# Methods for using just intonation to sweeten your chords



## TallKite (Aug 3, 2014)

When chords are tuned to just intonation, they sound -- well, I won't say better, because dissonance is a necessary part of music, so I'll say smoother or sweeter.

There's a problem with just intonation. On a fixed-pitch instrument like a piano, it's impossible to tune even a simple major scale so that all the notes are in tune with each other. This causes problems with any song that uses progressions like I-vi-ii-V-I. Classical string quartets, barbershop singers, etc. solve this problem with adaptive just intonation, imperceptibly shifting each note's pitch to get each chord in tune (or only imperceptibly off).

There have been attempts to adaptively tune virtual instruments. For example Hermode tuning, and Kontakt's Dynamic Pure Tuning (DPT). I've found that DPT simply stops working when it encounters certain progressions like I-ii, ii-V or i-V. The 12 little tuning columns all go to zero. Now I only have Kontakt 4, maybe they fixed this in Kontakt 5. Can anyone verify?

But there's another problem: DPT tunes a chord with some notes sharp of standard pitch and some flat, so that the "center of gravity", so to speak, is at 12-ET. The just minor 3rd is 16¢ sharp of standard tuning (100¢ = 1 semitone), so when you play an Am chord, the A & E notes must be 8¢ flat, and the C 8¢ sharp. If you play an E chord, the E & B would be 8¢ sharp and the G# 8¢ flat. If you go back and forth between Am and E, the E note would constantly be shifting by 16¢ (if DPT didn't stop working, that is). This would be quite noticable on a sustained E note. In general, in any i-V progression, the fifth would shift by the same amount, and in a ii-V-I progression, the second would shift, and in i-IV, the tonic would shift. In I-i, both the tonic and the fifth would shift. And I-III would make the third shift, and I-bVI-IV would make the tonic shift. I think this is why DPT just stops when you play certain chords.

I don't have Hermode tuning, but I think it works the same way, and the same problems would arise. Correct me if I'm wrong. Their website has very little technical informaion on how it works.

Now, I have a dog in this fight, as they say.  I've written a midi plug-in called alt-tuner that avoids these problems:
http://www.vi-control.net/forum/viewtopic.php?p=3808497
Of course, I'll be talking about why I think my software is best, but I don't know much about Hermode tuning, and I'm genuinely interested in what people have to say about it and DPT. 

Unlike Hermode and DPT, alt-tuner is not automatic. Unless your song is fairly simple, you don't just turn it on and sit back and let it tune things. You have to set it up for your chord progression and tell it which chords you're playing and when they happen. There's various methods to do this. If you're recording, you can put the chord roots in your midi file, perhaps in the range below A0, and alt-tuner will use them like keyswitches to adapt the tuning. If you're playing live, you can signal chord changes with foot pedals.

This approach is less convenient, but it works much better. Just intonation is simply too complex to automate. For example, the C7 chord can be tuned so that Bb is a just minor 3rd above G. Or it can be tuned so that Bb is two just fourths above C. You have to choose, because in just intonation, unlike standard tuning, these are two different notes. The choice depends on the musical context. For example, if you're in F, and the C7 is followed by a Bb chord, the 2nd tuning will be better because the 1st tuning causes a jarring 22¢ pitch shift for Bb. But if you're in Ab, and coming off of or going to an Ab add 9 chord, the 1st tuning is better because the 2nd causes a similar shift. 

The problem is compounded when you use 7-limit just intonation. C7 would have a Bb tuned to 7/4, the sweet "barbershop 7th" that's about a third of a semitone flat of standard tuning. If you follow this chord with a Cm7 chord, the Eb can be tuned a just 5th below Bb, making a rather narrow minor 3rd. Or it can be tuned to the usual minor 3rd. But this makes a fifth with Bb that's almost half a semitone flat, which sounds awful. So you would probably sharpen Bb by a half semitone, a very noticible shift!. A third option is to tune the C7 chord with the sharper Bb, making the C7 less sweet but avoiding the pitch shift.

In some situations, you might prefer the narrow minor 3rd, in others you might prefer the shifting minor 7th, in others you might prefer the less sweet C7 chord. There's no one right answer. It's an artistic decision, and IMO one that should be made by you, not your software.

Augmented chords are also tricky. C aug, E aug and Ab aug all look the same on the keyboard, but they're all tuned differently. With alt-tuner, you specifically tell it which one you're playing. Somehow, Hermode tries to guess which one you're playing. Does it do this based on previous chords? Or maybe the voicing?

And then there's what's called comma pumps, when you modulate a certain way, that cause the overall key to drift sharp or flat. There's all kinds of ways to get in trouble with just intonation! To the best of my knowledge, alt-tuner can handle all these situations. If you want to learn more about the technical problems of tuning in JI, check out my book on tuning, which also includes the alt-tuner manual:
http://www.TallKite.com/AlternativeTunings.html

Another drawback with DPT, and I think Hermode, is that they only work with certain VIs. (From what I can tell from the manual, the Hermode tuning in Logic Pro won't affect 3rd-party VIs, just the ones bundled with Logic. is this correct?) But alt-tuner is a midi-only effect that tunes your midi before it becomes audio. So it works with every VI out there, even ones not designed to be retuned. The only requirement is that it responds to pitch bends. So you're not limited to only using certain sounds; you can use all your sounds. The main method for retuning is to route the notes to different midi channels, and use different pitch bends on these channels. Unfortunately, this means you have to set up multiple instances of each VI, each one listening to a different channel. (Kontakt, Pianoteq, and Xen-Arts synths are easier to retune, they use other methods and only need a single instance.) So again, more work, but better results. Isn't that what music/art is all about?


----------



## Uncle Peter (Aug 12, 2014)

Very interesting. I've just seen this - I'll sit down and digest it over a cup of tea.


----------

