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Equal Temperament vs. Just Intonation - Which is Better for Harmonica?


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Hello! In today's harmonica lesson we'll explore the difference between Equal Temperament and Just Intonation, and discover which of these tuning methods works best for harmonica.


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One crucial feature that influences the harmonica's amazing sonic character is its tuning system. This is true both in the broader sense of note selection, and in a fine tuning sense of working out exactly how to tune a specific note. We'll be looking at this second sense today.


But surely a C is a C is a C?

It's actually a common misconception that there is a universal concept of what a note's exact pitch should be. In fact, different tuning systems exist in different historical eras and geographical areas.


The two most prominant tuning systems used in western popular music are Just Intonation and Equal Temperament. Each tuning system imparts distinct qualities to the harmonica's sound, making it a fascinating subject for exploration. In this article, we'll delve into the concepts of Just Intonation and Equal Temperament, their relevance for the harmonica, and the differences they make in the instrument's sound and the musical styles they suit.


Just Intonation

Just Intonation is a traditional tuning system based on pure mathematical ratios between frequencies. In this system, musical intervals (the distances between notes) are tuned to simple whole number ratios. This works great for simple music without modulation or complex chord progressions, and for this reason was used widely in earlier eras of traditional folk music up to and including the 1500's, and is still popular with instruments that can tune to each other easily. It creates beautiful chords and perfect harmonies. Here's a diagram of the ratios used for each interval:

Just intonation frequency ratios

Just Intonation is - in a sense - a natural phenomena, because it occurs as a result of the natural overtone series. To learn more about this, read this great article on The Physics of Music.


While just intonation creates beautifully pure harmonies, it leads to a problem if you want to play in different keys: the intervals are only perfect in one key, so change key and they will sound out of tune.


Equal Temperament

Equal Temperament, on the other hand, is a tuning system that divides the octave into 12 equal parts, resulting in all semitones being equally spaced. See below:

Equal temperament inteval distances in cents

This allows you to play scales in all different keys without experiencing the tuning problems that would surface with just intonation.


However, the intervals will not sound as beautiful or true. Essentially, everything (except the octave) is slightly out-of-tune, but you avoid a situation where some notes are absolutely perfect and others are way, way off. Every key you play in will sound equally good ... or bad! It is definitely a double-edged sword.


The development of Equal Temperament mirrored the movement to playing more complex musical styles from the 1600's onwards. Modern ears have become more accustomed to this tuning because modern pianos (and lots of other instruments) are tuned this way.


Check out this table of Equal Temp frequency ratios


A quick note on big scary words

I'm keen to keep this article easy to read. I hope you haven't been too confused by the terms I've used so far. I could go into a lot more detail about pitch, overtones, cents and more, but I think we'll get the crucial information without needing to define all those terms. If you'd like to go into more depth with the theory, check out this excellent article from Hod Rod Harmonicas.


Relevance for the Harmonica

The harmonica is a strange beast: it plays single notes and chords, and is used for a range of styles both rhythmically and melodically. Even more interestingly, it's a diatonic instrument so it's available in multiple keys. Everything to do with tuning is kind of exaggerated with the harmonica: if it sounds good, it sounds really good. If it's bad, it's really bad. These characteristics make the choice between Just Intonation and Equal Temperament a particularly important one. Let's explore how each tuning system affects the harmonica's sound and its suitability for various styles.


Just Intonation and the Harmonica

Just Intonation can enhance the harmonica's natural resonance, creating rich and pure harmonies. When certain notes or chords are played, the harmonics produced are closely aligned with fundamental frequencies, resulting in a warm and expressive sound. This tuning is especially well-suited for folk, blues, and traditional music, where the emotive qualities of the harmonica shine through in simple melodies and easy chord progressions.


Equal Temperament and the Harmonica

Equal Temperament tuning is more versatile for playing in various keys on the harmonica. Since each note is adjusted slightly from its pure ratio, it ensures that playing in any key sounds relatively consistent in terms of tuning. This makes the harmonica adaptable to different genres like jazz and classical, where modulation and key changes are common. The trade-off is that the harmonies might not be as pure as in Just Intonation, most notable if you are chugging or playing chords.


Want to hear the difference? Visit Pat Missin's great Audio Examples


Which tuning for my playing style?

So what are the differences between harmonicas tuned to Just Intonation and Equal Temperament? Here's a quick rundown:


Just Intonation Harmonica Sound

  • Pure and resonant harmonies.

  • Intervals sound "in tune" and naturally connected.

  • Well-suited for chords, chugging and simple chord progressions.

  • Single note melodies may sound out of tune.


Equal Temperament Harmonica Sound

  • Equally spaced semitones, facilitating key changes.

  • Versatile for playing in different positions.

  • Suitable for complex musical forms like jazz and classical music.

  • Chords and intervals will not ring as beautifully true.


Which harmonicas are tuned to Equal Temperament?

The most well-known Equal Temperament harmonica is the Hohner Golden Melody, so-called because of its suitability for melodic (rather than rhythmic) playing. Lee Oskar harmonicas are also tuned to Equal Temp. Below is a diagram of the tuning showing the offset in cents. This is a rather pointless diagram because there is no offset - all notes are equally spaced - though it does illustrate the difference from the Just Intonation diagram you'll see in the next section:

Equal temperament harmonica tuning offset

Melodies will sound sweet on these instruments, but the chords will sound rattly or jangly.


Which harmonicas are tuned to Just Intonation?

Up to the 1950s, harmonicas were more closely tuned to Just Intonation (this was before attempts to pacify modern playing styles). Here's an example of the sort of tuning offset you would have got in the 1950's:

Just intonation harmonica tuning offset

You can see that some notes are significantly flatter or sharper than on the Equal Temp harmonica. Harmonicas tuned to a true just intonation would give you lovely rich chords but melodies may sound off.


These days, most harmonicas are actually tuned somewhere between Equal Temp and Just Intonation. This is called a compromise tuning. Some harp will be closer to one tuning, some to the other - and in fact different areas of the instrument may be tuned differently to suit a certain playing style. If any of the chords are perfectly harmonised, it's usually at the bottom end of the instrument because that's where players are more likely to want them. There is no 'perfect' compromise tuning - the clue is in the name!


Compare the tuning of popular models in Örjan Hansson's Theory of Harmonica Tuning


Does fine-tuning really matter?

The answer to 'does harmonica tuning really matter?' is entirely down to your own ears. If you like the sound, who cares how it's tuned?! You might not notice a huge differece between tunings, at least when comparing absolute pitch. However, when hearing chords even an untrained ear can usually tell a good one from a bad one.


The reality is that even though harmonicas are said to conform to a certain temperament, manufacturing failures and the rough and tumble of postage mean that when you get your hands on a new harp, it's unlikely to be tuned exactly as advertised. In fact, some players (re)tune a harmonica as soon as they buy it. Even if you've got a tuning you're happy with, temperature and playing force will still affect the pitch of the reeds.


Your perfect tuning will depend on the mix of single note melodies, chords and octave splits that you use, as well as the complexity of the music you play. In the end, only you can decide!


Check out Andrew Zajac's article on creating your perfect tuning


Conclusion

The choice between Just Intonation and Equal Temperament tunings will influence the harmonica's sound and its compatibility with different musical styles. Just Intonation offers pure harmonies that are emotionally resonant, making it ideal for genres rooted in tradition and heartfelt expression. Equal Temperament, with its adaptability across keys, caters more to complex musical styles and unusual positions.


I hope this article has helped you understand a little about these different tuning systems, and which might be best for you.


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