Music Theory De-mystified Blogmode

16. Intervals 1: Major, Minor And Perfect Intervals

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.

Keys and key relationships are two of the most important concepts in music theory. If you’re not sure about these, please visit 11. Introduction To Keys and Key Signatures: Major Keys and the following two posts.

Interval names are equally important. Among other uses, interval names form the basis for understanding chords and chord names.

Melodic and Harmonic Intervals

An interval is the pitch difference between two notes. Intervals occur both as consecutive notes in a melody, or as two notes sounding together such as a melody and harmony. When more than two notes sound together, such as in a chord, there are multiple intervals between the various notes.

Not surprisingly, the interval between consecutive notes is called a melodic interval and that between two notes sounding together is called a harmonic interval (some call it a vertical interval). We count and name intervals the same way in both cases, from the lower note to the higher note.

Intervals are counted from the lower note to the higher note, even if the higher note comes before the lower note in a melody.

Singing A Scale

Trained musicians, including musicians who play by ear, are able to count the intervals from one note to the next in a melody or chord by mentally (or physically) singing the notes of a scale, starting on the lower note and finishing on the higher note. This is actually a very useful skill worth developing. Such general musical skills are called musicianship and form a bridge between theory and practice.

In the coming lessons I intend to look a a few basic musicianship skills including how to count intervals by singing.

Naming Intervals By Counting Scale Notes

So far we have described the interval between two notes in two ways; by counting letters and by counting semitones. Neither are enough.

Counting letters doesn’t distinguish between sharps, flats or naturals so the number of semitones can vary: A-C and A-C# are not the same interval.
Counting semitones doesn’t guarantee that we end up with the right note names: A-C# and A-Db have the same number of semitones but use different note names.

As we’ll continue to find out, note names are important. The choice of note name reflects how that note functions in a given context. We want a way of measuring the size of an interval that also tracks the note names; a method that counts both semitones and letters. Scale notes do just that.

To count in scale notes we use a major and a minor scale whose root note is the same as the lower note of the interval; the parallel major and minor. If the lower note is A, we use A major and A minor.

However, instead of using the aeolian mode, the natural minor, we use the phrygian mode. The phrygian mode has four notes that differ from the major instead of three; the 2nd, 3rd, 6th and 7th notes, as opposed to just the 3rd, 6th and 7th notes.

Think of the phrygian mode as being more minor than minor, or the super-minor…

Even though we’re now using the phrygian mode we still call it “minor” for interval names. I will mark this minor with an asterisk * as a reminder that it’s the phrygian rather than aeolian mode.

The Interval Ruler

We can hone this down a little: the 2nd, 3rd, 6th and 7th notes of the minor are 1 semitone lower than the major, so as a shortcut we can just write out the major scale and flatten the 2nd, 3rd, 6th and 7th note to find the minor intervals. I call this an interval ruler.

Remember that to flatten a note we lower it by 1 semitone without changing its letter. A sharp becomes a natural, a natural becomes a flat and a flat becomes a double flat.

Here is the interval ruler for an interval whose lower note is A. The degree numbers are written below. Each scale degree shows the number of semitones from the root note to that note.

Major, Minor and Perfect Intervals

There are three main types of interval names; major, minor and perfect, based upon the following conditions:

If the upper note of the interval is only in the major scale on the lower note, the interval is major.
If the upper note of the interval is only in the *minor scale on the lower note, the interval is minor.
If the upper note of the interval is common to both scales, the interval is perfect.

We call this part the quality of the interval.

Perfect-type intervals are marked in green and major/minor type intervals in blue.

The other part of the interval name is the degree of the interval; the number of scale notes or letters including the first and last.

For instance, in the interval A to C#, the upper note, C#, is the 3rd note of the major scale on A, the lower note. A-C# is a major 3rd.

How To Name An Interval:

Write the lower note of the interval in the ruler as the root note and add the notes of the major key.
Now flatten the 2nd, 3rd, 6th and 7th note for the *minor as indicated by the red arrows.
Next, look in the ruler for the upper note of the interval.
The interval name is made up of the quality; major, minor or both (=perfect), and the degree.

In the above example, A-C# is a major 3rd (= 4 semitones).

Similarly, A-C is a minor 3rd (= 3 semitones), A-D is a perfect 4th (= 5 semitones), etc.

1st, 4th, 5th and 8th are perfect-type intervals.
2nd, 3rd, 6th and 7th are major/minor type intervals, depending on which scale the upper note is in.

As well as the octave, we’ve already met three intervals:

Minor 3rd (3 semitones to the 3rd letter) – the interval between the root notes of relative major and minor keys.
Perfect 5th (7 semitones to the 5th letter) – the interval from any key to the next key in the cycle of 5ths.
Perfect 4th (5 semitones to the 4th letter)- the interval from any key to the previous key in the cycle of 5ths.

An Interval Name Is Based On The Lower Note

All the examples so far assume that A is the lower note of the interval, hence we’ve used A scales for our ruler. If we want to measure an interval with a different lower note we want the interval ruler to start on that note. For example, to name the interval from G to E we would need G scales and to name the interval from Bb to Db we would need Bb scales.

G-E

E is the 6th note of G major, so G – E is a major 6th (9 semitones).

