Tag: demystified

B1. Syncopation Basics: Playing Off The Beat

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. Please feel welcome to make a comment or ask a question.

A time signature has an inherent hierarchy of strong and weak points within the bar. Syncopation is the emphasis of weak parts of the time signature. This introduces a dynamic interaction between the time signature’s implied rhythm and the rhythm of the part; a sense of going “against the grain”.

The Back Beat

The simplest form of syncopation is to emphasise the weak beats instead of the strong beats. The classic example of this can be found in many popular music genres since the advent of rock & roll; the snare drum playing the “back beat”, emphasising beats 2 and 4 in a 4-beat bar.

A similar effect can be achieved on any instrument by accenting the weak beats. Below is an example of a quaver rhythm, first with accents on the strong beats, then on the weak beats. 

Tap, clap or play along to the following rhythms:

Playing Off The Beat

The back beat is only syncopation in the broadest sense. The term syncopation typically refers to emphasising weak parts within the beat a rather than just the weak beats.

The most common example of syncopation within the beat is to emphasise the 2nd quaver of each beat, the “off-beats” or “and”s, instead of the beat itself. 

The following example of a bar of quavers uses accents, first to emphasise each beat, then to emphasise each off-beat quaver. Listen to the rhythms then tap, clap or play along:

Listen again and this time, only tap on the accented notes.

Syncopation adds excitement to a rhythm. Even in rhythms which are largely on the beat, the odd syncopated moment adds life to a part. 

In the drum rhythm below, there is a brief syncopation is in the second half of bars 2 and 4.

Ways To Syncopate

Syncopation can be achieved in 2 ways: 

  • by emphasising a note or notes on a weak part of the bar as above, with an accent.
  • by de-emphasising a strong part of the bar, in particular by not playing a note there at all. This can be because there’s a rest or because the previous note is still sounding.

Note that when clapping or tapping, there is no audible difference between these two bars.

Zooming In

Syncopation doesn’t just refer to emphasising the off-beat quavers. A more aggressive version would be to syncopate by a semiquaver.

A couple of the rhythms we learnt in 20. How To Read Rhythms 1 had semiquaver syncopation within the beat, by not playing a note on the “and”, the 2nd quaver. We can see now why these felt harder to learn than the others… Here’s an example of a bar with these two rhythms. Tap or play along:

Once you’ve experienced it, syncopation feels quite “natural”. In many popular genres, singers seldom sing exactly on the beat, even if that’s how the melody is written. Instead, they instinctively apply a degree of syncopation so the melody doesn’t sound too rigid. Rhythmic players rely on syncopation to add dynamics and drive.

Learning To Syncopate

Like many rhythms, syncopation is best learnt initially using a metronome. The secret to being able to syncopate is to feel the beat – to know where the beat (or strong beat) is, and then to know what relationship your note has to the beat.

Some musicians find it easy to tap the beat with their foot while playing. If this works for you, then by all means tap instead of using a metronome. However, many find it awkward to tap on the beat while playing off the beat, especially when first learning a new rhythm.

Foot Tapping Tip: In simple time, use the action of lifting your toes between taps to represent the half-beats; the “and”s.

If the rhythm seems tricky, remember to slow down the tempo and zoom in, as discussed in 20. How To Read Rhythms 1.

Ultimately, once you know a rhythm well enough to be able to feel it, you will no longer need the metronome. Metronomes can become quite annoying over time(!) so it’s worth weaning yourself off it as soon as you can feel the rhythm properly.

Mixed rhythms

Many parts, rhythmic as well as melodic, have a degree of variation in their rhythm, often achieved by brief syncopations in between overall on-beat rhythms.

Try These…

  • Play the movies below and tap the rhythms with your hand on a bench top, or if you prefer, clap. Listen carefully to the metronome click so you remain aware of the beat…
  • Once you’ve learnt each rhythm, play it to a metronome at 60 bpm without the movie. Gradually increase the tempo to 100 bpm or more. You can play along to the following movies of the rhythms at 100 bpm to see how you went.
  • Being able to tap the beats with your foot while playing is a useful skill. Practice tapping the beats with your foot, together with the metronome, while playing or tapping/clapping the above rhythms with your hands. As you settle in, stop the metronome and try it by yourself.

Notation Tip

Rhythms are usually notated so that it’s clear to see where the beats are. For shorter notes, this is indicated by beaming. For longer notes, the note is split into shorter notes and joined by a tie (see 21. Note Values 2: Ties). 

