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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.

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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

13. Relative Major And Minor

In a hurry? You can scroll down to the summary here.

This lesson should really be called Relative Modes because the following applies equally to other traditional Western diatonic modes such as Dorian or Myxolydian. All these modes are relatives; they are all siblings.

First, a quick reminder about scales, keys and key signatures. You can read more on this in my beginner’s tip, Scales, Modes And Keys: What’s The Difference?

A key is made up of a root note and a mode (such as major or minor).
A scale is an ordered list of the notes of a key.
A mode is the pattern of intervals from one note to the next in a scale.
A key signature is an ordered list of the notes of a key which are sharps or flats. Those not listed in a key signature are naturals.
Keys/scales are named after their root note and mode.

Let’s start by looking at the naturals, A to G – a key signature of 0 sharps or flats. We already know that we can play a major scale by starting on C (C major). We can also play a minor scale by starting on A (A minor). These are the original major and minor modes.

Both these scales, C major and A minor, use the same notes; the naturals, and have the same key signature (0 sharps/flats). The same is true for any key signature.

For any key signature there is one major and one minor key. We call these relative major and minor, because they share the same notes (the same key signature).

Here we can see C major and A minor.

The Relationship Between Relative Major And Minor

The relationship between them can be seen by their root notes.

If you start with A minor, it’s relative major, C major, is the 3rd scale note up from the root note.
If you start with C major, its relative minor, A minor, is the 3rd scale note down from the root note (or, as in the above graphic, the octave of the root note, which of course is the same).

Note: When counting scale notes, we count the starting note as the first note. For example, the 3rd note up from A is C. We count A B C.

If you already have a key signature for the major it’s really easy to count scale notes to find the relative minor. From the major’s root note just count down to the 3rd letter: the key signature takes care of the sign.

If you know the key signature of the major scale, it’s easy to find its relative minor.

Note: To find the key signature of a major key, use the cycle of fifths. See 12. Major Keys And The Cycle/Circle Of Fifths for more.

What If We Don’t Know The Key Signature?

In the graphic of C major and A minor, we can also see that the root notes of the relative major and minor scales are 3 semitones apart. If we don’t know the key signature, such as when reading chord charts, it’s important to count semitones as well as letters.

How To Find The Relative Minor

From a major key to its relative minor, count down to the 3rd letter.
If we don’t know the key signature, count the number of semitones between the two notes.
If you count 3 semitones, you have the right answer.
If you count 4 semitones, sharpen the note (if it’s a natural, add a sharp sign).

Example 1: What is the relative minor of Ab major?

The 3rd letter down from Ab (including A itself) is F (count A G F)
Ab is 3 semitones below F, which is the right amount.
The relative minor of Ab major is F minor.

Example 2: What is the relative minor of A major?

The 3rd letter down from A (including A itself) is F (count A G F)
F is 4 semitones below A, so we have to sharpen it to make it 3 semitones below A = F#
The relative minor of A major is F# minor.

How To Find The Relative Major

From a minor key to its relative major, count up to the 3rd letter.
If we don’t know the key signature, count the number of semitones between the two notes.
If you count 3 semitones, you have the right answer.
If you count 4 semitones, flatten the note (if it’s a natural, add a flat sign).

Example 1: What is the relative major of E minor?

The 3rd letter up from E (including E itself) is G (count E F G)
G is 3 semitones above E, which is the right amount.
The relative major of E minor is G major.

Example 2: What is the relative major of Eb minor?

The 3rd letter up from Eb (including E itself) is G (count E F G)
G is 4 semitones above Eb, so we have to flatten it to make it 3 semitones above Eb = Gb
The relative major of Eb minor is Gb major.

We call the interval between the root notes of the relative major and minor a minor 3rd. Don’t worry, we’ll look at interval names properly later in this course- I only mentioned it in case you’ve heard of it. In a nutshell, when we count intervals we include the fist and last notes, hence we call from A to C a 3rd. A minor 3rd is only 3 semitones, not 4.

Note: When counting the interval between two notes as letters, always include the first and last letter.

Once you know the relative major, you can use your memory of the cycle of 5ths for major scales to find the key signature.

Patterns

C major is the original major. All other major scales have the same pattern of intervals from note to note, the same mode, as C major, so whatever we can observe with C major is true for all major scales or keys. The same can be said for A minor: whatever we can observe with A minor is true for all minor scales/keys.

This is good news! Unlike the scientific method, where every instance needs to be proven, with scales we can treat any one example as universal. So much easier, and so much easier to remember. If you forget the relationship between relative major and minor, just look at the keys you know best, C major and A minor.

Know Your Key Signatures

Classical students learn the key signatures of all major and minor keys by rote, usually at primary school age, and often gradually, over the same period of time as they learn to play in these keys.

However, there are a couple of other options which we’ll look at below. I would like to add, though, that it’s definitely worth learning at least the most commonly used keys for your instrument and genre.

The Cycle Of Fifths And Relative Minor/Major

In 12. Key Signatures: Major Keys And The Cycle/Circle Of Fifths we discovered the relationships between major keys and the order of key signatures. We also looked at using a mnemonic to remember the order of major keys and their key signatures.