Bb-Db

Db is the 3rd note of Bb minor, so Bb – Db is a minor 3rd (3 semitones).

By now you’ll see why I was so keen on learning key signatures of major scales: knowing them makes this process a lot quicker than having to work it out on the fly! Every time we look at the interval between a pair of notes with a different lower note, we need to use a different scale for our interval ruler.

At least by using the interval ruler we only need to learn the major scale, as we can flatten the 2nd, 3rd, 6th and 7th to find the *minor (phrygian mode).

Try These…

Name the following major, minor and perfect intervals:

F-Bb
F-E
F-Db
G-B
G-D
G-F
Bb-G

Answers at the end of this post.

Interval Names In Reverse: finding the upper note

So far we’ve named an existing interval. Now let’s recreate an interval from its name. We’ll pick a note to be our lower note and name the higher note based on the interval name.

For instance, let’s find the note that’s a minor 6th above E.

First we’ll create our interval ruler on E. We’ll start with E major. The key signature of E major is 4 sharps: F#, C#, G# and D#, so the scale of E major is E, F#, G#, A, B, C#, D#, E.
Now we’ll write E *minor below it by flattening the 2nd, 3rd, 6th and 7th notes.
Next we look for the interval, in this case a minor 6th. Minor 6th means the upper note is the 6th note of the minor built on the lower note, so we look for the 6th note of E *minor on our interval ruler.

Minor 6th above E

An interval name means:

The higher note of the interval is the …th (degree name) note of the … (major or minor or both) scale built on the lower note.

Saying it in this way may help to remember how interval names work.

Try These…

Find the upper note in the following major, minor or perfect intervals:

a minor 3rd above C
a major 6th above C
a minor 2nd above E
a perfect 4th above E
a minor 7th above E
a major 2nd above Eb
a major 7th above Eb

Interval Names As Scale Degrees

The different notes of a scale are called degrees. So far I have used the note’s position in the scale to indicate the degree, such as 3rd or 5th. We can refine this by calling the third note of a major scale the major 3rd, the 5th note of either scale the perfect 5th and so on.

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.

NEXT LESSON: 17. Listen & Sing: How To Sing The Major Scale

PART 1 CONTENTS: Basic Music Theory Course Contents

Answers To Try These…

F-Bb = perfect 4th
F-E = major 7th
F-Db = minor 6th
G-B = major 3rd
G-D = perfect 5th
G-F = minor 7th
Bb-G = major 6th

a minor 3rd above C = Eb
a major 6th above C = A
a minor 2nd above E = F
a perfect 4th above E = A
a minor 7th above E = D
a major 2nd above Eb = F
a major 7th above Eb = D

15. Modes

The chromatic scale

The chromatic scale is made up of every one of the 12 musical note pitches, each 1 semitone apart from the next. It is the parent of all modes (…except in cultures with more than 12 note pitches per octave…).

Apart from some largely academic genres such as serial music, chromatic scales are mainly used as musical effects, such as the rapid chromatic passages used to build tension and drama in film music.

As a key, the chromatic scale has no inherent tonality: there’s no way to tell the root note from any other note. That’s not to say that you can’t nominate a root note, just that it requires a lot of effort to make that root note felt in a piece.

I don’t mean that it has no musical character, either. It does, but it’s a very nebulous one…

Modes

A mode is the pattern of intervals that determines which of the 12 different note pitches within an octave are used to produce a scale/key. Apart from the chromatic scale and the “whole tone scale” (6 notes within an octave, with 2 semitones between each note and the next), modes have an irregular pattern to their interval structure. As long as the root note is highlighted from time to time this irregularity allows a mode’s unique character to permeate the character of the music.

Diatonic Modes

The traditional Western modes, such as ionian (major) and aeolian (minor), are made up of one- and two-semitone intervals. Such modes are called diatonic modes; modes whose scales only have two different size intervals between their notes.

Just to be confusing, they’re also called heptatonic modes, meaning that they have 7 different notes within an octave. The traditional modes are all made up of 7 different notes, where the eighth note is the octave of the first.

A mode doesn’t innately have these limits. For example, the harmonic minor (discussed later in this course) still has 7 notes but one of its intervals is 3 semitones, that between the 6th and 7th notes of the scale. Other modes have a different number of notes per octave, such as pentatonic (5-note) modes and the blues mode. Some modes even use one or more different notes ascending and descending. The melodic minor works like that, as do some Indian modes.

However, the most common modes in most Western genres are the traditional Western modes which evolved out of the Renaissance era.

Although often associated with period music and traditional folk music, some modes, such as the myxolydian mode, are commonly used in a variety of other genres. Jazz goes even further by using relative modes as an approach to improvising around extended chords.

What Are The Traditional Modes?

Let’s have a look at the natural notes for two octaves. Each note can be the root note of a diatonic mode (yeah, I wouldn’t worry about the “heptatonic” bit, it seldom crops up in conversation…).

Look at the notes for an octave, starting on each note in turn. Each root note produces a different pattern: a different mode.

We can compare their interval structure by lining them up underneath each other.

Each different mode has a unique quality that greatly influences the overall character of music played in that mode.

You can hear this, even by just playing a scale.
You can also teach yourself a new mode just by reading and playing the notes of the scale.
If you play by ear, follow its pattern of intervals on your instrument by counting semitones.