When crotchets fall halfway between beats, on the “and”s, they can be written as crotchets: it’s such a common occurrence that most musicians, once they see a crotchet after a single quaver or quaver rest, are familiar with this shortcut. 

However, crotchets which are a semiquaver off the beat must be split and tied to show where the beats are, otherwise the music is too hard to follow.

In the correct example above we can see that the next note starts just after each beat. The position of each beat is clearly shown by the beaming.

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 wth new posts, please subscribe.

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.

NEXT LESSON: B2. Intervals 2: Augmented And Diminished Intervals

PART 2 CONTENTS: Basic Music Theory Course Contents

How Can We Tell Which Key We’re In?

This post is one of a growing series of holistic investigations into various aspects of music theory. The full list can be found in the Posts page under the category Music Theory De-Mystified.

All comments are welcome. If you enjoy my post, please give it a like and share it or subscribe to my blog.

First I should say that there are two separate subjects here: the overall key and the key at a given point in the piece such as a visiting key. For the purpose of this post I’ll focus on overall key and assume a fairly simple melody but in principle, the same applies to sections and even individual phrases within the piece.

If you’re looking for a quick answer, scroll down to the summary.

When we play a scale, it’s easy to tell what the key is: it’s a combination of the root note and the mode. If we start and finish on C and play the major scale pattern of .2.2.1.2.2.2.1. (semitones), we’re in C major: C major is the major mode built on C.

But how can we hear/feel what key we’re in when the order of the notes varies, as in a melody?

If you’re reading notation, you could say, “look at the key signature”. This is true, but it’s only part of the answer. Within a key signature there are many possible tonalities. Even considering only the major and minor modes, you still need to find the right choice, to help interpret the music correctly. And if you’re listening or playing by ear, you need to be able to “feel” the key.

Look for the root note

To do this, we need to know what the root note is. For a given key signature (set of notes that make up a scale), the mode is determined by where we start the pattern i.e. the root note.

“The Spokes Of A Scale”

The best way to think of a scale is not as a strip of notes lying next to each other but as a series of spokes with the root note at the centre and the other notes around it. The double lines in the following diagram indicate the special bond between the root note and its octave (where the pattern repeats) and between the root note and the perfect 5th (more on that later in this post).

“The spokes of a scale”, diagram of the connections between the notes of a scale
“The Spokes of a Scale” over 3 octaves

(…I see it as a kind of spiral staircase extending up and down the octaves like storeys of an apartment block, where notes on the central column are octaves of the root note…)

Root Note Power

In a piece of music, it’s as much about the relationship of each note to the root note as it is from each note to the next. To be able to feel the key we need to be able to feel the root note.

There’s a good chance that the root note is first, or at least among the first few notes, and also at or near the end, but it’s not always the case. Fortunately there are many other ways it can be pointed out in a melody.

Longest, Strongest and Most 

In a melody, other than first and last, these are the three main ways we can highlight the root note.

Longest

Duration is power. Out of a series of different length notes, the longer notes are more prominent. If the root note is a long note it will stand out in the crowd.

Strongest

One way to emphasise the root note is to give it strength. There are two ways to do this:

  1. by playing that note louder than the others or giving the note an accent (a strong attack).
  2. by making the root note appear on the strongest parts of the bar. Time signatures have an implied hierarchy of strong and weak points- a default rhythm, if you like. Placing the root note on beat 1 gives it the most strength. In 3/4 and 4/4, beat 3 is also naturally strong. Similarly, on-beat quavers are naturally stronger than off-beat quavers.

Most 

Another way to reinforce the root note is to keep coming back to it. The more often we hear it compared to surrounding notes, the more we believe it.

Examples

Here are a few single-phrase “melodies” using just a single technique to highlight the root note. For the following examples, as you listen, try to hum the note that feels like the root note. Bear in mind that no single note will fit all the time. What we’re looking for is the note that fits most of the time. When you stop listening, which single note would you remember? Try a few if you’re not sure…

The examples are all in C major, so if the techniques I have described are effective, C should feel like the root note.

To make it a fair test, I have tried to make the (mini) melodies fairly random apart from the parameter we’re testing, so they’re not great. Real composers use a combination of these techniques when creating a melody.

