Intonation is the ability to play in tune. When we compare one note to another, how do we decide whether they sound in tune?
If the two notes are in unison and played together, the answer is easy. They’re in tune when they match. When two unison notes played together are in tune, their frequencies match and they sound like one louder note.
When they’re slightly different, two notes produce a difference frequency which we can hear as anything from a slow, swishing pulse to a more rapid, tremolo-like effect known as beating or beats. For more, including an audio example, please visit The Secret To Tuning: How To Tune An Instrument To A Reference Note.
If the notes are not in unison, how you play in tune depends on the context.
Playing In Tune
First, let me state the obvious. Fixed pitch instruments such as keyboards are unable to adjust their pitch on the fly. Playing in tune is entirely dependent on how well and how recently the instrument has been tuned. We’ll look at how they are tuned later in this post.
Two Types Of Intervals
An interval is the pitch difference between two notes.
- When two notes are played one after the other, as in a melody, it is called a melodic (horizontal) interval.
- When two notes are played together, either on a polyphonic instrument or on two instruments, it is called a harmonic (vertical) interval.
Other than solo melodies, music consists of both melodic and harmonic intervals. Melodic intervals make up the flow of a part as you move through time and harmonic intervals are the parts interacting at any given moment, such as a melody note with a bass note or the notes of a chord with each other.
Generally, it’s easier to tune to a harmonic interval because, to varying degrees, we can hear the sound waves interact, much like when tuning to unison.
Melodic intervals are easier to tune to if we can clearly recognise the key. One way to do this is to warm up on a scale in the same key as the passage you’re playing.
Two Types Of Intonation
Just Intonation
The earliest forms of music revolved around a single note; the root note or tonic. Other notes flowed towards or away from the tonic so the focus in tuning was on how well the other notes fit the root note.
Any harmonic interval has a “best fit”. Most intervals can be tuned to simple frequency ratios by listening to the difference frequency and adjusting the note so there is no beating effect. The stable sound makes chords extra strong and rich.
So why don’t we use just intonation all the time?
Just intonation is great while tuning to one root note, but over time Western music developed into a more outgoing direction. Rather than stay in one key all the time, melodies ventured from one key to another, exploring the relationships between different keys and chords.
The Problem With Just Intonation
With just intonation, the farther you move away from the original key, the more out of tune the notes sound. What’s more, the semitones aren’t even all the same size!
The simple ratios of just intonation only work while the reference note is that of the key you’re in. To change keys, you need to change the tuning of the notes on the fly…
If you work out the frequency of every note using just intonation, by the time you get back to the starting note the frequency is significantly different!
Equal Temperament
The solution to playing in multiple keys is equal temperament. In equal temperament, the cumulative error over all keys is averaged out. All semitones are musically the same size. In equal temperament music can be played in any key and pieces can travel from key to key with every note sounding equally in tune.
No single interval is perfectly in tune as far as difference frequencies go but the amount is so small that we don’t hear it as beating. The only thing we might notice is a slight softening of the clearest intervals such as perfect 5th which, if anything, adds a sense of warmth.
Equal temperament is perfect for keyboards and other fixed pitch instruments and is widely accepted as the predominant tuning system in Western music.
Tuning On The Fly
Small consorts, in particular string quartets and small vocal ensembles, have a reputation for being able to play perfectly in tune.
This is achieved by combining the best of both worlds. Equal temperament is great for melodic intervals as the music progresses through time, while just intonation can be used to fine tune harmonic intervals to suit a chord at a given moment.
The ultimate guide is your ear. In any key, any note has a best fit. Be responsive to what you hear and you’ll find that best fit.
Feeling a bit nerdy? If you’d like to know a bit more about just intonation and equal temperament, please visit the Shop page for a FREE DOWNLOAD of my e-book, Intonation: From Pythagoras To Equal Temperament.
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