Below is a scale of each mode starting on A, so we can compare their character..

A aeolian (natural minor)

A locrian

A ionian (major)

A dorian

A phrygian

A lydian

A myxolydian

The character of each mode is easy to identify in a melody. Have a listen to this short, simple melody played in each of the modes…

Simple melody in A aeolian (natural minor)

Simple melody in A locrian

Simple melody in A ionian (major)

Simple melody in A dorian

Simple melody in A phrygian

Simple melody in A lydian

Simple melody in A myxolydian

Modes And Key Signatures

The way in which key signatures are used for modes other than major or minor depends on genre and school. There are two approaches: like major/like minor or the mode’s actual key signature.

Like Major or Like Minor

Classical musicians are brought up on a strict diet of major and minor (as well as two variations of the minor, melodic minor and harmonic minor). A classically trained player is only going to look for two possible root notes when interpreting a key signature. Music in a less familiar mode would be hard to interpret on first reading; the root note would seem to conflict with the key signature.

The most important notes of a scale are the root note and the note 7 semitones above the root note, called a perfect 5th (don’t worry about the interval name, we’ll look at interval names soon). The perfect 5th helps stabilise the root note.

There is one other important note, the 3rd note. One reason the 3rd is important is because it’s the most significant difference between major and minor. In the major mode the 3rd note is 4 semitones above the root note and in the minor it’s 3 semitones above the root note.

We can categorise the other modes as being “like major” or “like minor”, based on the 3rd note.

Below is a list of the modes staring on A, grouped in “like major” or “like minor”. The note in the other modes that differs from the major or minor is highlighted.

Note that the locrian mode is not in either list! The locrian mode wasn’t used in Western music, or even named, until relatively recently because it lacks the essential ingredient of a perfect 5th. By not having a note 7 semitones above the root note, music written in this mode is elusive. We naturally listen for a root note but we either can’t find it or we’re misled by other possible root notes that do have a perfect 5th but don’t hang around long enough to feel convincing.

It’s VERY hard to make the root note stick in the locrian mode. Modes without a perfect 5th need almost constant reinforcement of the root note in order to be musically stable. One way to achieve this is by having a drone accompaniment, where the root note persists throughout the piece.

Accidentals

For modes which are like major, we use the key signature of the parallel major mode; the major mode on the same root note.
For modes which are like minor, we use the key signature of the parallel minor mode; the minor mode with the same root note.

This requires the use of an accidental. Anyone who’s seen music written in the melodic or harmonic minor will be used to accidentals used in this way.

For example, let’s look at one of the more common modes, the myxolydian mode.

Using only naturals (key signature of 0 sharps/flats), the myxolydian mode starts on G. The actual key signature of G myxolydian is 0 sharps/flats.
The myxolydian mode is like major, so for a ”like major/like minor” key signature we would use the key signature of the major mode on G, G major, which is 1 sharp (F#).
To preserve the intervals of the myxolydian mode we need to flatten the 7th note, the note which differs from the major of the same root note, F# (remember, in the cycle of 5ths, the latest sharp is the 7th note of the scale…).
When we flatten F# we get F natural, so for the first F in every bar that has one, we write a natural sign as an accidental.

*NOTE: An accidental is only written for the first instance of a given note in each bar.

Try These…

Like Major, Like Minor

Write the scale of the following modes for 1 octave ascending using the key signature of its parallel major or minor (the major or minor key with the same root note) and an accidental where required. Base your decision on whether the 3rd note belongs to the parallel major or parallel minor.

NOTE: Accidentals aren’t written as part of the key signature. They must be written beside the first instance of that note in every bar where that note occurs.

A dorian
D lydian
C ionian (trick question… just seeing if you were paying attention)
C myxolydian
B phrygian
F# dorian
Bb myxolydian

Answers at the end of this post.

Actual Key Signature

Players of early music and traditional folk music, as well as a number of other genres, are quite familiar with the traditional modes. Typically, in such genres the actual key signature is used.

In the above example, G myxolydian is written in the key signature of 0 sharps/flats, rather than in the key of G major with F natural as an accidental. It’s cleaner and simpler to read (as long as you interpret the key signature correctly when reading).

When first reading a piece knowing only it’s key signature, you might wonder how to determine the root note of the piece, with so many modes to choose from. The approach is the same as when you’re just looking for major or minor. Look for an obvious note near the start and end of the piece.

For more on how to tell which note of a piece is the root note, please have a look at How Can We Tell Which Key We’re In?

Pentatonic modes

Pentatonic modes (5 notes per octave) are quite popular in various genres. Having only 5 notes, we can think of them as a subset of the traditional heptatonic modes that we’ve already looked at.

The most well known of these is the minor pentatonic mode, notes 1, 3, 4, 5 and 7 of the natural minor/aeolian mode. In this instance, we would use the key signature of the “parent” minor key. Other Western pentatonic modes are also subsets of parent modes, so we would use the key signature of the “like major” or “like minor” mode of which it is a subset.

Here are the two most common Western pentatonic modes.

Not all pentatonic modes are related to a parent Western mode. Any combination of 5 notes within an octave can be used as a pentatonic mode.