Longest
Strongest
Most

Lowest & Highest, Direction 

Although not as significant overall, the lowest and highest notes of a passage within the melody will be naturally emphasised. I see this more as a sense of direction. When listening, we follow the direction of a scale-like series of notes, upward or downward, to its destination. The series directs us to the destination, giving that last note emphasis, before changing direction. 

A scale played ascending then descending is as good an example of this as any. Scales are essentially very simple melodies with no detours.

Lowest, highest, direction

Harmonic Reinforcement 

The perfect 5th, a great support act

The 5th note of a scale is almost as special as the root note itself and warrants a post of its own. I will say that it has both the capacity to blend well with the root note to support it (even if the notes are one after the other rather than played together) and to be a convenient destination for the melody to visit, a temporary root note of its own.

As a supporting note it is second to none. A 5th nearby will reinforce the presence of the root note by “pointing to it”. The 3rd note, especially the major 3rd, can also help in this way.

Some melodies place all 3 notes of the home key’s triad (chord) near each other, virtually acting as an arpeggiated chord, providing an even stronger emphasis.

Harmonic reinforcement from the perfect 5th

Accompaniment 

We haven’t talked about chords yet. Chords have an enormous say in what feels like home. Chords (at least the basic types) feature the three most important notes of a key, the 1st (the root note), the 3rd and the 5th. These notes blend so well together that they reinforce the chord’s root note. 

While the chord sounds (if it sounds for long enough), it’s hard not to feel that its root note is, temporarily, the root note of the piece.

The most prominent chord overall, especially towards the beginning and end of the piece, is generally that of the home key.

Other chords can also feel like home for a while if they sound for long enough, providing visiting points in the melody. This is one of the tools a composer can use to create music that has a journey, a sense of going places, rather than being stuck at home the whole time like a COVID lockdown.

The techniques described in this section are also used to establish the new key after a modulation (key change).

Even when no chords are played, the melody’s sense of direction and use of the above techniques can suggest some of these temporary keys. Chords can also be played melodically, as a series of notes called a triad. Many melodies are largely made up of scale-like passages and triads.

In A Nutshell

To answer the title question: look for the root note. The music makes sense when you can hear/feel how the other notes relate to the root note.

Look for a strong note or a strongly supported note early in the piece and towards the end. Feel the flow of the melody’s phrases- where the phrases start and end, which notes are emphasised. When a phrase is arriving home, you will hear it.

Once you know the root note, the mode will become evident, because you’ll interpret the other notes from the root note’s perspective. You can confirm this by playing the notes of the melody as a scale starting on the root note. If you have chosen the root note correctly, the tonality of the scale will match the overall tonality of the piece.

Much of the content is based on my upcoming music theory reference, Music Theory De-mystified, which is currently planned for release as an e-book by the end of 2022.

Please feel free to comment. I have a slightly unorthodox way of presenting music theory concepts but the concepts themselves are well established. If you like my posts, please subscribe so you can be informed of new posts.

A Melody Is A Journey

This post is one of a growing series of holistic investigations into various aspects of music theory. The full list can be found in the Posts page under the category Music Theory De-Mystified.

All comments are welcome. If you enjoy my post, please give it a like and share it or subscribe to my blog.

This is a key tenet in my approach to music theory. However, if you disagree, feel free to comment.

Most music has both a melody and chords. Even a melody by itself is usually built on chords, it’s just that we don’t hear them. We call this an implied chord progression (when no chords are written, we can deduce the likelihood of potential chords by the evidence provided in the melody such as phrase structure, the actual notes used and the use of accidentals).

A chord represents a key- at least basic major and minor chords and their common variants do. How effective they are at establishing their key depends on low long they’ve got. Yes, time. The longer the time spent on a chord, the more it feels like THE key. 

A melody is a journey. Typically it starts at home (in the home key) then travels to one or more visiting keys, represented by the main chords along the way, eventually arriving home again.

Just like a physical journey, the trip can be long or short, fast or slow, bumpy or smooth, visiting nearby or exotic places on the way. Everything that applies to a physical journey has its parallel in a musical journey.

There are three parts to any trip- the departure (including any prep such as packing), the travel and the arrival. Similarly, pieces (and the phrases within them) have a start, a middle and an end.

Time, Space and Culture Shock

A journey can be brief or extensive, or anything in between. The places you see can be familiar or exotic, near or far.

