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B13. Degrees Of A Scale: Relative Note Names

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.

Scale Degrees

As we’ve seen in 10. How To Find The Notes Of A Scale, we can name the notes of a scale by using the interval pattern of its mode to find the right notes.

If we want to look at scales in a more general way, we can replace the actual note names by degree names; numbers representing the position of each note in the scale, such as 2nd, 3rd, 4th etc. The exception is the root note, which is either called the root note (RN for short) or tonic.

Interval Names As Scale Degrees

Further, we can distinguish notes in the major from the parallel minor by thinking of each degree as an interval above the root note and include the quality in the name.

For instance,

the 3rd note of a major scale is called the major 3rd
the 6th note of a minor scale is called the minor 6th
the 4th note of both major and minor scales is called the perfect 4th

Interval names as scale degrees allow us to describe scale notes in relative terms, so we can look at an example in one key and apply what we notice to any key.

Degree Names Quick Tip

For major and natural minor scales,

the 3rd, 6th and 7th are major or minor, as per the scale
the 2nd is always major
the 4th and 5th are always perfect

Note: we don’t use a quality for the 1st/octave.

The harmonic minor has a major 7th. The rest of the notes have the same degree names as the natural minor.

Why use degree names when we already have note names?

Degree names are a great analysis and learning tool.

As mentioned earlier, degree names make it easy to apply something we noticed in a particular key to any other key. This could be in the melody but it applies equally to chords.

Degree names are particularly useful for understanding chords: notes in a chord are also described as intervals above the root note.

Try These…

The first note in each exercise is the root note/tonic.

Use the key signature to work out if the key is major or minor.
Name the key.
Name the following notes as scale degrees.
Don’t forget to include the interval quality in the degree name, as described above.

Example

Note: if you prefer text to music notation, the exercises are written as text here.

Answers at the end of this post.

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

NEXT LESSON: B14. Chords 1: Major/Minor Triads And Modal Chords

PART 2 CONTENTS: Basic Music Theory Course Contents

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Answers To Try These…

Try These… (Text Version)

(text version of exercises)

D major: D, E, F#, A
B minor: B, E, F#, A
Eb major: Eb, Bb, C
C minor: C, Ab, Eb

To view the answers, click here.

B12. Bar Numbers And Pickup Bars

Is There Life Before Bar 1?

Bar Numbers

Each complete bar has a bar number. In a printed part, the bar number is usually written at the start of each stave except the first. Some parts number every bar or every few bars. Others, especially parts for shorter pieces, don’t include bar numbers at all.

Bar numbers are useful in longer pieces to identify sections that need practice.

How Bar Numbers Are Counted

A barline signifies the end of the current bar (and the start of the next bar).

The first complete bar is Bar 1. Typically Bar 1 starts on the first note or rest after the time signature. Bar 2 starts after the first barline.

Upbeats/Pickup Bars

I say typically because it’s not unusual for a part to start a note or two before the beginning of the first bar, as a lead-in to the first strong beat.

An example of this is when a song lyric starts with a preposition, such as “in the town”, “by the light” etc. where the emphasis is on the noun, “town” or “light”.

Lyrics or not, lead-ins are quite common. Usually a lead-in is just one or two quick notes, but longer lead-ins are also possible.

A lead-in is formally called an anacrusis. In popular music it is called an upbeat or a pickup bar.

Personally, I find the term “pickup bar” confusing because it isn’t a complete bar.

A pickup bar/upbeat/anacrusis consists of one or more notes before the start of bar 1.

Looping The Loop

Note that in the above example the last bar is 3 beats long instead of 4.

If the piece were to repeat, the timing would add up to whole bars and provide a smooth transition into the repeat.

If a piece starts with a partial bar, then it should finish with another partial bar equal to the remainder of that bar.

How To Recognise An Upbeat

An upbeat is less than a bar long. If the length of all the notes and rests before the first barline is less than a whole bar, it is an upbeat.

Bar 1 is always a complete bar. Anything less than a complete bar is an upbeat, not bar 1.

How To Work Out When To Come In

Add up the length of the notes in the incomplete bar
Subtract it from a whole bar to work out where the first note starts
Imagine rests being written from the start of the bar to the first written note.

For example, if there is 1 beat worth of notes before the first barline and the piece is in 4/4, there are 3 unwritten beats (4-1=3): the first note is on beat 4. Imagine rests where beats 1, 2 and 3 would go.

Counting In

When starting a piece, it’s always good to count a bar at the intended tempo before starting to play. In an ensemble this is essential, so everyone can come in on time, but even for solo playing, it helps to establish the tempo and time signature in your mind before you start.