Potentially we could learn another mnemonic that starts on A instead of C for the minors but we don’t need to. If we know the major key of a key signature, we can find its relative minor by counting down to the 3rd note.

How To Find The Minor Key Of A Key Signature

As we saw with our earlier example, the key signature of three flats,

Remember (or look at) the cycle of fifths to find the major key for that key signature.
Then simply count down to the 3rd scale note to find its relative minor.

How To Find The Key Signature Of A Minor Key

You can also use this in reverse. To find the key signature of a minor scale, count 3 semitones up to the 3rd letter to find its relative major, then use the cycle of fifths to remember/look up the key signature.

First, find the relative major by counting up to the 3rd letter.
Check that the interval is 3 semitones. If it’s 4 semitones, flatten the note (if it’s a natural, add a flat sign).
Now use the cycle of 5ths for major scales, either from memory or by looking below, to find the key signature.

Example: What is the key signature of G minor?

Count up to the 3rd letter = B
Count semitones =4
If 4 semitones, flatten the note = Bb. The relative major of G minor is Bb major.
Look up the relative major in the cycle of fifths (try to do this by memory): Bb major has two flats, Bb and Eb.
The relative minor, G minor, also has two flats, Bb and Eb.

Try These…

Exercise 1:

Name the major and minor keys that have the following key signatures.

Use your memory of the Cycle of fifths or see the graphic below below to find the major key, then find its relative minor by counting down to the third note. Be sure to look at the key signature to see whether that note is a sharp, flat or natural.

Exercise 2:

Now try it the other way round. Name the key signature of the following minor keys.

B minor, C# minor, Bb minor, C minor

Answers at the end of this post.

if you’ve forgotten the cycle of fifths for major keys, here it is…

The Cycle Of Fifths For Majors And Minors

For those who just want the ultimate shortcut and have their phone on hand, have a look at The Cycle (circle) Of Fifths which shows the cycle of fifths for both major and minor keys in the same image.

How To Tell Whether A Piece Is Major Or Minor

When you see a notated part, the key signature itself doesn’t tell you whether the piece is in the major or minor key of that key signature. It is expected that the player will be able to tell, once they look at the notes.

What a player looks for is the root note. The root note is the obvious difference between relative major and minor. Once we know both the key signature and the root note, as we play, we can listen to the notes from the perspective of the intended tonality and interpret the music correctly.

So how can we tell which note is the root note?

Looking For The Root Note

In a typical piece, the root note will be evident in the first bar and again in the last bar. By evident, I mean that the note will stand out in relation to the surrounding notes. It may be the longest or strongest note, the note most repeated, or just the note that the neighbouring notes lead towards it.

This is a very broad statement and is mostly, but not always, true.
It applies to music which is familiar to the ear: music which we might describe as “musical”, “melodic” or “understandable” when we listen to it.

Note: For more detail on how to find the root note of a written part, please have a look at How Can We Tell Which Key We’re In? This post includes some short examples of what to look for.

It may seem daunting to find the root note out of 7 possible notes but it’s not as bad as all that. The vast majority of music is based on the major or minor modes (and variations of the minor, but more on that in a later post) so for most genres we only need to look for one of two possible notes, not 7. Most of the other modes are more typically used in early music or folk music and publishers of these genres often specify the mode as text, in which case we don’t need to look any further…

Once we know which two notes to look for, we can have a look at the first and last bars of the music to find which one is more prominent.

Summary

To find the relative major of a minor key, count up to the 3rd note in the key signature.
To find the relative minor of a major key, count down to the 3rd note in the key signature.
When counting, don’t forget to include the note you start on in your count.
If you don’t have a key signature, such as when reading chord charts, make sure that the two root notes are also 3 semitones apart (not 4 semitones). This may require you to use a flat or sharp sign.

To find the key signature of a minor key, find its relative major as above and use the cycle of 5ths for major scales to find the key signature.

NEXT LESSON: 14. The Relationships Between Keys

PART 1 CONTENTS: Basic Music Theory Course Contents

Answers

Exercise 1:

G major and E minor
F major and D minor
A major and F# minor
Ab major and F minor

Exercise 2:

2 # = F#, C#
4# = F#, C#, G#, D#
5b = Bb, Eb, Ab, Db, Gb
3b = Bb, Eb, Ab

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.

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.

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#

The Note Naming Rule For Scales And Keys

Each note in a key or scale must have its own letter.

Most Western scales have 7 notes. Including those with a sharp or flat in their name, most notes have two possible names.
We have 7 letters for note names and 7 pitch positions per octave on a stave. It makes sense that each note in a scale has a different letter as it’s name.

(Graphic, dots, D major scale with wrong crossed out and right notes)

(Sib graphics of D major melody, wrong/right notes)

If there are two possible names for a note, always choose the name that’s not used by any other notes in that key or scale.

