How to Tune Your Harmonica – Choose Your Tuning Goals and Measure Your Work… by entering the:

War of the Musical Worlds! (Equal Temperament vs. Just Intonation)

When you decide to start tuning your harmonicas you get into musical challenges that most people with “normal” instruments never have to struggle with. Harmonica reeds have this crazy rich swamp of tone that can sound gorgeous, but can also sound obnoxious and irritating when the tuning gets away from you. Everything about tuning gets exaggerated in harmonicas. When harmonicas sound good, they sound very very good, and when they sound bad they sound horrid.

When you play with other musicians, they will be happier with you if your tuning sounds very very good. This is a lot easier when you know what to listen for when you tune your harmonica. When you have a clear idea of the result you are going for and know how to measure what you are doing. That is the purpose of this article.

There are two main systems for tuning a harmonica.  One system focuses on melody, the other on harmony. Here they are:

Equal Temperament – also known as 12 tone Equal Temperament (12TET) for Melodies

Equal temperament gives you melodies that sound in tune no matter what key you play in.  12TET is great for jazz; fiddle tunes, and any style that focused more on single notes than chords. The Hohner Golden Melody is a good example of an Equal Temperament harmonica.

Just intonation (JT) for Harmony, Smooth Chords

Just Intonation is the harmonica sound of the classic blues recordings of the 30s, 40s, and 50s. JT gives you smooth chords and harmonies. It is great for steam train imitations, solo harmonica pieces, and harmonica styles that feature chords and intervals. . The original Hohner Marine Band harmonica was tuned to Just Intonation.

 

When you study equal temperament and just intonation you need to understand the words you are reading. Some of these words have long, complicated definitions when you look them up. There are also many words that mean almost the same thing. It is enough to drive you crazy! So let’s take the words you will use to understand ET and JT and explain them in plain English…

Pitch

The word pitch refers to the rate of vibration of a musical note. You can also use the term pitch to mean a musical note. Every pitch you hear has a main vibration that you can measure with a tuner. You identify pitches as particular notes – “A”, “A flat” or “B” and so on…

Fundamental

The main vibration of a note is the “fundamental”, or “fundamental pitch”. But you hear much more than “fundamentals” when you listen to notes from a musical instrument:

Overtones, Harmonics, Partials

Inside the sound of musical notes are more pitches that vibrate with the fundamental. You can use the words “overtones”, “harmonics”, or “partials” for these extra frequencies or pitches. Each one of these words describes one of the qualities of these additional pitches:

Overtones: These tones or pitches are higher, or “over” the main pitch, or fundamental.

Harmonics: These pitches vibrate in perfect harmony with the main pitch.

Partials: These pitches are “part” of the overall sound that you are hearing.

Overtone Series

These overtones, harmonics, or partials come in a series of vibrations that follow a pattern, and this pattern is called the “overtone series”. Many of the overtones in the overtone series are notes you are familiar with.  For example, in the overtone series for the note C, we find a G, an E, a B flat, a D, and other scale tones. As you go up the overtone series, the pitches get closer together, and some pitches sound strange because they are in between the notes you find in major and minor scales. The notes of the overtone series all vibrate in perfect harmony with the fundamental pitch that they came from.

Timbre

We don’t hear the overtone series as directly as we hear the main pitch. We hear these overtones, harmonics, or partials as “tone color”. Another word for tone color is timbre. Timbre or tone color is what makes a violin sound different than a piano even when they play the same note.

Every musical instrument or human voice has a distinct pattern of strong and weak frequencies or notes in its overtone series. A trumpet has one pattern. A violin has another. Your voice has a different pattern than mine. This is what we mean by different tone colors or timbres. So these voices and instruments “sound” different as a result.