For a partial bar, count a complete bar followed by the unwritten part of the bar. This ensures that you can feel the rhythmic structure correctly.

A time signature has a hierarchy which is implicit in every bar (See 6. Time Signatures 1 – Simple Time and B8. Time Signatures 2: Compound Time). Beat 1 is the strongest part of a bar. By counting a whole bar plus the unwritten part of the pickup bar, it’s easier to feel where within the bar the upbeat starts.

Try These…

Rewrite these melodies with rests before the first note to make up a whole bar.
Count in 1 bar plus the rests and tap, clap or play the rhythm.

Answers at the end of this post.

Upbeats Within A Piece

Upbeats don’t just occur at the beginning of a piece. Any musical phrase can start before the first full bar of that phrase. To do this, there has to be enough room at the end of the previous bar to fit the upbeat in.

In the above example, the first phrase finishes before the end of the bar to make room for the upbeat of the second phrase.

Practising A Phrase With An Upbeat

If you want to practise a phrase which starts with an upbeat without having to play all the way from the start, treat it like it’s the start of the piece: count rests over the end of the previous phrase so you know which part of the bar you come in on.

NEXT LESSON: B13. Degrees Of A Scale: Relative Note Names

PART 2 CONTENTS: Basic Music Theory Course Contents

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Answers To Try These…

B11. Playing Music With Swing

What Is Swing?

Swing refers to a particular rhythmic character which features prominently in many popular genres including blues, rock and jazz: that of “uneven halves”; pairs of quavers with the first quaver lengthened and the second one shortened.

In compound time we would write this as a crotchet plus a quaver; 2+1.

In some genres, compound time isn’t very popular as a form of music notation. For musicians with a firm upbringing in simple time, having to interpret a dotted crotchet as one beat goes against the grain.

We could write the same rhythm in x/4 as a triplet group, as discussed in the previous lesson, B10. Note Values 3: Triplets, but it makes the music look cluttered.

With Swing

Instead, we can use a shortcut.

We can write it in x/4 as pairs of quavers, with the term “swing”, “with swing” or “swung eighths” written at the start of the piece, next to the tempo or character marking.

The term ”swing” is equally used in text notation such as chord charts.

Note: Quavers are often beamed in groups of 4. These are played the same as if they’re beamed in pairs. Every odd quaver is lengthened and every even quaver shortened.

Swing notation only works when the beat is predominantly divided into the swing pattern. Occasional variations based on thirds of a beat can be written as triplet groups.

Alternatively, the score can be written in compound time.

Degrees Of Swing

I don’t mean a PHD in swing…

Swing, or lopsidedness, can be applied in varying degrees, from hardly any to a lot. There is no formal way to notate this: it depends on what’s authentic to a particular genre and on the player’s personal interpretation.

The default interpretation is as described, 2/3 of a beat for the first “quaver” of the pair and 1/3 of a beat for the second.

Extreme swing, typically 3/4 of a beat + 1/4 of a beat, is usually notated formally in simple time as a dotted quaver + a semiquaver.

Try These…

Re-write the following melodies with swing in compound time, using the appropriate time signature (hint: check how many beats are in a bar).
Tap, clap or play the rhythm of the melodies as you have written them.
Once you feel the rhythm, try reading the version with swing as you play/tap.

For example,

Answers at the end of this post.

Swing And Compound Time

Although it’s seldom written on the score, the concept of swing can also be applied to compound time.

The typical way of giving a group of 3 quavers swing is to lengthen the first and shorten the 2nd, just as in simple time. The remaining quaver is generally left as a normal quaver.

This can also be notated formally as follows:

As with swing in simple time, the degree of swing applied when not notated formally is subject to interpretation and can vary from subtle to blatant.

A subtle degree of this type of swing is often used in traditional folk tunes such as jigs.

For a refresher on compound time, please visit B8. Time Signatures 2: Compound Time.

NEXT LESSON: B12. Bar Numbers And Pickup Bars

PART 2 CONTENTS: Basic Music Theory Course Contents

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Answers To Try These…

B10. Note Values 3: Triplets

In B8. Time Signatures 2: Compound Time we saw that we can regularly divide a beat into thirds and sixths by using a time signature in compound time. But what if we just wanted the occasional beat in thirds while the rest of the piece contains half and quarter beats?

Triplets

In simple time, we can divide an individual beat into thirds by using triplets, in this case triplet quavers.

Triplets are indicated with a triplet sign; the number 3 written outside the beam.

In terms of duration,

1 crotchet = 2 normal quavers = 3 triplet quavers

It’s not just crotchets that can be divided into triplets: any standard note value (excluding dotted notes) can. If the note value is too long to use beams, a square bracket is used to indicate the grouping.

