How We Make Our Music (3/5)

Just Intonation

Why change the tuning?

Throughout history and around the world, there have been many systems of tuning the different notes of a scale.  Most modern music uses "equal-tempered tuning" to determine the actual frequencies of the notes.  This system divides the octave into 12 equal intervals (called half-steps) and is widely used because it sounds equally good in all keys.  Synthesizers (with few exceptions) use equal-temperament to determine the actual frequency of their notes.

More information about equal-temperament can be found here:

http://en.wikipedia.org/wiki/Equal_temperament

However, the acoustical phenomenon called the "harmonic series" is the fundamental starting point of all music.  When two or more frequencies line up mathematically, they sound pleasing to the ear, and this is what makes music different from just random noise.

More information about the harmonic series can be found here:

http://en.wikipedia.org/wiki/Harmonic_series_(music)

The problem with equal-tempered music is that the chords don't quite line up with the harmonic series, so they don't sound as good as they should.  Good singers and musicians who play instruments that can alter their tuning note-per-note often adjust for this, sometimes subconsciously.  Some of the best musicians, especially those with classical training, analyze the chords in the music they play and intentionally make small adjustments to the pitch to get closer to the mathematical ideal frequencies.  The system of tuning in which certain notes are adjusted is called "just intonation."  I think that many people dislike the sound of synthesizers because they are perfectly equal-tempered and therefore the chords don't sound that great.

This is an excerpt from "Legacy Begins with Me" tuned to equal-temperament.  Also note that this track has few effects and is not mixed, etc. Our process for that will explained in the next couple of posts.

And another example, and excerpt from "We Are the Robots."

This is the chart of how to tune each chord so that it lines up perfectly with the harmonic series:

So the next step is obviously to tune all the chords in the song so that they sound better, right?  Well, it's not quite that easy.  Often there are common-tones (the same note played in two different chords) that are tuned in different ways.  For example, if you have a C-Major chord (C-E-G) followed by an a-minor chord (a-c-e), two of the notes will be played in succession, but tuned 14 to 16 cents differently.  This is not a good sound and should be avoided.  We at Zweiforce invented a system that averts most of these bad sounds and also is fairly simple to implement.  We also didn't want our music to sound too different from the equal-tempered sounds most of us are used to hearing in electronic music.

Zweiforce's system of just-intonation

Here are the same excerpts we heard earlier but tuned using our system:

Try listening to both pairs of examples a few times to really hear the difference.  Yes it is a very subtle difference, but we think worth the effort.  We think example02 and example04 sound smoother and more satisfying.  The major chords have more finality and the minor chords have more tension.

We simplified all of the + and - tunings to just +12, -12, or 0.  This is enough of a change to make the chords sound smooth without messing with the melodies.  The - number and the + number need to be the same in order to make our system work.  A Major chord can be tuned as 0 for the root, -12 for the third, and 0 for the fifth, or it can be tuned +12 for the root, 0 for the third, and +12 for the fifth.  Either tuning will result in a resonant sound, we choose one or the other tuning to make it match the surrounding chords.  A song with typical chords can be tuned this way:

Major:

I 0 -12 0

ii 0 +12 0

iii -12 0 -12

IV 0 -12 0

V 0 -12 0

V7 0 -12 0 -12

vi -12 0 -12

vii' -12 0 -12

minor:

i 0 +12 0

ii' 0 +12 -12

III +12 0 +12

iv 0 +12 0

V 0 -12 0

V7 0 -12 0 -12

v 0 +12 0

v7 0 +12 0 +12

VI +12 0 +12

vii' -12 0 -12

VII +12 0 +12

Our songs obviously feature key-changes and many borrowed chords from other keys, etc.  So in those cases it's trial-and error.  We just try to keep common-tones tuned the same way if possible while making the chords resonate.  For non-chord tones we leave them equal-tempered if it's part of the melody or not obviously part of the harmony.  But there are some more advanced chords in the chart above, and those chords we approximate as best as we can.  For instance, Major 6th and Major 7th chords both have lowered notes beyond the triad, and we -12 those notes.

Implementation

We mainly use Sunvox for composition, and it is quite simple to implement our tuning system within Sunvox.  The first step is to make two additional copies of each synth.  Then in "Module properties" set one of the copies to -30 Finetune and the other to +30.  Because Sunvox uses a binary math system, it's not +-12 it is +-30.  Just trust us on this, it will work.  We do sometimes also use other synth programs, and the process is the same so far except other synths typically fine tune the notes with cent values.

When we look at the notes, it looks like this initially:

The number "18" refers to the synth that plays that note.  We just need to change the Major 3rds to be played by one of our altered synths, the one tuned -30 lower, in this case "1A".  It will look like this:

In Protools and some other programs this step is more tedious because we have to duplicate the midi tracks containing all the notes, then route each track to the correct synth.  Then we have to delete notes from each track so that only the notes we want altered are played by the synths that have been pitch-adjusted and not from the original synth.

So that's it!  Feel free to contact us if you have any questions.  Our next post will be focusing on how we add effects and beef up the sound.  Then the final post will be about mastering.