Music Theory De-mystified Blogbeats

The Secret To Tuning: How To Tune An Instrument To A Reference Note

Have you ever had trouble tuning to another instrument? If so, read on…

In any ensemble, big or small, all the instruments need to be in tune with each other. If not, no matter how skilled the players, the music will not sound musical.

Who Tunes To What?

All the players need to agree on a pitch reference that everyone can tune to. This can be an external source, such as a tuner, or one of the instruments.

If your instrument is tuneable, you can tune a note on your instrument by matching it to the same note on a tuner or other instrument. We do this by listening for a disturbance called beating.

If you have a fixed pitch instrument such as a piano, your instrument becomes the reference and others tune to you.

Note: On fretted string instruments such as guitar or bass, once you’ve tuned one string to an external reference you can play a fretted note on that string as the reference for the next higher string and progressively tune the other strings.

How to Tune To A Reference Note: The Difference Frequency

When two (or more) notes are played together their sound waves combine. This combination wave has a frequency which is the difference between the frequencies of the two notes.

If the two notes are identical, there is no difference frequency. The notes lock together and sound like one louder note.

If your note is almost but not quite the same pitch as the reference note, the individual frequencies take many cycles before they match. This results in a very low (slow) difference frequency. The closer to unison, the lower the difference frequency.

Here is a diagram of 2 notes of nearly the same pitch (blue and green). Up/down represents amplitude. We hear amplitude as volume.

The difference frequency is produced by the overall shape of the composite waveform, shown here in yellow.

Look at the composite (yellow) wave:

where both notes go up or down together, the composite wave is taller/louder
Where they oppose each other, the composite wave is shorter/quieter
If they oppose each other by the same amount, there is silence

Over one cycle, the composite wave gradually shifts from loud to silent (or near-silent) and back, creating a pulse.

Beating

We can hear the difference frequency as a pulse known as beating or beats. When both notes match, there is no pulse. When they’re almost in tune, there’s a slow, gentle pulse, maybe only 1 or 2 Hz (times per second).

As you tune your note away from the reference, the pulse becomes faster and the beating effect becomes more noticeable. This happens quite quickly, so make gradual adjustments!

Note: once the pulse is faster than 20 Hz we can’t hear the individual beats anymore. Instead, we start to hear two distinctly different notes. By now we’ve gone way too far…

Tuning the other way, as you get closer to matching the reference, the pulse slows down, then disappears when you’re in tune.

Example

Here is an example using 2 synthesiser notes, starting off in unison. After a couple of seconds, one note drifts flat, then back to unison, then sharp, before returning back to unison. I have chosen this sound because, like an organ, the notes don’t decay.

In the above example, the note is only just over a quarter of a semitone out at the furthest points. By then we can hear that the note sounds distinctly out of tune.

Sharp Or Flat? Listen For The Beats

Note that the beating effect is the same whether your note is slightly sharp or slightly flat. The beating only indicates how far you’re out: faster means further out, slower means closer.

Method

As you adjust your note, listen to the beating. Is it getting faster or slower?

If the beating becomes faster, you’re getting farther out of tune. Change the direction of your adjustment; tune the other way.
If the beating becomes slower, you’re getting closer to being in tune. Keep going. When the beating is slow, adjust more carefully.
When the beating is gone, the two notes will sound as one. Even with an electronic tuner, where the timbre of the reference is nothing like your instrument, the notes will feel like they’ve locked together.

If you’re not sure whether you’re sharp or flat, keep going in the same direction! Sooner or later it will either lock in because it’s in tune or the beating will have become fast and obvious enough to tell you that you’ve gone too far and you need to turn around.

Make slow, gradual adjustments as you listen.

Above all, don’t panic! If you make random adjustments you may end up tuning to a different note altogether, or you may end up going back and forth without ever reaching the note.

Stay calm, listen for the beating and stick to the method outlined above.

Plucked Strings Take Note

Beating is more noticeable when the notes sustain well. On many acoustic plucked string instruments, notes don’t sustain for long before they fade away.

One solution to this is to play repeated notes; each note long enough to hear the beating but not so long that they die down. For an acoustic guitar, once every 3 or 4 seconds should work. Instruments with a small body and nylon strings, such as the ukulele, have less sustain and you will need to play more frequent, louder notes in order to hear the beating clearly.

What Note Do We Tune To?

It doesn’t really matter what the note is, as long as everyone agrees. Different instruments find certain notes easier to play than others. Ideally, the note used for tuning is an easy note for all involved.

A 440 – Concert Pitch

It’s possible for a keyboard or tuner to play different notes for different instruments to tune to. However, the tuning process is much quicker and more straightforward if everyone tunes to the same note. This is particularly true for large ensembles such as orchestras.

The closest to a universal tuning standard is A 440 Hz, or just A 440, also known as concert pitch.

Lower instruments can match A in a lower octave. Beating works when tuning notes at different octaves just as it does in unison.

Are Instruments Always Tuned To Concert Pitch?

The short answer is no.