In general terms, 3 triplets of any note value are the same total length as two normal notes of that value. They equal one of the next longer note value.

Other Combinations

Any rhythm based on dividing a note into thirds rather than halves can be used within the triplet group, such as a triplet crotchet plus a triplet quaver or a series of triplet semiquavers.

Any rhythm in compound time can be written as triplet groups in simple time.

Note that because a triplet crotchet-quaver group has no beam, a square bracket is used to allow us to see where the beats are.

Sometimes square brackets are written over beamed triplets as well.

How To Play Triplets

When you first try to tap or play triplets in simple time, it’s often hard to keep them even.

The most common mistake is to play the first and second quavers too fast and the last one too slow, resulting in 2 semiquavers and a quaver. This has quite a different character.

Hopefully you’ll already be familiar with the character of triplets from compound time. If not, please revisit B9. How To Read Rhythms 2: Compound Time.

Try These…

Practise these rhythms made up of triplet groups. If you find them difficult, slow the tempo down.
Rewrite the rhythms in 12/8 (tip: each triplet is equal to 1 beat of compound time).

Answers at the end of this post.

Swapping Between Quavers And Triplets

Before being able to freely swap between quavers and triplets,

Practise each rhythm separately to a metronome at a medium-slow tempo, say around 80bpm.
Once you feel fully settled, try 4 beats of each, then 2.
Eventually you will be able to alternate at will.

The trick to learning rhythms is repetition. Play each rhythm till you can do it instinctively.

Any rhythm, even a simple one, needs to be so familiar that you can remember it by its character or feel, rather than having to figure it out from scratch every time you play it.

Avoiding Clutter

Triplet signs, especially those with brackets, make the music look unusually cluttered. This is fine for the odd triplet in the midst of normal note values but these common groupings could easily be the main rhythm of the piece. Imagine a whole piece written in triplets!

Pieces which predominantly use triplets are either written in compound time or by using a shortcut which we’ll look at in the next lesson.

NEXT LESSON: B11. Playing Music With Swing

PART 2 CONTENTS: Basic Music Theory Course Contents

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Answers To Try These…

B9. How To Read Rhythms 2: Compound Time

Simple Rhythms In Compound Time

Note: There are a number of exercises in this lesson, so it may take a little longer to complete. Take as long as you need… You can the first few rhythms now and come back to the harder ones later.

One-Beat Rhythmic Modules

Below are some simple 1-beat rhythms in compound time, written as individual bars of 3/8. Tap, clap or play along with these until you are familiar with them and can play them by yourself.

Although not indicated in the part, each rhythm is played 4 times.

To start learning each rhythm, count each quaver as a beat, as demonstrated in B8. Time Signatures 2: Compound Time.

Once you’re comfortable with these exercises at a quaver beat of 180 bpm, try counting every bar of 3/8 as a single, dotted crotchet beat at 60 bpm.
From there, you can continue to increase the tempo, counting dotted crotchet beats.

Practice Tip: Beats are easier to feel if you emphasise notes which are on the beat by playing an accent. Accenting the beats will help transition from playing with a metronome to without.

These rhythms can be combined to form complete bars of 6/8, 9/8, 12/8 etc. You can make up your own combinations. There are a few common examples at the end of this post.

Rhythms with semiquavers

Any quaver in the above rhythms can be substituted by a pair of semiquavers. In the following rhythms, look at pairs of semiquavers as halves of a beat, “1 and”.

Note: As you continue to increase the tempo, the semiquavers become too fast to be able to say the word “and”. Hopefully, by then you can feel them without having to count aloud.

The above are by no means every possible combination involving semiquavers. However, these are the most common; familiarity with these rhythms will make it easier to learn new ones.

Syncopation

Below are three common syncopated rhythms within a beat in compound time. Again, they are written as individual bars of 3/8.

Each rhythm is preceded by a similar rhythm which you have already learnt in the previous exercises. To create the syncopation, simply hold the dotted quaver (or quaver in the last example) through the first of the pair of semiquavers in the previous bar, as indicated by the counting lyrics.

Bars Of One-Beat Modules

Each of the above rhythms in 3/8 amount to a single beat in compound time. They (and other 3/8 rhythms not listed here) can be combined to form rhythms of 1, 2 or more bars.

Below are a few common 1-bar rhythms for you to practice. Rather than having to learn the whole bar as a new rhythm, look for the individual 1-beat rhythms you have already learnt then join them together.

As recommended earlier, if you have any difficulty counting dotted crotchet beats, start by counting each beat as a bar of 3 quaver beats.

