2004 P.Missin - Details

Audio Examples of Just Intonation and Equal Temperament Applied to the Harmonica

One of the questions I am most commonly asked regarding the tuning of harmonicas, is about the subject of temperament. In several pages on this site I go into some detail about this subject, however there is no substitute for actually hearing these differences. There follows a selection .mp3 audio clips of chords and scales played on the same harmonica (a standard Lee Oskar in the key of C major), but with slightly different fine tunings. The tunings presented are 12-Tone Equal Temperament (the most commonly used tuning system in modern Western music and the only tuning of which many people are aware) and three different "flavours" of Just Intonation. The differences between the JI clips are due to how the hole 5 draw reed is tuned. As explained on various pages on this site, this note (and its octave partner hole 9 draw ) can be a "problem child" for the standard major diatonic harmonica tuning. The three JI variations here are the traditional 7-limit tuning (where the 5 draw is substantially flatter than its 12TET equivalent), a 19-limit version (where the 5 draw is tuned almost the same as its 12TET equivalent) and a 5-limit version (where the 5 draw is tuned higher than its 12TET equivalent). All of them have their advantages and disadvantages.


C major scale in traditional 7-limit Just Intonation
C major scale in 19-limit Just Intonation
C major scale in Equal Temperament
C major scale in 5-limit Just Intonation

The first scale is played with the harp in 7-limit Just Intonation, the traditional tuning for diatonic harmonicas. You may notice that the fourth of the scale (the 5 draw reed) sounds a little flat. The second example also uses Just Intonation, but with the 5 draw reed tuned as a 19-limit note, quite close to its Equal Tempered value. This makes the scale sound a bit more natural, although it does add some roughness to the chords (see below). The third example is in strict equal temperament, but when played unaccompanied, most people would be unable to tell it from the second example. The fourth example is in Just Intonation, this time with 5 draw tuned as a 5-limit note. Some ears might find it to be tuned a little sharper than they would like. Of course, when playing music on the harmonica (as opposed to demonstrating tunings) any notes that are a little sharp can be bent downwards into tune, although it is of course not possible to bend flat notes upwards.


Holes 2, 3 and 4 draw in Just Intonation
Holes 2, 3 and 4 draw in Equal Temperament

This is a G major triad - you should be able to hear that the JI version is a lot smoother than the ET version (there should really be no beating at all, but few things in this world are totally perfect...!). In fact, many (most?) people would say that the tempered version sounds "out of tune".


Holes 3, 4 and 5 draw in 7-limit Just Intonation
Holes 3, 4 and 5 draw in 19-limit Just Intonation
Holes 3, 4 and 5 draw in Equal Temperament
Holes 3, 4 and 5 draw in 5-limit Just Intonation

Again, the first example should sound a lot smoother than the others.


Holes 4, 5 and 6 draw in 7-limit Just Intonation
Holes 4, 5 and 6 draw in 19-limit Just Intonation
Holes 4, 5 and 6 draw in Equal Temperament
Holes 4, 5 and 6 draw in 5-limit Just Intonation

Things start to get a little interesting here. The first example is very smooth, but strictly speaking it is a sub-minor triad rather than a minor triad, so it may be inappropriate for certain contexts. It would generally sound better when used as the upper tones of a G9 chord than as a Dm triad in its own right. The 19-limit example sounds rougher, but not horribly unpleasant, giving a chord with the ratio 16:19:24, which many find to be a very good voicing of a minor triad. The 12TET version is quite close to the 19-limit JI version and gives a good example of how 12TET minor chords tend to sound somewhat better than 12TET major chords. The 5-limit JI version givs a chord in the ratio 10:12:15 which is actually a pure minor chord. It may sound a little strange because of the difference tones - something which is explained in some detail on this page.


Holes 5, 6 and 7 draw in 7-limit Just Intonation
Holes 5, 6 and 7 draw in 19-limit Just Intonation
Holes 5, 6 and 7 draw in Equal Temperament
Holes 5, 6 and 7 draw in 5-limit Just Intonation

The first one should sound quite smooth, all the others quite harsh.


Holes 6, 7 and 8 draw in Just Intonation
Holes 6, 7 and 8 draw in Equal Temperament

You be the judge...


For more information on the subject of Just Intonation, check out the web site of The Just Intonation Network


Return to Tunings PageReturn to Main Index