 to the octave instead of 12.
Why 19? Well, it's the next equally divided octave (EDO) up from 12 (the standard tuning of modern Western music) that works well for triadic harmony (the most basic chords). Not only does it sound good, it's actually better than normal tuning at approximating 5-limit just intonation. Any piece written for standard tuning can actually sound a little bit purer if it's played in 19-EDO. For example, in 12-EDO a major third is 13.7 cents sharp from the "sweet spot" of the just major third (5:4), but in 19-EDO it's only 7.4 cents flat. Even better, the 12-EDO minor third is 15.6 cents flat from just (6:5), but in 19-EDO it's less than 0.15 cents sharp! Also, as inversions of the thirds, these benefits apply to the major and minor sixths as well.
Of course, there's still more to gain: 19-EDO offers 7 more pitches per octave than standard tuning. The main benefit here is the introduction of some extremely useful new intervals: the traditional second, third, sixth, and seventh are all available in not only two varieties (major and minor) but four each: supermajor, major, minor, and subminor. Additionally, the tritone of 12-EDO is split into two distinct intervals, one for the augmented fourth (the real tritone, a stack of three whole tones) and the other for the diminished fifth. Utilizing these extra intervals opens up broad new expressive possibilities, both melodically and harmonically.
| CENTS | INTERVAL |
| 0.0 | Unison |
| 63.2 | Subminor 2nd |
| 126.3 | Minor or Neutral 2nd |
| 189.5 | Major 2nd |
| 252.6 | Supermajor 2nd or Subminor 3rd |
| 315.8 | Minor 3rd |
| 378.9 | Major 3rd |
| 442.1 | Supermajor 3rd |
| 505.3 | Perfect 4th |
| 568.4 | Augmented 4th |
| 631.6 | Diminished 5th |
| 694.7 | Perfect 5th |
| 757.9 | Subminor 6th |
| 821.1 | Minor 6th |
| 884.2 | Major 6th |
| 947.4 | Supermajor 6th or Subminor 7th |
| 1010.5 | Minor 7th |
| 1073.7 | Neutral or Major 7th |
| 1136.8 | Supermajor 7th |
| 1200.0 | Octave |
Now, given this list, it's clear that the minor second and its inversion, the major seventh, deviate from 12-EDO by 26.3 cents, which is significant enough they could be considered "neutral" (halfway) intervals. Fortunately, they both fare better as approximations of their respective just intervals (16:15 and 15:8), deviating only 14.6 cents; this is still a distinct difference, though it's slightly less terrible than the 15.6-cent deviations from just that the minor third and major sixth exhibit in 12-EDO. If those intervals are tolerated, certainly these can be as well.
With such a different system, you might think I'd need to relearn how to play every scale and every chord. In fact, the new frets that correspond to the equivalent old frets won't have moved far, so the same hand positions will sound the same scales and the same chords. Effectively, the standard frets will only have shifted up or down the neck a little to make room for the new arrivals. They will be different enough that they will sound "out of tune" if played alongside a 12-EDO instrument; however, 19-EDO is actually more "in tune" to pure intervals than the current standard!
At least the fingerboard layout is similar enough to ease transitioning from 12-edo to 19-edo. For the keyboardist, there is no easy way to divide a prime number!
ReplyDeleteIndeed! I have seen a piano retuned to 17-EDO, and I can make sense of it for one octave, because the upper C falls on what would have been the F above it, but the layouts of the octaves above and below would take a lot of getting used to. I've also seen YouTube videos of a 19-EDO piano with sticky notes on each of the keys. ;-)
ReplyDeleteYes there is, Re-key your halberstadt boards!!!!!
ReplyDeleteIf you mean to split the black keys (distinguishing between sharps and flats) and add extras at B-C and E-F, or some other physical modification, very few people have the means and know-how to do so, whether for an acoustic piano or a synthesizer. I'm certainly not about to attempt such a surgery on my Korg Triton. If I had the budget, I would definitely be interested in a specially-made instrument, or buying one and having it professionally modified.
ReplyDeleteIf, on the other hand, we're talking about selecting a 12-pitch subset of 19-EDO and tuning to those, I do that all the time! ;-)