Over the centuries the tuning reference has varied considerably, both above and below the current 440Hz. Some ensembles specialising in period music will use the appropriate pitch reference for the era.

More generally, apart from digital instruments, fixed pitch instruments don’t stay perfectly in tune forever and may end up sharp or flat overall. All other players will need to tune by ear to make sure they are in tune with that instrument.

As long as everyone tunes to a common reference, it doesn’t matter whether it’s in concert pitch or not.

Note: Beating can also be heard when other consonant intervals like a perfect 5th or perfect 4th are out of tune. You can tune to these intervals in the same way as tuning to unison.

If you found this post helpful, please feel welcome to like, share or leave a comment. If you have any questions, leave them as a comment and I’ll respond as soon as I can. To stay up to date with new posts, please subscribe.

5. How Long Is A Note? Note Values 1

This post is one of a 2-part series of free basic music theory lessons on my blog, musictheoryde-mystified.com. You can see the complete list here. Please feel welcome to make a comment or ask a question.

Note Length

In 3. Beats, Tempo And Timing we saw that the length of a note is counted in beats, and that the length of a beat is determined by the tempo. For instance, when the tempo is 60 bpm (beats per minute), 1 beat is 1 second long: for a tempo of 120 bpm, 1 beat is 1/2 second long. Notes can be any length, from a number of beats to a fraction of a beat.

Note Values

Although we count in beats, not all notes are a beat, or even a whole number of beats, in length. Some are longer, some shorter.

The symbols for note length are called note values. How we interpret these symbols depends on the time signature. Time signatures are a subject for a later post, but let me say for now that the most popular time signature, common time, as well as several others, use the crotchet (quarter note) to represent one beat. For the rest of this post I will refer to a crotchet as 1 beat.

Tempo markings often include the note value which represents 1 beat. When a crotchet = 1 beat, a tempo of 60 bpm is indicated as follows:

60 crotchet beats per minute

Funny Names

There is both an English and an American name for each note value. The American name is a fraction based on a whole note equaling the number 1 (1 = whole). The next shorter shorter note is half its length and is called a half note, etc. The “1” refers to 1 bar in the most common time signature of all, 4/4, which has 4 beats per bar.

The English names are old-fashioned names meaning various degrees of “short”, harking back to the original Medieval runes and the gradual evolution of note symbols since.

On the whole I will be using the English names to avoid confusion between a half note and half a beat, etc. However, I recommend learning the American names as well: note values as fractions are the key to interpreting time signatures. In the table below, I have listed both names.

Table of Note Values

The following table lists the most common note values from longest to shortest. The “Usual Length” column shows the length in beats in common time.

Regardless of time signature, the note values are always proportional to each other. Each note value in the table always equals two of the note value below it. A semibreve = 2 minims, a minim = 2 crotchets etc.

The longest note value is called a semibreve because originally there was an even longer note, the breve. The breve is seldom used these days because, at 8 beats long, most time signatures don’t have bars long enough to be able to fit a breve within a bar.

Don’t be daunted by all these symbols. Just focus on the note values that are 1 beat or longer to start with; the ones bordered in green. It’s much easier to add beats together to play longer notes than to divide a beat into halves or quarters. Later you can include quavers, and eventually, semiquavers. Demisemiquavers are much less common.

Stem direction

All but the longest note values have a stem. The stems in the above tables are shown as extending upward from the notehead.

In 2. Notes On a Stave: Pitch we saw that on a stave, the stem’s position and direction depends on where the notehead sits on the stave.

Notes which are on or above the middle line of the stave have their stems on the left of the notehead, extending down.
Notes below the middle line of the stave have their stems on the right of the notehead, extending up.

Tails and beams are always at the outer end of the stem.

Tails and Beams

Notes shorter than a crotchet have a tail. The shorter the note, the more lines make up the tail. When there are several short notes in succession, their tails are joined together to form a beam. Beams generally join the notes in 1-beat groups such as 2 quavers, 4 semiquavers etc. This allows us to see which notes are on the beats, making the music easier to follow. It’s also a cleaner, less cluttered look.

The exception is quavers/ eighth notes, which can be joined together in one-, two- or even three-beat groups.

Below is an example of the different note values, with the shorter notes beamed in groups. In this example the quavers are beamed in groups of 2 beats (4 quavers).

The vertical lines, called barlines, occur every 4 beats, as in the time signature 4/4. In 4/4, a semibreve lasts for 1 bar.

As you listen, you will hear a metronome tick at 80 bpm and repeated notes of the different note values played over it. The use of different note pitches is just for listening convenience.

Notice that the demisemiquavers have only their outer tail beamed in whole beats: the inner tails are beamed in half-beats. This is a popular convention for an even cleaner look but not necessary. Some publishers beam all demisemiquaver tails in whole beats.

Dotted Notes

A note can be any length. For example, we may want a note to last for 3 beats rather than 2 or 4 beats. One option is to use a dotted note.