  • A trip to the local shop to get staples might be a 5-minute walk around the corner or up the street. You spend just long enough to do a common task in familiar surroundings and head back. This is the most basic journey; familiar and short.
  • You might drive across town to visit a close friend or family. Again, you are in familiar surroundings, yet you travelled beyond your immediate neighbourhood. This still feels like a small and safe journey yet you may spend hours on your visit and be surprised by the changed traffic or weather conditions coming home. A tiny bit more complex journey than the first example.
  • Maybe you’ve chosen to visit someone out of town or in another state. You might be invited to stay a few days. Longer distance means a little less familiarity: you don’t know the roads so well, where the post office is, the bed feels a bit different, etc. After a day or two, you start to get used to this. The longer you’re there, the more it feels like home.
  • While you’re there, you might take mini trips within the journey- go to the shop, the beach, maybe even camping out.
  • If you stay away long enough, when you come home it feels a bit strange at first. You almost turn the door key the wrong way, the colour of the wallpaper isn’t quite as you remembered it, you didn’t realise you were low on a few staples.
  • What if you set out on a grand adventure to visit strange and distant cultures? The journey is either massive, with strange and mysterious stops on the way, like an ocean journey, or super fast, almost like a blur, as in a flight. When you arrive, it’s almost alien. Everything’s different: the living conditions, the language, the food… Stay there for a while, however, and you gradually pick up a few basic words, learn a bit about the local neighbourhood and start to feel more settled.
  • Were you to stay in an exotic culture for long enough, it would start to feel like home, and your memories of your real home become less and less clear. Coming home after living there for years, home itself would feel like a very strange place at first. Stay somewhere long enough and you might even come home with a foreign accent!

All this can be mirrored in the way a piece of music progresses. The melody is the traveller, the main chords are the visiting points. Time is time.

The relationship between each chord and the home key (as well as between one chord and the next) is the relationship between home and the various places visited on our travels. As a (basic) chord represents a key, the main chords mark out the visiting keys in the journey.

Chord relationships are key relationships. A topic in itself, this is worthy of revisiting in at least one separate post. However, in general, keys (and chords) are related by how many notes they have in common. There are basically three types of key relationships:

The Cycle (or Circle) of 5ths

The cycle of 5ths is a sequence of all major and minor keys in increasing and decreasing key signature order, usually represented as a circle. Octaves are unspecified, as it’s just a list of keys. Adjacent keys in the cycle of 5ths have only one note different in their scales and both chords are made up of notes in the home key.

See my Beginner’s Tip for a graphic of the cycle of fifths, including relative majors/minors.

Adjacent keys in the cycle of 5ths are the closest companions. Many pieces only use 3 chords: that of the home key, previous key and the next key in the cycle, otherwise known as the Tonic, Subdominant and Dominant or I, IV and V. As we progress away from our neighbours, the keys sound less closely related and the chords a little more independent. Distant key relationships produce a startling or disorienting sensation in the listener.

Relative major and minor

All the common tonalities used in Western music have either a major 3rd or a minor 3rd from the root note. In this way, modes can be categorised as “like major” or “like minor” and be represented by a major or minor chord accordingly. It’s reasonable to talk in terms of major and minor chords, even if the piece is in another mode.

For every major scale, there is a minor scale with the same key signature (and vice versa). When the music changes between relative major and minor, the root note and tonality change but the notes all belong to the home key. As a chord progression, going from relative major to relative minor (and vice versa) feels more like taking a small step back rather than a significant change in key. Relative major/minor chords are often interchangeable in an accompaniment, depending on whether a more direct or a slightly indirect and more sophisticated effect is desired.

Major and minor on the same root note (parallel major and minor)

A major and a minor scale on the same root note have 3 notes that differ between them, so they only have 4 notes in common. In the cycle of 5ths that amounts to keys which are 3 steps apart, a relatively indirect relationship, yet they sound like they’re much more closely related. As it happens, only one of the three chord notes is different-the 3rd. The root note and 5th are both the same. The only thing that seems to change is the mood, the tonality.

Back to the present…

In short, closely related chords feel comfortable, almost predictable, as the melody arrives there – the friendly key next door…

Of course this is mitigated by the directness of the trip. We could potentially weave through a myriad of other keys before arriving next door, blindfolded and bedazzled, and it might then take us a while to realise where we are, but by and large, closely related keys can be freely visited in comfort.

More adventurous journeys use less direct key relationships or follow a cascading progression of keys in the cycle of 5ths to arrive in a new land.

When listening to a piece, try to feel not just the more rapid flow of the melody, but the deeper, underlying flow of the progression of keys through which the melody travels.