Try These…

Answers at the end of this post.

NEXT LESSON: B10. Note Values 3: Triplets

PART 2 CONTENTS: Basic Music Theory Course Contents

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Answers To Try These…

These are played at a moderately slow tempo you can play along to. You may be able to play faster than these “answers”…

B8. Time Signatures 2: Compound Time

The standard note values make it easy to to indicate lengths of half or quarter of a beat. This suits some rhythms but not all. Many others are based on dividing a beat into thirds.

Dividing A Beat Into Thirds

Rhythms based on 1/3 beat subdivisions have a slightly more lelaxed feel compared to semiquavers; they sound a little less intense…

That’s not to say that these rhythms can’t be powerful and driving!

Compound Time

So how can we divide a beat into thirds of a beat when the standard note value symbols are based on halves?

We do this by using a symbol for 1 beat which naturally has 1/3 beat subdivisions, the dotted crotchet.

A dotted crotchet is the same length as 3 quavers.

In simple time we count beats and half beats as ”1-and 2-and” etc.
In compound time we count ”1-and-a 2-and-a” etc.

Time Signatures With A Dotted Crotchet Beat

To make a beat which naturally divides into thirds, we want the dotted crotchet, not the crotchet, to be the symbol for 1 beat. So how do we distill this into a fraction name?

A dotted crotchet = a crotchet + a quaver. As a fraction, that’s 1/4 + 1/8 = 3/8. The dotted crotchet is a 3/8 note.

Time signatures are written as the number of beats in a bar x the note value for 1 beat.

A bar of 2 dotted crotchet beats is 2 x 3/8 = 6/8
A bar of 3 dotted crotchet beats is 3 x 3/8 = 9/8
A bar of 4 dotted crotchet beats is 4 x 3/8 = 12/8

And so on…

Review: Time Signatures In Simple Time

Time signatures are fractions. In simple time, the upper note, the numerator, represents the number of beats in a bar and the lower note, the denominator, represents the name of the note value which represents 1 beat.

Split up, a time signature in simple time looks like this:

3/4 = 3 x 1/4 note (crotchet) beats per bar

Other note values can also be used to represent 1 beat. For example,

4/8 = 4 x 1/8 note (quaver) beats per bar
2/2 = 2 x 1/2 note (minim) beats per bar

Reserved Time Signatures

When we see a time signature like 6/8 we would normally assume that there are 6 beats in the bar, each of which is a quaver (1/8 note). However, 6/8 and higher multiples of 3/8 (not 3/8 itself) are reserved for music which requires a dotted crotchet beat.

These time signatures aren’t what they appear to be; they need to be broken down to be understood. Appropriately, they are collectively known as compound time.

It takes a little while to get used to reading music in compound time. We’re so used to seeing a crotchet as 1 beat that it’s hard not to think of a dotted crotchet as 1 1/2 beats…

The trick for reading compound time is to think of each dotted crotchet as a fast bar of 3. More on this later…

Hierarchy Of Compound Time

Bars have strong and weak beats. This is true for both simple and compound time. The only difference is whether a beat naturally divides into halves or thirds.

Below are the hierarchies of strong and weak points in 6/8, 9/8 and 12/8.

How To Read And Play Compound Time

In simple time, we can make a piece easier to learn by slowing it to half the tempo and counting every half-beat as a beat. For a reminder, please visit 3. Beats, Tempo and Timing.

In compound time, the same method would have us slow down to 1/3 of the tempo so each quaver can be counted as a beat. Practically, we don’t need to slow down quite so much, but the principle is the same.

Think of each dotted crotchet grouping as a miniature bar of 3 quaver beats, a bar of 3/8. Three beats per bar at a fast tempo is familiar to many as a waltz. If you know what a fast waltz feels like, you’re well on the way… if not, practice each dotted crotchet’s worth of notes as a separate bar of 3 until you feel the rhythm.

Once you can feel character of each beat of 3/8 as a simple 3-beat rhythm, you can start to speed up the tempo a bit until each bar of 3/8 feels like a beat in the overall time signature.

For example,

Zoom in a little. Think of each beat as a bar of 3.

It may look more familiar if we rewrite it as 3/4. Simply double each note value.

If you’re familiar with simple rhythms in 3/4, you’ll be able to play them at the tempo of a fast waltz.

Tap, clap or play along:

3/8 has the same beat structure as 3/4, it just looks different. Just count quavers as beats instead of crotchets…

Once you’re used to the character, increase the tempo until it’s quite fast, say 180 bpm.

As you speed up, you’ll start to feel each group of 3/8 as a single beat.

Once you feel the character of the whole rhythm, you can increase the tempo further if needed.

