What is Just Intonation?
I know how to tune a harmonica. That is easy for me. Understanding what I am doing and explaining it to someone else is a totally different thing.
There is something about this subject that makes me a little bit crazy. I keep wanting nice, simple answers to my questions and I keep getting long, complicated answers full of strange words and numbers. Many of the dictionary definitions for the words used to describe sound vibrations or tuning systems are incomplete or misleading.
This article focuses on the main words and ideas that you need to know to understand Just intonation and Equal Temperament. It is like the trunk of the tree and the main branches. The little branches are like the details. They grow out of the main ideas. When you know the main ideas and most important words, the details are much easier to understand.
Just intonation is a way to tune a harmonica so all the notes that you play at the same time sound smooth and, well, harmonious. To understand Just Intonation you need to understand the other main way of tuning a harmonica: Equal Temperament.
Equal Temperament is a way of tuning a harmonica so the melody notes will sound relatively in tune no matter what key you play in. The trade-off is that you lose the smooth harmonies.
Equal temperament also gives us the way that we measure the notes we are tuning. It is the standard that we measure against. So a formula for Just Intonation tells us how sharp or flat a note or interval is compared to the same note in Equal temperament.
My dictionary defines intervals as: “a space between two things, a gap, the difference in pitch between two musical sounds”.
When you see a tuning formula it is usually explained in the number of cents sharp or flat a note is. What the tuning formulas usually DON’T tell you is that this means sharp or flat compared to Equal Temperament.
What does this mean? Cents are the units of measurement for sound vibrations. The dictionary definition is “one hundredth of a half step”. For example from A to A sharp, it is one hundred cents.
What the dictionary definition leaves out is that it is 100 cents from one half step to the next in Equal Temperament.
When I look up Equal Temperament in the same dictionary, it states: “the adjustment of intervals in tuning a piano or other musical instrument so as to fit the scale for use in different keys; in equal temperament, the octave consists of twelve equal semitones”.
What THIS definition leaves out is what intervals are being adjusted FROM.
In Equal Temperament, the intervals are being adjusted FROM the intervals of Just Intonation. Stick with me here and this will soon make sense.
Mother Nature has a different way of creating musical intervals than dividing the octave into 12 equal semitones or half-steps, and that is what Pure Just Intonation is based on.
Here is how the note intervals are created in Pure Just Intonation: When you sing a single note, or play a note on most instruments, you are hearing a series of vibrations all happening at the same time.
There is the main note, or Fundamental Pitch, and there are a series of other, quieter, pitches that you also hear that vibrate in perfect harmony with that fundamental pitch.
These other pitches that play at the same time are called the overtone series. Overtones are also called harmonics or partials because they are OVER the fundamental pitch, HARMONIZE with it, and are PART of the overall sound that you hear.
One way we hear overtones is in tone color. When a violin plays the same note as a flute, the overtone series of the violin has a pattern that is strong in some overtones and weak in other overtones. The flute has a different pattern of strong and weak overtones. So the overall sound of a violin is different than a flute as a result. The same thing happens with your voice and my voice. Different patterns of overtones give you a different overall sound.
The other way we hear overtones is with harmonies. When two or more notes played at the same time match the overtones of one note, then they sound smooth and harmonious.
When you perfectly match the notes or intervals of a scale or chord to the overtone series of one note, then you have pure just intonation and smooth harmonies.
These intervals or notes will not match the half and whole steps that you get with Equal Temperament. Some will be higher (sharp), some lower (flat) compared to Equal Temperament. Some notes in Just Intonation are so close to Equal Temperament that most people cannot hear the difference. Others are so far away from Equal Temperament that it is painfully obvious to almost everyone.
You have three basic ways to fine-tune a harmonica: Pure Just Intonation, Straight Equal Temperament, or some combination of the two systems. As you gain the advantages of one system, you lose the advantages of the other. There is no way around this. You cannot have all the advantages of both systems in one harmonica.
Most of the time I wasted tuning and re-tuning harmonicas was because I secretly wanted to have all the advantages of both systems in one harmonica. This is insane, and now that I am totally convinced of that, it takes me a lot less time to tune a harmonica. I hope this article helps you to make clear decisions about tuning and then stick with them. It will really save you a lot of time in the long run!
Author, Turbocharge Your Harmonica, Volume1
Builds high end custom harmonicas and harmonica tools, teaches harmonica technology, performs on harmonica, guitar, and vocals, and does harmonica workshops in the U.S. and abroad.