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Sleight of Ear: the effect of musical context on perception

This post is one of a growing series of holistic investigations into various aspects of music theory. The full list can be found in the Posts page under the category Music Theory De-Mystified.

All comments are welcome. If you enjoy my post, please give it a like and share it or subscribe to my blog.

Musical context

Individual intervals and chords can be listened to by themselves, out of context, or within the context of a particular piece.

Any interval or chord has an effect; a character, based on how the notes interact. However, the context of the surrounding notes can produce “sleight of ear”. The interval or chord can appear to sound different than when played by itself or in another musical context.

Musical context is a combination of the overall key and mode and the development of the piece. Many pieces visit various keys along the way, resulting in a temporary key. As the music progresses through these visiting keys there is interplay between the home key and the visiting key and the listener’s viewpoint shifts.

Altered notes in either the melody or chords can also result in sleight of ear.

Sleight of ear example 1

Here are two examples of changing from an A major chord to an E major chord. The first example the melody feels like A is the home chord and we’re venturing out to E. In the second example, just one slightly different note in the melody suggests that E is home and we’re arriving home from a visiting key. This is especially noticeable when we hear the progression repeat itself.

Interestingly, the addition of D# in the melody implies the key of E major, and that’s how we hear it. To reflect this, the above example is written with the key signature of A major for the first example and E major for the second.

Sleight of ear example 2

The classic example of sleight of ear is the interval between the 6th and 7th notes of the harmonic minor, which is 3 semitones despite being consecutive scale notes (letters). This interval gives the scale an exotic quality reminiscent of Gypsy music.

From the 6th note to the 7th sounds like an unusually large step, a stretched out 2nd. It is called an augmented 2nd, reflecting how we hear it in the scale.

Normally, 3 semitones is a minor 3rd. When we hear this interval by itself we assume the first note to be the root note: it sounds like the first 3 notes of a minor scale with the 2nd note left out, or the start of a minor chord or minor triad.

The same size interval feels unrecognisably different in these two different contexts.

Please feel welcome to share this post, make a comment or ask a question. if you find this post useful, please give it a like.

Videos taken from Music Theory De-Mystified, due for release as an e-Book late 2022.

F flat Is a Note

This post is one of a growing series of holistic investigations into various aspects of music theory. The full list can be found in the Posts page under the category Music Theory De-Mystified.

All comments are welcome. If you enjoy my post, please give it a like and share it or subscribe to my blog.

Most notes have at least two possible names. For example, F# is the same pitch as Gb. Even naturals have alternative names. E could be called Fb and F could be called E#. And that’s not to mention double sharps and double flats. G could be called Abb and so on.

Why so many choices? First, some background…

Modes

Major and minor keys are based on patterns of 2 and 1 semitone intervals between consecutive notes. We call such a pattern a mode. The series of notes generated by the mode is called a scale. Typical Western scales have 7 notes per octave, the eighth note being the octave of the first (hence the name “octave”).

The starting note of the scale is called the root note or tonic. The root note is easy to recognise when playing a scale because it is first and last. Melodies make the root note apparent by highlighting it in various ways so we can tell which mode we’re in when we listen to the music.

The choice of mode imparts an overall character to the music, called tonality.

Keys

A key is the combination of a mode and a root note. Keys allow us to choose the mode and the root note independently.

Let’s look at the major mode as an example. The original major, made up of only naturals, is C major. The name C major indicates that this key uses the major mode with C as the root note.

C major

Any other major key needs at least one sharp or flat. By starting the mode on a different root note we need some different notes in the key to preserve the pattern of intervals from note to note. The pattern of intervals defines the mode, in this case, major.

We can work out the notes needed for a chosen key by placing the new root note at the start of the pattern and counting the semitones from note to note. Let’s look at D major; the major mode starting on D.

D major

The note naming rule

There is one simple rule that determines the right choice of note name. In a standard Western mode such as major or minor, each scale note must have its own letter.

The letters indicate consecutive scale notes, just like they are written on a stave. A musical stave only has positions for notes as letters: sharps and flats are written as symbols beside the note.

When we work out the note names for a key, we start from the root note and count up. As we go, each following note must use the next letter as its name. In the example above, D major, the 3rd note is called F#. Gb is the wrong name because the third letter up from D is F, not G.