In the next lesson we will look at some common rhythms in compound time.

* Audio extract from Another Hopeless Situation by Erik Kowarski

NEXT LESSON: B9. How To Read Rhythms 2: Compound Time

PART 2 CONTENTS: Basic Music Theory Course Contents

B7. How To Notate Very High And Very Low Notes

Note: This lesson looks at how very high and very low notes are written in music notation. When note pitches are written as text, their exact pitch is indicated by octave numbers. For more on text notation and octave numbering, including some examples and exercises, please visit Text Notation: Pitch And Octave Numbering.

Pitch Ranges Of Instruments

The piano keyboard spans over seven octaves, yet the great stave, the treble clef and bass clef combined, only covers about four octaves, even if we use a couple of ledger lines.

Most instruments only read one stave, yet the issue is the same. Treble instruments often have an extended range of high notes, well above the top of the treble clef. Many bass instruments have a lower range which extends well below the bottom of the bass clef. (For more on pitch ranges of different instruments, please visit Pitch Ranges).

Sure, it’s possible to use more ledger lines to increase the range, but lots of ledger lines are hard to read and take up a lot of space outside the stave. It looks even scarier when there’s a whole passage of notes with several ledger lines.

Octave Signs

When there are several very high notes on the treble clef, we can write them one octave lower and add an octave sign above the first note, followed by a dotted line which extends over the affected passage. A small bar at the end of the dotted line indicates the end of the octave sign.

For very low notes on the bass clef, we write the passage one octave higher. The octave sign, dotted line and bar appear below the affected notes.

Note:

The exact point at which you start and finish an octave sign is up to the writer: it’s okay to have some notes with a couple of ledger lines.
Octave signs can start and finish anywhere in a bar.
Octave signs are seldom used for a single note. They work best when covering several notes or more.

8va and 8vb extend the range of the great stave from over 4 octaves to over 6; even more when combined with the use of a couple of extra ledger lines.

High Octave, Low Octave

Notice a subtle difference in the two signs: the octave up sign is 8va and the octave down sign is 8vb.

8va stands for ottava alta which is Italian for a high octave
8vb stands for ottava bassa, meaning a low octave

I think of these as:

8va is an octave above what’s written
8vb is an octave below what’s written

Alternatively, you can just write 8 in either case.

Need to go even higher or lower? You can use the 2-octave up or 2-octave down sign.

15ma means 2 octaves up
15mb means 2 octaves down

If you wondering why the sign for 2 octaves is 15 rather than 16, it’s because, when counting intervals between one and two octaves, one letter is counted twice. For more on large interval names, please visit How To Name Intervals Larger Than 1 Octave.

What if we want to write very high notes in the bass clef?

This is less common, as bass instruments tend to have a limited treble range, just as treble instruments tend to have a limited bass range. However, for instruments with an extended range such as synthesisers, both octave signs can be used in either clef.

The great stave is considered as a single stave, so in piano music, 8va is only used on the treble clef and 8vb only on the bass clef.

Clef Changes

Another method of changing the displayed pitch of notes is to temporarily change clefs. Like octave signs, these are best used for passages of several notes or more.

Admittedly, this approach suits keyboard players best, as they are well versed in reading both treble and bass clefs. For readers of a single clef, octave below signs may be preferable.

Changing Clefs

In the bass clef, switch to the treble clef for very high notes. The bass clef stays in effect until the next treble clef. No dotted line is needed.

Like octave signs, clef changes can occur anywhere in a bar.

In the treble clef you can switch to the bass clef for very low notes.

Try These…

The exercises below involve both the treble and bass clef. If you only read one or the other, the illustration at the top of the post may help…

Ledger lines involve careful counting. These exercises are good examples of how octave signs and clef changes make reading easier.

Note: The “answers” supplied at the end of this post are not the only option of where to start and finish the octave signs or clef changes. As stated earlier, this is a subjective choice: a few ledger lines are acceptable in standard music notation.

A) Rewrite the following passages using octave signs

B) Rewrite the following passages using either octave signs or temporary clefs

Answers at the end of this post.

NEXT LESSON: B8. Time Signatures 2: Compound Time

PART 2 CONTENTS: Basic Music Theory Course Contents

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Answers to Try These…

A

B

Basic Music Theory Course Contents

Part 1

Module 1: Pitch and Note Length

Module 2: Simple Time

Module 3: Scales

Module 4: Keys and Key Signatures 1

Module 5: Keys and Key Signatures 2

Module 6: Intervals 1

Module 7: Singing Intervals

Module 8: Rhythm 1

Part 2

Module 1: Syncopation, Intervals 2

Module 2: Melodic and Harmonic Minor

Module 3: Intervals 3

Module 4: Compound Time

Module 5: Triplets and Swing

Module 6: Major and Minor Chords 1

Module 7: Major and Minor Chords 2

Module 8: Chord Relationships

B6. How To Name Intervals The Quick Way

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

There are many occasions when we need to name an interval, whether to describe a quirky jump in a melody or notes in a chord. So far, naming an interval has involved finding the major scale built on the lower note of the interval. Every time we want to name an interval with a different lower note, we need a different scale!