Each note value can have a dot beside it, to the right. The dot adds half the length of the note value: the dotted note is one and a half times the length of the note without the dot. Effectively, the dot represents the note value directly below the note in the note value table above. For example, a dotted minim (3 beats) = a minim (2 beats) plus a crotchet (1 beat).

The best way to get used to note values is to try to play some written music; notation means nothing until you try to play what you see. Start with something simple such as a children’s song or a melody that you’re very familiar with. If that seems too difficult, please visit my earlier post, 3. Beats, Tempo and Timing, which has some simple timing exercises that might provide a good starting point.

For more, see 7. Rest Values, How To Count Rests. In upcoming posts I hope to provide more information on note length, time signatures and rhythm.

Please feel welcome to like, comment or to share this post. If you have any questions, pleased leave them as a comment and I will respond as soon as I can. If you enjoy my posts and would like to be kept up to date, please subscribe.

The movie is taken from Music Theory De-mystified, my upcoming music theory e-book, due to be released in 2023.

NEXT LESSON: 6. Time Signatures 1 – Simple Time

PART 1 CONTENTS: Basic Music Theory Course Contents

4. Bars, How To Count In Bars And Beats

Structure

When we listen to music, we can generally “follow the music”: we have a sense of where we are within the piece. This is because, other than ambient music, much of what we recognise as music has a structure. Let’s zoom in on a piece from the outside…

Most pieces are made up of sections. In a popular work a typical section might be a verse, chorus or bridge. A classical work might have large-scale sections called movements as well as smaller sections within a movement such as exposition, development and recapitulation.

Within each section, the music is made up of phrases. In the language of music, phrases are the equivalent of phrases in speech. Question marks, full stops and commas all have their musical equivalent.

In music, each phrase is typically made up of a number of bars. Bars provide a way of dividing a phrase up into manageable chunks that we can see and hear.

In Western music culture we seem to be attracted to the number 4. Phrases in many genres are often 4 bars long. In a typical 4-bar phrase, we can feel the phrase get started in the first bar and arrive at a note or chord in the 4th bar. Please note that this is a very general statement for illustration purposes: music is certainly not restricted to phrases of 4 bars, or even of a whole number of bars. Overall, though, many melodies are made up of 4-bar phrases.

Bars

Each bar is made up of a number of beats. Usually all the bars in a section have the same number of beats (but again this isn’t always the case). The boundary between one bar and the next is marked by a vertical line through the stave called a barline. Barlines are convenient markers to help navigate through the notes. Without barlines it would be easy to get lost when trying to read music.

The following example has bars which are 4 beats long:

Bars aren’t just visual: they form part of the structure of the music. Not only can we count the number of bars in a phrase, but we can count the number of beats in a bar. The beats are a reference for where we are in a bar, just as bars are a reference for where we are in a phrase.

A bar can be any number of beats in length but if a bar is too long we feel the need to mentally divide it into smaller chunks. Bars are easiest to feel when they have a small number of beats. Most typically, bars are made up of 2, 3 or 4 beats.

The first beat of a bar has an implied emphasis. This can be articulated in the music by making the note on the first beat of each bar stronger/louder. Even when the music is intended to be played smoothly and evenly, musicians tend to “play” that emphasis in their mind as they count.

Counting in bars and beats

Being able to count or tap to the music in beats and bars is an essential skill for the aspiring musician. In the previous post, 3. Beats, Tempo and Timing, we looked at some basic counting exercises. There we counted to 2, so there were 2 beats in each bar.

Try This…

As a quick exercise, listen to a piece of music you enjoy and tap where you feel the beats might go. Once you settle into the tempo, try counting “1,2”, then “1,2,3” then “1,2,3,4” and see which of these seems to fit the structure of the phrases. As you count, emphasise “1” a little.

If the piece has a rhythmic accompaniment, beat 1 might be emphasised by one or more of the accompanying instruments. For instance, in a typical rock song, the bass drum plays the first beat of the bar. Even without such accompaniment, the right number of beats per bar will “make sense” and fit the phrases, whereas the wrong number will, at times, feel out of step.

As 4 is two lots of 2, the difference between counting to 2 and to 4 isn’t always obvious, but counting to 3 feels quite different than 2 or 4.

Example

Below is the audio only for two simple melodies. One has 2 beats per bar, the other has 3. Listen to both and count “1,2” or “1,2,3”. See if you can tell which is which… (the answer is at the end of this post).

NOTE: Both melodies are at a medium-fast tempo but the tempo is slightly different for each. For each melody, listen first and tap along to the tempo. Only start counting when you feel that you’ve settled in to the tempo.

This post is one of a growing series of free basic music theory lessons on my blog, musictheoryde-mystified.com. You can see the complete list here.

Parts of this post, including the movie above, are taken from Music Theory De-mystified, my upcoming music theory e-book, due to be released late 2023.

NEXT LESSON: 5. How Long Is A Note? Note Values 1

PART 1 CONTENTS: Basic Music Theory Course Contents

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Answer: The first melody has 3 beats per bar, the second melody has 2 beats per bar.