Just Intonation

Just intonation is a way of tuning a musical instrument to create perfect harmony when you play two or more notes at the same time. You tune the notes of your harmonica to match the vibrations (or frequencies) of the overtone series of one note.  They will then be in perfect harmony. The notes blend together so perfectly that a chord in just intonation sounds like one big full sound instead of separate notes that are playing at the same time. This is the sound of a good barbershop quartet. It is also the sound of the harmonicas that you hear in many classic blues recordings from the 30s, 40s, and 50s. Most of these recordings were made on harmonicas that were tuned to pure just intonation.

When you tune a harmonica to just intonation you only need to focus on the notes you can play at the same time. You can’t play blow notes and draw notes at the same time on a harmonica. So you tune all of the blow notes to harmonize with one blow note, and you tune all of the draw notes to harmonize with one draw note.

On a C harmonica, the blow notes are C, E, and G. These are the notes of a C chord. You tune the E and G notes to match the overtone series of the C note. The chord will then be harmonized and sound smooth.

The same process works for the draw notes. You pick one note and harmonize the other notes to it. On the C harmonica the G chord is the main draw chord, so you harmonize all of the other draw notes by tuning them to match the overtone series of the G note.

Scale Degrees

There is another way of naming the notes that you tune. You use numbers instead of the letters of the Alphabet. We call these numbers scale degrees. When you tune diatonic harmonicas that come in twelve different keys, it is easier to remember the tuning pattern if you think in scale degrees because the scale degrees are the same for all twelve keys.

The scale degrees refer to the notes in a major scale. This is the scale we get when we sing Do Re Mi Fa So La Ti Do. Here are the notes of the C scale followed by scale degrees in numbers:  C (1st or root), D (2nd), E (3rd), F (4th), G (5th), A (6th), B (7th) and C, (which would be called the octave from the Latin word for 8). When a scale degree pitch is a half-degree above or below the notes in a major scale, the scale degree is then called flat or sharp. For example “flat 7 (b7)” is one half step below the seventh note of a major scale.  This will make more sense later on in this article when we define semitones.

Scale degrees also tell us how a particular note relates to the root note that we are tuning to or harmonizing with. On the C harmonica blow notes, the Cs are the root (or 1st) notes, the E notes are the 3rds, and the G notes are the 5ths. On the C harmonica draw notes, the G is now the root note, the Bs are the 3rds, the Ds are 5ths, the F notes are b7ths, and the A notes are 9ths. The F notes are b7ths (flat7ths) because they are a half step down from the seventh note in the G scale (remember, we are using the G note as our root) The G major scale has an F# instead of F note in it. The A notes are called 9ths here because the A note that is part of this chord is the note after the octave, or eighth note.

Equal Temperament

Equal Temperament is a way of tuning a musical instrument based on making all the half steps (semitones) the same distance apart. This gives you melodies that sound “in tune” no matter what key you play in. The downside is that you never get smooth harmony; there is always a rough quality to chords. Equal Temperament (or something close to 12TET) is the most popular way to tune musical instruments in the Western world. It is what you are used to hearing if you grew up listening to mainstream music from the United States or Europe.

The reason for the popularity of ET comes from the main limitation of Just Intonation. When you start playing melodies in different keys on an instrument tuned to Just Intonation, some of the notes will sound out of tune.  If you tune one harmonica to the overtone series of a C note and another harmonica to the overtone series of an A note, some of the notes will not match, even though they have the same name. The E note in the overtone series of an A note is not the same frequency as the E note in the overtone series of a C note. The gorgeous harmonies that you hear in pure just intonation are made from notes that can sound out of tune when used as melody notes in other keys.

Semitones

Semitones are musical notes that are a half step apart. “A” to “A sharp” is a semitone. “A sharp” to “B” is another semitone. There are 12 semitones, or half steps in an octave. The major scale is a seven-note scale made with a combination of whole steps (2 semitones or half steps) and half steps (1 semitone or half step). The most common way to measure the distance from one semitone to the next is the unit called cents.