Scales are great for learning to pitch (sing or play) intervals and they help explain how interval names work but it’s not a quick way to name intervals. Let’s see if we can streamline this rather time-consuming process…

If you’re impatient and want to go straight to the ultimate shortcut, click here. Else read on for more detail…

Counting Intervals

Interval names are a way of describing both the size (number of semitones) and degree (number of letters). To name an interval we need to count both the number of semitones and the number of letters (inclusive).

Have a look at the list of all interval names within an octave:

If you have a good memory you could simply learn the complete list of interval names and their sizes in semitones from unison to octave, by memory, just like we learn our times tables.

How To Name An Interval Using The Interval List

Count letters, including the starting and ending letter of the interval. The number of letters make up the degree of the interval name.
Count semitones.
Find the row with the correct number of semitones in the list and look for the correct degree to the left or right in that row.

Example: A#-F

A#-F is 6 letters. A#-F is a 6th
A#-F = 7 semitones
7 semitones = perfect 5th or diminished 6th
We already know from step 1 that A#-F is a 6th, so A#-F is a diminished 6th

Less Is More

The list of interval names is rather large, so let’s reduce it a little.

Visualise

Remember the hierarchy of interval qualities. In your mind’s eye, see their effect on the size of an interval. For a given degree, augmented is 1 semitone larger than major or perfect and diminished is 1 semitone smaller than minor or perfect.

Inversions

Remember also that the larger an interval, the smaller its inversion. Using inversions for larger intervals cuts the list in half.

The Ultimate Shortcut For Naming An Interval

Learn the major, minor and perfect intervals from 0 to 7 semitones. You can leave out 6 semitones for now, as it doesn’t have a major, minor or perfect interval quality.

I prefer to use a single letter for the quality. It makes this list look tiny… P for perfect, M for major, m for minor (I also use a for augmented and d for diminished).

For 0 to 7 semitones, that’s

P1, m2, M2, m3, M3, P4, _, P5

That’s not a very intimidating list to learn, is it?

How To Name An Interval

To name an interval, we need to know the number of letters AND the number of semitones. If it’s 7 semitones or less, we can directly find it in the list.

For example, C-Eb

C-Eb is 3 letters so the degree is a 3rd
C-Eb is also 3 semitones
Check the list: the interval name for 3 semitones is a minor 3rd
That answer matches the degree: C-Eb is a minor 3rd

If large, Invert, then Invert the Answer

If the interval is larger than 5 letters, we can invert the interval: the larger the interval, the smaller the inversion. Once we have the inversion’s interval name, we can invert the name.

For example, C-B

C-B is 7 letters so it’s a 7th
Invert to get B-C
B-C is 2 letters so it’s a 2nd (7+2=9)
B-C is 1 semitone
The interval name on our tiny list for 1 semitone is a minor 2nd
B-C is a minor 2nd
Invert the interval name: minor goes with major, 2nd goes with 7th
C-B is a major 7th

Augmented and Diminished: Bigger or Smaller than Normal

Diminished and augmented intervals aren’t in this tiny list. That’s ok because we can work out if the interval is diminished or augmented by comparing the upper note to that of the nearest interval in the list.

For example, C-F#

C-F# is 4 letters, so it’s a 4th
The only 4th in our mini list is a perfect 4th, 5 semitones.
A perfect 4th above C is F
C-F# is 1 semitone larger than C-F
1 semitone larger than perfect is augmented
C-F# is an augmented 4th

How To Name Any Interval Within An Octave

This method covers all eventualities outlined above.

Count letters, including the starting and ending letter of the interval. The number of letters make up the degree of the interval name.
If more than 5 letters, invert the interval (invert the notes of the interval) and count its letters or subtract the original interval degree from 9.
Count semitones.
Find the number of semitones in the list.
Compare the degree in step 4 to the degree in step 1.