The Blues Scale

The most common mode in blues is a hexatonic (6-note) mode based on the minor pentatonic, with an extra note added between the 4th and 5th notes. From a notation viewpoint, there is no room in the naming system for the extra note to have its own letter: instead, it is considered an alternative to the 4th or 5th note and should be named according to its use. Either option requires an accidental.

Other Modes

Most musical cultures around the world have a concept of modes, a system of choosing a set of notes within an octave based on a root note and the intervals between its scale notes. Some use different intonation (tuning) systems: such modes can sound unfamiliar to the Western ear. Many are based on the same intonation as Western music, 12-Tone Equal Temperament, yet may have different numbers of notes per octave or notes that differ when ascending or descending. If you wish to experiment, you can create your own mode for a new composition or improvisation.

Freedom From Modes

The Western modes were originally used as a rigid framework for determining which notes were used in a composition. Over time, as music developed towards the journey through various visiting keys that it largely is today, the use of accidentals became more and more common, to accommodate these temporary keys.

Accidentals are also used for embellishment (ornamentation). Ornaments are treated as effects: an ornament may well use notes outside the key, requiring an accidental. This may extend to chromatic passages involving several accidentals.

The contemporary view is that a key is based on the overall use of the notes of a major or minor key, with the option of sharpening/flattening notes or incorporating other notes as desired.

NEXT LESSON: 16. Intervals 1: Major, Minor And Perfect Intervals

PART 1 CONTENTS: Basic Music Theory Course Contents

Answers to Try These…

12. Major Keys And The Cycle/Circle Of Fifths

The Order Of Keys

Look at the list from the last lesson, 11. Introduction To Keys And Key Signatures: Major Keys.

Now that the keys are in key signature order,we can make one more observation:

The order that the keys come in (the order of the root notes of the keys) is the same as the order that the sharps or flats come in, just starting on a different note than the root note, as shown here by the red arrows.

For sharps keys, the next key is the 5th letter above the current key.
For flats keys, the pattern is reversed. The next key is the 4th letter above the current key, which is the same as saying it’s the 5th letter below the current key. We call this sequence the Cycle of 5ths (see below).

Sharps Keys

The sharps keys start with G major (one sharp) and go up 5 letters at a time.
The sharps themselves start with F#, the 7th note of G major.
The latest sharp of a key signature is the 7th note of the scale or one letter below the root note.

Flats Keys

The flats keys start with F major (one flat) and go down 5 letters at a time.
The flats themselves start with Bb, the 4th note of F major.
The latest flat of a key signature is the 4th note of the scale, the 4th letter counting up from the root note.

Why Are Some Notes Missing?

Notice also that some note names aren’t on this list. The list of keys above only goes up to 7 sharps or 7 flats. It could go further, but scales in those keys would have more sharps or flats than notes! We would need to use double sharps or double flats in order to preserve the note naming rule (see 10. How To Find The Notes Of A Scale).

Most notes have two possible names. If the root note isn’t on the list, simply re-spell the note (re-name it with the alternative note name) and it will be there. With the alternate spelling, the same sounding key uses only a few single sharps or flats instead of doubles and is much easier to read. For this reason, keys with more than 7 sharps or flats are seldom used.

For example, G# major has 8 sharps including F double-sharp. The note G# can also be called Ab. Because it’s the root note there is no special reason to use a particular name as long as we have the right pitch. G# can be re-spelled to Ab. Ab major only has 4 flats; Bb, Eb, Ab and Db.

The Cycle (Circle) Of 5ths – The Ultimate Shortcut

The cycle of fifths (aka circle of fifths) is the ultimate shortcut for finding keys and key signatures. It’s just the list of keys we’ve already looked at above, but in condensed form.

Since keys and key signatures follow the same pattern, we don’t need to write them out separately. Here’s how it works:

This is a very long line… We can shorten it a bit by putting the sharps and flats sections on top of each other. The sharps list reads from left to right, the flats list from right to left (see arrows). The green dotted line represents where the sharps and flats themselves start.

To find the key signature of a scale:

Find the root note. For example, D major is in the sharps row, Db major is in the flats row. F major is in the flats row, F# major is in the sharps row.
If you can’t find the root note, its key signature has more than 7 sharps or flats. These are seldom used. Re-spell the name and look again.
The number above (or below) the root note is the number of sharps or flats in the key signature.
From the start of the row, follow the direction of the arrow until you cross the green dotted line. The first note after that line (the first letter with a sharp or flat) is always the first sharp or flat in the key signature.
Continue reading the following sharps or flats up to the number that’s written above (or below) the root note.
On each stave of the piece, write the sharps or flats after the clef, in the order that you found them. Be sure to write them at the standard octave for key signatures, as listed in the previous post, 11. Introduction To Keys and Key Signatures: Major Keys.

Examples

E major

E major is in the sharps row and has 4 sharps.
Reading from left to right, the first sharp is always F#.
Continue counting sharps until there are 4: F#, C#, G#, D#.

Ab major

Ab major is in the flats row and has 4 flats.
Reading from right to left, the first flat is always Bb.
continue counting flats until there are 4: Bb, Eb, Ab, Db.

The first sharp is always F# and the first flat is always Bb. If you remember BCEF, you already know this…

So far we’ve only looked at major keys. For minor keys we could use a similar list as the one above but the sequence would start on A, the minor with no sharps or flats, rather than C. The pattern would be the same but all the numbers would be different.