B#, Cb, E# and Fb

Remember BCEF? (see my beginner’s tip). This is the extreme end of BCEF. These notes look like they should never be used because they have equivalent pitches which are just naturals. B# = C, Cb = B, E# = F and Fb = E, so why use them? In truth their use isn’t all that common, but they do get used in certain keys.

For example, B# is used in C# major and Fb is used in Cb major.

This potentially begs the question, why use C# major as the name of a key when it could be called Db major? C# major has 7 sharps whereas Db major has only(?) 5 flats…

A valid question. I can’t answer it comprehensively in this post but there are three main reasons:

  • ease of playing/reading on a given instrument
  • movement within the piece from the home key to other keys
  • altered notes in the melody or chords

Easy keys

Players of some instruments such as guitar find sharps keys easier to read and play. Brass players, on the other hand, prefer flats keys. It depends on the base key and playing logic of the instrument.

Singers can be very specific about their choice of key for a particular song based on how the melody suits the different registers of the singer’s voice. This may force the rest of the ensemble to play in a key which is awkward to read, whichever name they choose.

For example, F# major has 6 sharps and Gb major has 6 flats. F# major has the note E# and Gb major has Cb.

Keys within a key

Typically a melody starts in the home key and goes on a journey. This journey takes it through various, usually related, keys, some of which are fleeting moments in the journey while others are visiting points; temporary homes. Campsites, if you like.

Visiting keys are named according to how closely related they are to the home key: in other words, how many notes they have in common. In general, if we start in sharps we continue in sharps, and the same for flats.

For example, in E major, a major key 2 semitones up would be called F# major, not Gb major. This is because F# is a note in the home key (E major) and Gb is not. In fact, none of the note names in Gb major are used in E major.

Which keys are related to which? That’s for another post.

Altered notes: weird note names in normal keys

Sometimes a melody or chord uses a note that doesn’t belong to the key. This could be as a variation or ornament, or the melody just might not be in a conventional mode.

We think of such a note as a replacement of the normal scale note or chord note. The context of the music determines which scale note has been replaced. To preserve the note naming rule, the new note is named with the same letter as the note it replaces.

  • if the altered note is a semitone higher than the scale note it is sharpened
  • if the altered note is a semitone lower than the scale note it is flattened

Sharpening or flattening allows the music notation to reflect which scale note is being altered, just as we would hear when playing and listening. However, depending on the key of the piece, this may require a double sharp or double flat.

NOTE: To avoid too much rambling I have only given a brief outline of the various topics raised in this post. I hope to cover some of these in future posts.

Please feel welcome to share this post, make a comment or ask a question.

Graphics taken from The Tiny Music Theory Book, a short, easy to read guide to the essentials of music theory and notation, available here.

Why Are Octaves Special?

This post is one of a growing series of holistic investigations into various aspects of music theory. The full list can be found in the Posts page under the category Music Theory De-Mystified.

All comments are welcome. If you enjoy my post, please give it a like and share it or subscribe to my blog.

Every musician discovers early on that octaves are special.

Notes which are one or more octaves apart have the same note name – that in itself means a lot. Furthermore, changing octaves feels more like changing voice or register than going to a different note.

Why is this so?

When we play a note, a sound wave is produced. Each pitch produces a wave which vibrates at a certain frequency: the higher the pitch, the higher (greater) the frequency.

Graph of a low pitch and a high pitch showing that higher pitches have a higher frequency and a shorter wavelength

The frequency is measured in cycles (vibrations) per second, called Hertz, Hz for short. You may have heard of A440, the frequency tuners are calibrated to. 440 means 440 Hz. A440 vibrates 440 times per second.

Playing a note an octave higher doubles the frequency: an octave above A 440 Hz is A 880 Hz. As the frequency gets higher, the length of the wave becomes shorter, so double the frequency is half the wave length.

When we play these two notes together, the higher note’s sound wave fits exactly twice inside the lower note’s sound wave. No other combination of two notes has such a direct relationship between their sound waves as an octave. This perfect fit is why the higher note of an octave sounds like it fits inside the lower note: because it literally does.

Graph showing 2 sine waves an octave apart
Graph showing the sound waves of two notes an octave apart such as A440 and A880. Twice the frequency = half the wavelength

Low and high octaves are large and small versions of each other. A musical part can be played at a different octave without introducing any new notes: it will still fit all chords and other parts equally well.

Please feel welcome to post a comment or ask a question.

*Graphics taken from Music Theory De-mystified, my upcoming music theory book, due to be released late 2022.