If the degree in step 4 matches the degree in step 1 we have the answer
If the degree in step 4 is larger than the degree in step 1 the interval is augmented
If the degree in step 4 is smaller than the degree in step 1 the interval is diminished

6. If the interval was inverted, invert the interval name.

Examples

Example 1: A-C#

A-C# is 3 letters, so A-C# is a 3rd
(If more than 5 letters, invert the interval and count its letters. N/A)
A-C# = 4 semitones
4 semitones is a major 3rd
The interval is a 3rd and the list for 4 semitones is a major 3rd.
(If the interval was inverted, invert the interval name. N/A)

A-C# is a major 3rd

Example 2: A-B#

A-B# is 2 letters, so A-B# is a 2nd
(If more than 5 letters, invert the interval and count its letters. N/A)
A-B# = 3 semitones
3 semitones is a minor 3rd
The interval is a 2nd and the list for 3 semitones is a minor 3rd. A-B# is a 2nd which is the size of a minor 3rd, 1 semitone larger than than a major 2nd.
(If the interval was inverted, invert the interval name. N/A)

A-B# is an augmented 2nd

Example 3: A-Cb

A-Cb is 3 letters so A-Cb is a 3rd
(If more than 5 letters, invert the interval and count its letters. N/A)
A-Cb = 2 semitones
2 semitones is a major 2nd
The interval is a 3rd and the list for 2 semitones is a major 2nd.
A-Cb is a 3rd which is the size of major 2nd, 1 semitone smaller than than a minor 3rd.
(If the interval was inverted, invert the interval name. N/A)

A-Cb is a diminished 3rd

Example 4: A-G

A-G is 7 letters. A-G is a 7th
Invert A-G to get G-A, which is 2 letters. G-A is a 2nd
G-A = 2 semitones
2 semitones is a major 2nd
The interval is a 2nd and the list for 2 semitones is a major 2nd.
G-A is a major 2nd
Major goes with minor and 2nd goes with 7th

A-G is a minor 7th

Example 5: A-Gb

A-Gb is 7 letters, so A-Gb is a 7th
Invert A-Gb to get Gb-A, which is 2 letters.
Gb-A is a 2nd
Gb-A = 3 semitones
3 semitones is a minor 3rd
The interval is a 2nd and the list for 3 semitones is a minor 3rd.
Gb-A is a 2nd which is the size of a minor 3rd, 1 semitone larger than than a major 2nd.
Gb-A is an augmented 2nd
Augmented goes with diminished and 2nd goes with 7th

A-Gb is a diminished 7th

Try These…

a) Learn the list of normal interval names from 0-7 semitones as outlined above, then name the following intervals.

F-A
C-A
F#-G
F#-D
Bb-G
B-E
C#-Ab
G#-G
Ab-B
Ab-G#

Answers at the end of this post.

Short-cut 4ths And 5ths

There’s an easy way to spot perfect 4ths and 5ths.

A 4th or 5th is perfect if both notes have the same sign
UNLESS the letters are B AND F (remember BCEF?)
If the letters are B AND F, to make a perfect interval, Bb goes with F and B goes with F#

Count letters.
A 4th or 5th is perfect if both notes have the same sign, unless the letters are B AND F. To be perfect, Bb goes with F and B goes with F#.
If a 4th or 5th is not perfect you can work out whether it’s diminished or augmented by looking at whether it’s 1 semitone larger or smaller than a perfect 4th or 5th.

Example: Ab-E

Ab-E is 5 letters so Ab-E is a 5th
We know Ab-Eb (or A-E) is a perfect 5th because both letters have the same sign
Ab-E is 1 semitone larger than Ab-Eb so the interval is augmented

Ab-E is an augmented 5th

Try These…

b) Name the following 4ths and 5ths. Answers at the end of this post.

E-B
E-Bb
Ab-Db
Ab-D
F-C
F-C#
Bb-F
B-F (hint: visualise)
Db-G
G#-C#

What About Intervals Larger Than An Octave?

The easiest way to describe an interval larger than an octave is in two parts: a number of whole octaves and the remaining interval.

For example, C4 to A5 = 1 octave and a major 6th.

For more information about naming large intervals, including method of using a single interval name and a few exercises, please visit How To Name Intervals Larger Than 1 Octave.

NEXT LESSON: B7. How To Notate Very High And Very Low Notes

PART 2 CONTENTS: Basic Music Theory Course Contents

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Answers to Try These…

Thanks to Adiela for finding two errors in my answers and letting me know

a)
major 3rd
major 6th
minor 2nd
minor 6th
augmented 6th
perfect 4th
diminished 6th
diminished 8th
augmented 2nd
augmented 7th

b)
perfect 5th
diminished 5th
perfect 4th
augmented 4th
perfect 5th
augmented 5th
perfect 5th
diminished 5th
augmented 4th
perfect 4th

B5. Inversions Of Intervals

What’s An Inversion?