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

5. How Long Is A Note? Note Values 1

Note Length

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

Note Values

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

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

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

60 crotchet beats per minute

Funny Names

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

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

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

Table of Note Values

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

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

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

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

Stem direction

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

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

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

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

Tails and Beams

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

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

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

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

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

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

Dotted Notes

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

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

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

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

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

NEXT LESSON: 6. Time Signatures 1 – Simple Time

PART 1 CONTENTS: Basic Music Theory Course Contents

Pitch Ranges

Below are the pitch ranges of some common musical instruments. The note names and octave numbers are written below the piano keyboard. Middle C and A440 are marked.

For more on pitch and note names, please visit 1. Note Names, Semitones and Octaves.

For more on octave numbers as used in this post, please visit Text Notation: Pitch And Octave Numbering.

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.

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.

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.

1. Note Names, Semitones and Octaves

If note names mean nothing to you, start here…

In my posts:

A PIECE is any musical work.
A PART is one instrument’s component of a piece.
An ENSEMBLE is any combination of instruments collaborating to perform a piece, be it one person singing and playing, a band, choir or orchestra.

Note names

Most musicians are familiar with the note names A to G. After G comes A again and the pattern continues repeating from the lowest pitches to the highest.

A B C D E F G A B C etc.

Over the audible pitch range there are many A’s, many B’s and so on.

From one A to the next is an octave, as is from any letter to the next instance of the same letter.

Octaves

Notes which are an octave (or several octaves) apart enjoy a special relationship. When played together, the higher note blends in to the lower note. If they’re perfectly in tune (that’s for a later post), the higher note blends in so well that it almost merges inside the lower note. Even when played one after the other, what we hear sounds more like a change in register (or voice) than a different note.

Try this on your instrument. If you can play two notes at once or play one and sing the other, the effect will be the clearest, but you can still tell by playing one after the other.

Now try combinations of two different notes, such as A and G or A and C. None feel as closely connected as when they’re an octave apart (or a unison; two notes of exactly the same pitch).

In musical terms, in an ensemble, any part can be played an octave higher or lower without clashing with the other parts. All chords or harmonies will still fit. It is because of this relationship that notes which are octaves apart can, and do, share the same note name.

Intervals

The difference in pitch between one note and another is called an interval. A to the next A, an octave, is an interval, A to G is an interval, F to C is an interval.

Intervals can be measured in octaves and semitones. Each octave is divided into 12 musically equal intervals called semitones. This gives us 12 different notes, the 13th being an octave. The semitone is the centimetre (or inch) of pitch.

On a piano, 1 semitone is the interval between consecutive keys, regardless of the key’s colour.
On a guitar, 1 semitone is the interval from one fret to the next (or from an open string to the first fret).

We started with the letters A to G, followed by A etc. that’s 7 letters, the 8th being the octave of the first (as it happens, octave means 8th). So how do 7 letters add up to 12 semitones?

Not all letters are 1 semitone apart: in fact, most are 2 semitones apart. This is how the letters are spaced:

A . B C . D . E F . G . A
2 1 2 2 1 2 2 = 12

This means that 5 of the 12 different notes (per octave), the ones represented here by dots, have no name.

On a piano keyboard, all the named notes are white keys. You can see when two white keys are 2 semitones apart because there is a black key to represent the so far un-named note between them.

Piano keyboard layout showing naturals for 1 octave

On a guitar, you can find the named notes by starting on an open string, then following the above pattern by skipping a fret for every 2-semitone interval. The dots above represent the frets you skip.

Guitar fingerboard layout, A string, showing naturals for 1 octave

The named notes are called naturals. The un-named notes can be described as being 1 semitone higher or 1 semitone lower than the nearest natural.

Sharps and flats

Any natural can be raised by 1 semitone by adding the sharp symbol, #.
Any natural can be lowered by 1 semitone by adding the flat symbol, b.

For instance, the note between A and B could be called A# (A plus 1 semitone) or Bb (B minus 1 semitone).

This may seem confusing: we’ve gone from having no names for some notes to having two names. Fear not. For now, either name will do. The most common note names in general terms are:

A Bb B C C# D Eb E F F# G G# or Ab

Once we look at the notes in the context of a piece of music, the choice of note names will matter but by then it will be quite obvious which names to use. The correct note names for a piece are based on its key, a subject for a future post.

The graphic below shows how any natural can be raised by 1 semitone by adding a sharp or lowered by 1 semitone by adding a flat, resulting in two possible note names for most notes. Notice that even some of the naturals have an alternate name, although their use is relatively uncommon in most keys.

In my next basic post we will look at how note pitches are written on a stave.

Try These…

How many semitones between the following pairs of notes? (count up from the first note until you reach the second note of the pair):

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

Answers at the end of this post.

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: 2. Notes on a Stave: Pitch

PART 1 CONTENTS: Basic Music Theory Course Contents

Answers to Try These…

A to C = 3 semitones
A to C# = 4 semitones
A to E = 7 semitones
A to G = 10 semitones
Bb to F = 7 semitones
B to F = 6 semitones
C to A = 9 semitones
C# to A = 8 semitones
D to Bb = 8 semitones