There is an easier way to do minor keys. We’ll visit that in the next lesson, so for now we’ll just stay with the major keys.

Try These…

Here are a few keys for you to look up in the cycle of 5ths, using either the line version or the circle version below. Find some paper and a pencil and write down the name of each key with the key signature next to it, with the sharps or flats in the correct order. Answers at the end of this post.

G major
B major
Gb major
Bb major

What’s a 5th?

We haven’t formally looked at interval names yet, that’s for a future post. Essentially, we count the interval (pitch difference) between notes in letters, including the first and last letters of the interval.

From a note to itself, such as C to the same C, is one letter. This interval is called a 1st.

From C to D is 2 letters is a 2nd, from C to E is a 3rd, etc. all the way up to an octave, from C to the next C above (or below) it, the 8th note. Octave means 8th, hence the name “octave”. A 5th is 5 letters, such as from C to G.

Real interval names go a bit further than that but in essence, interval names are based on counting letters.

The cycle of 5ths is so named because the interval from one note to the next in the cycle is a 5th. Reading from left to right, for sharps keys, the cycle goes up in 5ths, while reading from right to left, for flats keys, it goes down in 5ths.

The Circle Game

Many people say Circle of 5ths rather than Cycle of 5ths. This is because, instead of showing the pattern across a page, potentially trailing off each margin forever, it can be shown as a circle. The circle is the most popular way of representing the Cycle of 5ths. It works just the same as the line version we used, with left-to-right (sharps) being clockwise and right-to-left (flats), anticlockwise.

Here’s the circle representation of the cycle of 5ths for major keys.

The circle of 5ths is often shown without the extra sharps/flat: after all, these just follow the same sequence as the root notes. Instead, the key signature is displayed next to each key, as below. This is great as an image on your device but not as clear for committing to memory.

For jotting down quickly on paper from memory, I find the line version easier, but if you have the image to look at, the circle version with key signatures is great. The circle also has the added benefit of being able to show minor keys on the same image. We’ll come back to minor keys in the next post but if you want to have a look, visit The Cycle (circle) Of Fifths.

Know Your Key Signatures

Much of what we’ll learn in the rest of this course is dependent on knowledge of key signatures and the cycle of 5ths. Keys and key signatures are essential concepts in the language of music.

Furthermore, the cycle of 5ths is more than just a list of keys. It also represents the musical relationships between chords within an overall key, possibly the most important topic of all (but that’s for a future post).

TIP: It’s worth learning all the keys and their key signatures, or at least the common keys for your instrument or genre. Start with the major keys. Later I’ll show you a schortcut for minors.

I’m not a fan of unnecessary rules but any language has a basic vocabulary and syntax. Music is no different. Just as we need to learn the symbols for note pitch and duration, the “key” to musical success in almost any genre is to become familiar with keys and key signatures.

A Mnemonic Can Help

In primary schools, the Cycle of 5ths is taught as a mnemonic. Mine was a boring one, Go Down And Enter By Fifths, with a C at each end. I’m sure you can come up with your own… A mnemonic is a good idea because keys are the times tables of music and should be deeply embedded in your mind.

Keys are the times tables of music.

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 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.

Much of the material in this post, including the custom diagrams, is taken from Music Theory De-mystified, my upcoming music theory reference.

NEXT LESSON: 13. Relative Major And Minor

PART 1 CONTENTS: Basic Music Theory Course Contents

Answers to “Try These”

G major has 1 sharp, F#
B major has 5 sharps, F# C# G# D# A#
Gb major has 6 flats, Bb Eb Ab Db Gb Cb
Bb major has 2 flats, Bb Eb

11. Introduction To Keys and Key Signatures: Major Keys

This post and the next two cover two important musical concepts. If you need to read them more than once, please do so. If you have any questions, please post them as a comment. I’ll be happy to answer them.

Scales And Keys: What’s The Difference?

A scale is a list of a series of consecutive notes adding up to an octave, based on and named after its first note, the root note, and its mode (e.g. major or minor).

A key is the musical use of the notes of a scale. A piece is said to be in a key, (e.g. C major), when it is largely made up of the notes of the scale (e.g. of C major) and we can hear the tonality of the mode (e.g.major). For more detail, please visit How Can We Tell Which Key We’re In?

I prefer to think of this in reverse priority:

A key is music, a scale is a list of notes that music is made from.
A key is the cake, the scale is the ingredient list.
A scale is the notes of a key, listed in consecutive pitch order.

Keys and scales have the same name, except if you’re writing or playing a scale you say the word “scale” in the description:

“This piece is in C major” means “this piece is in the key of C major”.
Else you would say “play the scale of C major” or “play the C major scale”.

In other words, when talking about actual music we say “key”, not “scale”.

Practical Tip: To easily play in a key you need to be familiar with its scale.

A Scale Has A Key

Since a scale is also a basic melody, a scale itself is in a key. For example, the scale of C major is in the key of C major.

Unless we’re actually playing scales, we talk in terms of keys rather than scales.

Key Signatures

Apart from C major and A minor, other major or minor keys require some notes that are sharps or flats. So far, we’ve written them in before each note. That’s no big deal if it’s just a scale but in a piece, some of those notes might be used many times. It’s hard work when writing and the music ends up looking cluttered.