To invert an interval is to turn it upside down: to take the lower note and move it up an octave, or take the higher note and move it down an octave. The order of the notes is reversed.

Interval + Inversion = Octave

A Special Relationship

Octaves have the unique property of being musically interchangeable.
Going up or down by an octave is like going up or down a flight of steps in an apartment building. Each octave is a higher or lower version of the next.

This means that there is a strong musical relationship between an interval and it’s inversion.

Melody And Harmony

Take a melody and a harmony, for instance.

A typical close harmony more-or-less follows the melody, adjusting here or there to fit the key (and the chords, but more on that in a future post). Usually, the harmony is sung higher than the melody.

The above example is played at the pitch of a female or young child’s voice. Now imagine that the harmony is sung by a lower voice such as that of an adult male.
Typically, adult male voices are typically about an octave lower than female or children’s voices. This would put the harmony an octave lower: lower than the melody.

As you can hear, the notes fit together just as well as the original. Sure, you can tell that the harmony is lower than it was, but they fit together just as well – as they should, because the note names are still the same.

Inversions And Interval Names

Theory is meant to reflect reality. If there’s an audible relationship between an interval and its inversion then their interval names should reflect this relationship.

Fortunately, they do.

Semitones And Letters

An interval plus its inversion equals an octave.

Consider the following example:

The first interval, A-E, is 7 semitones. Its inversion, E-A, is 5 semitones. This adds up to 12. An octave is 12 semitones, so that’s what we expect.

It doesn’t matter which way round we view this. Just as E-A is the inversion of A-E, so, too, the other way: A-E is the inversion of E-A. They are inversions of each other.

Now let’s look at their interval names. A-E is a perfect 5th and E-A is a perfect 4th. 5+4=9, yet the total is an octave, which is 8 letters.

The simple reason for this is because when we count an octave as two intervals, we count the middle note twice; once as the upper note of the first interval and again as the lower note of its inversion.

An interval plus its inversion equals 12 semitones
Also, an interval plus its inversion equals 9 letters

Let’s look at a few more, this time on G:

From these, we can add another observation:

The inversion of a major interval is a minor interval
The inversion of a perfect interval is a perfect interval
The inversion of an augmented interval is a diminished interval
Also:
The larger the interval, the smaller its inversion

NOTE: There is nothing inherent in determining which is the interval and which is the inversion. They are interchangeable. They are inversions of each other.

How To Invert An Interval Name

To invert an interval is easy: we reverse the pitch order of the two notes. We can name the new interval from scratch using an interval ruler as shown in B2. Intervals 2: Augmented And Diminished Intervals, but there is a quicker way.

If we know the name of the original interval we can invert the interval name by using our observations of how the names of interval and inversion are related.

In general, the names invert as follows:

For example:

G-A is a major 2nd. What is its inversion?

The degrees add up to 9
9 – 2 = 7
A-G is a 7th
As for the quality, major goes with minor
A-G is a minor 7th

Eb-G# is an augmented 3rd. What is its inversion?

The degrees add up to 9
9 – 3 = 6
G#-Eb is a 6th
As for the quality, augmented goes with diminished
G#-Eb is a diminished 6th

F#-C# is a Perfect 5th. What is its inversion?

The degrees add up to 9
9 – 5 = 4
C#-F# is a 4th
As for the quality, perfect goes with perfect
C#-F# is a perfect 4th

Try These…

a) Name the following intervals
b) Invert the following intervals
c) Name the inversion by inverting the interval name

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

Example: C-E

a) C-E is a major 3rd
b) To invert an interval, reverse the pitch order of the notes. C-E becomes E-C
c) To invert the interval name, major becomes minor and 3rd becomes 6th. E-C is a minor 6th

NEXT LESSON: B6. How To Name Intervals The Quick Way

PART 2 CONTENTS: Basic Music Theory Course Contents

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Answers To Try These…

a) G-Bb is a minor 3rd
b) Invert G-Bb to get Bb-G
c) The inversion of a minor 3rd is a major 6th

a) G-D is a perfect 5th
b) Invert G-D to get D-G
c) The inversion of a perfect 5th is a perfect 4th

a) D-B is a major 6th
b) Invert D-B to get B-D
c) The inversion of a major 6th is a minor 3rd

a) D-G# is an augmented 4th
b) Invert D-G# to get G#-D
c) The inversion of an augmented 4th is a diminished 5th

a) E-Db is a diminished 7th
b) Invert E-Db to get Db-E
c) The inversion of a diminished 7th is an augmented 2nd

a) F-Gb is a minor 2nd
b) Invert F-Gb to get Gb-F
c) The inversion of a minor 2nd is a major 7th