Hertz, Cents, and Calibration

Hertz are cycles per second, or rate of vibration. You measure hertz by counting the number of cycles per second. Hertz are used in tuners to calibrate your tuner (set the standard that you use for tuning). You will usually see Hertz represented as the abbreviation Hz. Hertz gives you a way to set a standard by defining the number of vibrations of a specific note. When you see “A= 440” That tells you that a note vibrating at 440 cycles per second is the standard being used. All the other notes will then be tuned in relation to this note.

Cents are units used to measure the differences between musical pitches. Cents give you the way to set a different standard, the one used in Equal Temperament.  There are 100 cents from any one note to the next note a half step higher. The distance from a C note to the C note an octave higher is divided into1200 cents. It is almost impossible to hear a difference of a cent or two, but it gives us a very accurate way to measure and compare different musical notes.

Here is the main feature of Equal Temperament: In Equal Temperament the distance from one semitone (half note) to the next is always 100 cents.

As a result E notes (in the same octave) will have the same number of cycles per second no matter what key harmonica you are playing.

Equal Temperament is the standard we use to measure other tuning temperaments. When you say a note is sharp or flat, you mean sharp or flat compared to the note as tuned in Equal Temperament.

A tuner shows you a note tuned to Equal Temperament by pointing to zero with a needle or lights. When the needle or lights are above zero, the note is sharp compared to ET. When the needle or lights are below zero, the note is flat compared to ET. The tuner may tell you exactly how many cents above or below ET the note is. Some tuners just have lights and when the light in the middle glows you are in tune with ET.

For More information on the difference between Hertz and Cents go to this article.

Tuning Formulas for the Harmonica

How do we as harmonica players use this information? We have two different systems with different results: 1. Just Intonation: smooth chords, melody notes that sound out of tune. 2. Equal Temperament – melody notes sound in tune, chords sound rough.

One of the best ways to understand the difference Equal Temperament and Just Intonation is to play harmonicas tuned to JI and ET and compare the way they sound.

Let’s look at the tuning formula for Pure Just intonation. We will use a C harmonica as an example. We will identify the note and tell you what scale degree it is.  We will then tell you how many cents flat or sharp it is compared to Equal Temperament.

Blow notes:

The C notes are the 1st or the root notes. They are at zero cents (no difference).

The E notes are the 3rds. They are 14 cents flat (14 cents lower than equal temperament).

The G notes are the 5ths. They are 2 cents sharp (2 cents higher than equal temperament).

Draw notes:

The draw notes are usually tuned to the main chord in the first octave, which is a G chord on the C harmonica.

G is the root or 1st = 0 (no difference)

B notes or 3rds are14 cents flat

D notes or 5ths are 2 cents sharp

F notes or flat7ths are 32 cents flat

A notes or 9ths are 4 cents sharp

When we look at this tuning formula, it is easy to see the one note that has the biggest difference between Equal and Just. It is the flat 7, the F note on the G draw chord on a C harp, the 5 & 9 draws.

The tuning formula for Equal Temperament is easy – all notes are at 0.

Mixed, Combination, or Compromise tuning formulas

Now you know the basics of the two main systems for tuning the harmonica. You can use this information to tune your harmonicas in three ways.

1. Pure Just Intonation.
2. Straight Equal Temperament
3. A tuning that uses elements of JI and ET, usually called a “Compromise Tuning”.

If you want to explore the whole range of possibilities, I would suggest picking one key harmonica that you play a lot, get three harps in that key and tune them to just, equal, and then some kind of compromise tuning. Mark them so you can easily tell which one is which, play them, and see what works for you. As you use any tuning formula, remember that what your ears tell you is as at least as important as what the tuner tells you. Tuning is an art as well as a science.

I have restricted my focus in this article to the Richter tuned diatonic harmonica. The Richter tuning is the most common tuning layout of notes for the diatonic harmonica, or “blues harp”.

The study of alternative tunings is yet another vast subject and the best source of information on that subject is:

www.patmissin.com

Pat has compiled a vast storehouse of valuable information on reed instruments in general and the harmonica in particular. I highly encourage you to check out his site and leave him a contribution for his efforts while you are there. He deserves it and you will respect yourself more in the morning if you do.