Melody in A major without key signature

A key signature uses the space on the stave just after the clef, before the time signature or any notes, to store the sharps or flats of that key for the whole length of the stave. Now they don’t need to be written next to the notes. The music looks cleaner and it’s quicker to write.

A key signature is a list of the sharps or flats used in a key.

The note naming rule states that each letter is only used for one note in the scale (7 scale notes, 7 letters), so the scale notes which are NOT in the key signature are naturals.

For example, the key signature of D major is 2 sharps, F# and C#. All the other letters are naturals.

Note: unlike time signatures, key signatures are written at the start of every stave.

The notes of a key can be played at any octave. If that note is a sharp or flat, it’s symbol is written next to the note; at the same octave as the note. In a key signature, however, a sharp or flat is only ever written at one particular octave and it applies to all octaves. It simply tells us that, for a given key, that note is a sharp or flat.

A key signature is a shortcut for writing out a scale. If we start on the root note and play the notes of the key signature, we’re playing the scale for that key.

It’s important to check the key signature, else you may play some wrong notes!

Here are two scales that look the same apart from the key signature. Carefully read the notes as you listen. In these two scales, every note is different because of the key signature!

The Order Of Sharps and Flats

The sharps or flats in the key signature are always written in the same order, regardless of the order in which the notes are played in the scale, and always in the octave shown below.

For sharps, the order is F# C# G# D# A# E# B#. F# is always the first sharp. Each sharp is the 5th letter above the previous sharp.

For flats, it’s the reverse, Bb Eb Ab Db Gb Cb Fb. Bb is always the first flat. Each flat is the 5th letter below (or the 4th letter above) the previous flat.

Don’t worry if you can’t remember all this, we’ll come back to it later…

Let’s look at A major, for example. In the scale, C# comes before F#, but in the key signature, F# appears before C#.

One big advantage to having a set order is that a player only needs to glance at the key signature to know which notes are sharps or flats. If you know the order, you only need to see how many there are.

Here’s the key signature order on the stave in the treble and bass clefs:

Note the octave where the symbols are written. For example, F# is written in the high octave rather than the low octave.

Why This Order?

Let’s say we worked out every major (or minor etc.) scale by counting semitones. If we looked at them all we would notice three things:

There are no scales with both sharps and flats.
The number of sharps/flats is unique. For example, there is only one major scale with 3 sharps.
Sharps and flats are cumulative. Once a sharp (or flat) is used in one scale, all the scales with more sharps (or flats) include that one.

We can reshuffle our list of scales in increasing key signature order. Here’s what the list of major scales looks like. To save space I have listed their key signatures rather than the whole scale:

Note: In the next post we’ll look at key signatures for minor keys as well as some shortcuts for learning key signatures.

NEXT LESSON: 12. Major Keys And The Cycle/Circle Of Fifths

PART 1 CONTENTS: Basic Music Theory Course Contents

Scales, Modes And Keys: What’s The Difference?

These three terms are often confused. They refer to the same subject but in different ways.

Scale

A scale is a series of (usually 7) consecutive note pitches finishing an octave above the first note.
The series can be extended over several octaves and is either played in ascending or descending order.
The first (and last) note of a scale is called the root note or tonic.

Mode

A mode is the pattern of intervals between the notes of a scale.
The pattern is based on the first note of the scale, the root note.
Western modes are made up of an irregular combination of (usually 1 and 2 semitone) intervals. This gives each mode a unique character called its tonality.

Key

A key is the use of the notes and tonality of a scale in a piece.
A piece is “in a key” when it uses the notes of a scale in such a way that the tonality of its mode is apparent overall when listening/playing.

Tonality

Tonality is the unique character of a mode, common to all keys in that mode.
The tonality of a mode is simply indicated by the mode’s name.

We should learn to recognise the tonality of the more common modes, both in a scale of that mode and in music written/played in that mode.

Names Of Scales And Keys

Scales and keys have the same names. They are named as the name of the root note followed by the name of the mode. For example:

the major scale on C is called C major.
Music using the notes of C major is in the key of C major.

For more on scales, modes and keys see 8. What is a scale?, 10. How To Find The Notes Of A Scale, 11. Introduction To Keys And Key Signatures: Major Keys.

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10. How To Find The Notes Of A Scale

In a hurry? You can scroll down straight to the summary (but you’ll miss all the fun…)

A scale is the combination of a root note and a mode. It’s even named that way. C major means C is the root note and major (Ionian) is the mode. The same for A minor: A is the root note and minor (Aeolian) is the mode.

In 8. What Is A Scale? we saw that a scale is a selection of (typically 7) notes within an octave, and that our sense of tonality depends on knowing which of these notes is the root note. In a piece that has a clear tonality the notes are organised so that the root note (tonic) is highlighted, especially near the beginning and end.

We also discovered that the reason the root note is so important in allowing us to hear the musical character is because typical Western scales have uneven intervals from note to note. Changing the root note effectively changes the pattern, changing the mode and thus its character.

Scales On Different Root Notes

If you know the character of the mode, you can sing a scale in that mode. As long as it’s within your range, you can sing that scale starting on any note (without even knowing what that note is!). As long as you don’t change the mode it will sound the same, just higher or lower.

The same is true for writing music. You can write a scale on any note. Here’s how it works:

Let’s look at the the major mode, which naturally starts on C. C major is made up of only the naturals.

We can pick any other note as the root note and build a major scale on that. All we need to do is make sure we stick to the major mode, the pattern of intervals from note to note that matches C major, or else we’ll change its character.

Let’s say we want D major. If we just started on D and used the same notes we would have a different pattern of intervals – a different mode – a different character.

It would sound like this:

This scale has quite a different character to C major.

Instead, we use the same pattern of intervals as C major, write D as the root note and then, working from left to right, count the number of semitones from each note to the next to work out the other notes. This will involve using one or more sharps or flats.

The 2nd note should be 2 semitones higher. 2 semitones above D is E.
The 3rd note is 2 semitones higher than E. F is 1 semitone higher than E and G is 3 semitones higher so we want the note in between. This could either be called F# (F+1) or Gb (G-1). What should we call it? We’ll come back to that shortly. We can put in both for now.
The 4th note is just 1 semitone further which is plain old G, and so on until the 7th note, 2 semitones above the 6th note, B. Again we have 2 options, C# or Db, and again we’ll write in both for now.
And, of course, the 8th note, 1 semitone above the 7th, should be exactly the same as the first, as it is the octave.

OK, time to look at what we’ve got… If we choose Gb for the 3rd note we have Gb AND G but no F, whereas if we call the 3rd note F# we have one F and one G. The same goes for the 7th note: Db uses the same name as the root note but a different sign, whereas C# allows one C and one D.

Now that we’ve worked out the notes in D major, let’s have a listen.

Now compare it to C major. The character should be the same, even though one scale is a little higher than the other…

The Note Naming Rule

For scales, there is one simple rule: the next note in a scale should have the next letter in its name.

Each note in a scale must have its own letter.

There’s a good reason for this: there are 7 note names, 7 notes in a scale and 7 pitch positions per octave on a stave.

Music notation is very visual. We can see the notes climb and descend as the melody itself climbs and descends. As we can see from the two versions of D major below, if two different notes in a scale share the same note name there are two different pitches sharing the same place on the stave and needing constant accidentals (sharps/flats/naturals) to show which is which. There is also one unused position, leaving a gap in the visual that we don’t hear.

Below is D major as notes on a stave showing both sets of note naming options. Try to read the notes while you listen. Which one is more visual (and less cluttered)?

Note: We can make a scale look even less cluttered by using a key signature. We’ll look at key signatures in the next lesson.

How to find the notes of a scale

Now that we know how to work out what notes we need to write a major scale starting on D instead of C, we can do so for any mode and any root note.

As the most common modes are major and minor, let’s find the notes for some other major and minor scales.

Choose a mode, e.g. major or minor.
Write the note that you want to build the scale on as the 1st note (root note).
Working from left to right, count how many semitones to the next note. Where there are two names for the same note, choose the name using the letter after the previous note.
(safety check: if you’ve added it up right, the 8th note’s name should be exactly the same as the first).

TIP: Learn the patterns that make up the major and minor modes (I think of them as phone numbers).

Major .2.2.1.2.2.2.1.

Minor .2.1.2.2.1.2.2.

Example: D minor

Have a go…

Here’s the answer…

OK, this one’s minor and has a flat. Pure fluke! There is no connection between being major or minor and having sharps or flats.

Try These…

Grab some paper and a pencil and try a few more… Bb major, A major, C minor, F# minor.

Answers at the bottom of this post. Here’s what a blank major and minor look like:

Practical Tip

Pick a major or minor scale that’s easy to play on your instrument, find its notes and doodle around with those notes. Just in one octave will do for a start, then try 2 octaves worth – it’s more fun. As long as you highlight the root note every now and again, for instance by making it long or strong, you should be able to feel the tonality of the mode you’ve chosen, or at least keep coming back to it if the music goes elsewhere. For a bit more on how to highlight the root note, visit How Can We Tell What Key We’re In?

Summary

A scale is a combination of a root note and a mode.
The root note is the first note of the mode.
A mode is a set of (usually 1 and 2 semitone) intervals from note to note adding up to an octave. The most common modes are major and minor. Of these, only C major and A minor have no sharps or flats.
Due to the irregular pattern of intervals from note to note, each mode has a unique musical character.
To make a scale on a different root note, choose the mode with the character that you want, e.g. major or minor, and write in the note you want to be the root note.
To find names for the other notes, start with the root note and count 1 or 2 semitones to the next note, according to the mode. Write the 2nd note in, count semitones to the 3rd note and so on, all the way to the octave.
Each note of a scale should have its own letter. Work from left to right, using the next letter each time, as you go.

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.

NEXT LESSON: 11. Introduction To Keys and Key Signatures: Major Keys

PART 1 CONTENTS: Basic Music Theory Course Contents

Answers

Bb C D Eb F G A Bb

A B C# D E F# G# A

C D Eb F G Ab Bb C

F# G# A B C# D E F#

8. What Is A Scale?

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

A scale is both a sequence of note pitches you can play by itself as a simple melody (usually for practice) and the basis of a piece of music.

In 1 Note Names, Semitones and Octaves, we saw that there are 12 different musical note pitches within an octave, each 1 semitone apart. We also saw that there are only 7 letters used to name music. On a musical stave there are also only 7 pitch positions per octave, one for each letter.

This is because most music in Western culture is usually made up using only 7 of the 12 notes at a time, the eighth note being the octave (hence the name “octave”). Such a selection of notes is called a scale. The first note of a scale is the reference note for music written in that scale.

Note: It is possible for a scale to have more or less than 7 notes (such as the 5-note pentatonic blues scale) but the vast majority of music in Western culture, both historically and in modern times, is based on 7-note (heptatonic) scales.

How Far Apart Are Scale Notes?

For 7 notes to make up an octave (12 semitones), the notes can’t all be spaced evenly. Most of the notes are 2 semitones apart, but there are two pairs which are only 1 semitone apart. For example, let’s look at the naturals; the notes that have just a letter as their name.

The naturals from A to A with note spacing in semitones

C major

Although the notes are named starting on A, C is the starting point for the most common scale of all, C major. We’ll talk about major and minor shortly, but for now, let’s look at the notes starting on C.

The naturals from C to C with note spacing in semitones

C major is made up of the naturals starting on C. We can see that C to D is 2 semitones, as is D to E, then E to F is only 1 semitone, etc. This is quite easy to see on a piano keyboard, as the named notes are the white keys and the others, the black keys. The interval from one key to the next is 1 semitone, whether between adjacent white keys or between a white key and an adjacent black key. (The staggered layout of a piano’s keys is for practical reasons- so one hand can span an octave).

Note: In scales, the intervals marked as 2 semitones are usually called a “tone” rather than “2 semitones”. Other schools use the terms ”steps” and ”half-steps” for the 2- and 1-semitone intervals between the notes of a scale.

In this blog I will always name intervals by semitones or by their musical interval name. For my reasons, see A Story Of Tones And Semitones.

The Root Note

When we play a scale, we usually emphasise the first and last note, in this case, C, by playing those notes louder, longer or both. Playing a scale in this way helps us feel that the starting/ending note is the home note and that the other notes either lead away from that note or towards it.

The first note of a scale is called the root note or tonic and it is the most important note in a scale. The root note represents home in a musical journey and the start of the pattern of intervals from note to note that defines the scale.

Modes

Let’s play a scale using only the naturals, from C to C and back.

Now let’s play the same notes but starting on a different root note, such as A. We’ll play A to A and back.

Sure, one was slightly higher than the other, but did you notice a difference in character/flavour/mood? Have another listen…

… (I’ll wait)…

This difference in character is even more noticeable in a real piece than just a scale.

Now let’s compare the spacing of the notes.

Notice the difference in the order of the 2’s and 1’s in relation to the root note? It is this pattern that determines the scale’s character.

The pattern of intervals that determine the note spacing of a scale is called a mode. When using just the naturals, each time we start on a different note, the pattern of note spacing is different. There are 7 different naturals, each of which is the root note of a mode. Of the 7 modes produced, six are quite common in various genres and one, the one starting on B, is seldom used (but that’s the subject of another post).

Earlier on, I called the first scale, starting on C, C major. The term major refers to the mode. Major is the most commonly used mode in modern Western music, hence the name. The one on A is called A natural minor or just A minor for short. Minor scales are usually used in a slightly different way to major in that there are two popular variations on the natural minor. We’ll look at how these variations are used in part 2 of this course so for now we’ll use the natural minor as our minor example.

The major and natural minor modes are also known by Greek names based on modes in the renaissance era.
Major = Ionian mode. Natural minor = Aeolian mode.

What About Keys?

You’re more likely to hear people talk in terms of keys rather than scales and modes. A key is simply the notes of a scale when they are rearranged to make music.

For instance, any music which is based on the scale of C major is in the key of C major.

The major or minor (or any mode, for that matter) can be made to start on any root note. The major mode on D is called D major. The minor mode on F is called F minor. We’ll look at how this works in coming posts..

Scales and melodies

We can tell the difference between C major and A minor when we play the scale because we’re emphasising the root note – by playing it first, last and longer than the other notes. Furthermore we can hear the progression of ascending or descending notes arrive on the root note. But how can we recognise the mode when the notes are all mixed up in a melody?

It’s all about being able to recognise the root note.

Melodies rely on a range of techniques to highlight the root note including those I’ve just mentioned. A melody isn’t a random selection of notes. The structure of the phrases that make up a melody and the relative length and strength of notes all contribute to our ability to recognise the root note as home. Some of these techniques are mentioned in a little more detail in How Can We Tell Which Key We’re In?

Summary

A scale is a selection of (usually 7) pitches within an octave, which form the basic pitch elements of a piece. The notes can be played at any octave.
The root note or tonic is the first note of the scale and the reference/ home note for music written using that scale.
The interval spacing of the notes of a scale is called a mode. The most common modes are called major and minor.
Each mode imparts a unique character to the music because of its unique combination of 1 and 2 semitone intervals from note to note.
We can hear the character of the mode because the music is written in such a way as to highlight the root note. For some examples, visit How Can We Tell Which Key We’re In?

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.

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 2023.

NEXT LESSON: 9. Accidentals, Sharpen and Flatten

PART 1 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).

(…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:

by playing that note louder than the others or giving the note an accent (a strong attack).
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.