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A great deal of music is made up of sections which are played more than once. Special barlines and other symbols can be used to indicate such sections, substantially reducing the number of pages required to notate a piece.
In a score, navigation text and signs are written above the stave for each part in Bold.
Navigation works a bit like a model railway, with signals directing the player through and around various sections of the music.
Although originally devised for music notation, navigation markings can equally be used on text-based notation such as chord charts or abc notation.
Navigation markings
Section End
A section end is a double barline of the usual thickness. As the name suggests, it indicates the end of a section of the music. When you see a section end, keep playing unless other symbols indicate a pause in the timing.
Final Bar/Double Bar
The final bar is a double barline with an extra-thick second line. It indicates the end of the whole piece unless other symbols indicate otherwise.
End Repeat Sign
An end repeat looks like a final bar but with two dots to the left.
If no begin repeat has been passed, go back to the beginning of the piece and play it again, else go back to the nearest begin repeat sign and play again.
Once you reach the end repeat a second time, continue onwards.
Begin Repeat Sign
A begin repeat sign is the reverse of an end repeat. When you encounter one, keep playing: it has no meaning until you reach an end repeat sign. Think of a begin and end repeat as a pair of brackets enclosing a section which is to be played twice.
Play X Times
The words “play x times” above an end repeat indicate that the repeated section is played the total number of times indicated here by “x”, such as “play 3 times”.
1st And 2nd Time Bars
In a repeated section, first and second time bars allow different endings for leading back to the start after the first time through and playing on after the repeat. First and second time bars can be made up of more than one bar, as indicated by the length of the line.
Da Capo or D.C.
As well as repeated sections, the whole piece may be repeated, including any internal repeats. A repeat sign at the end is confusing because someone reading the music would be looking for a matching start repeat that doesn’t exist. Such larger scale repeats are indicated with the Italian words “da Capo” (“from the head”), to play again from the beginning.
The abbreviation D.C. is often used instead of the full wording.
Note: In some genres, internal repeated sections are not repeated the second time.
The diagram below shows how the navigational symbols are interpreted. To keep the example tiny, each section is represented by only 2 bars (at a very fast tempo!)
Common navigation markings
All navigation markings must be written over a double bar. If there is no repeat sign or final double bar, a section end (thin double bar) must be used.
Da Capo al Fine, D.C. al Fine
(go back to the beginning and repeat until the word “Fine”)
The piece is played again from the beginning, stopping the second time on the word “Fine” (“end”).
If you found this post helpful, please feel welcome to like, share or leave a comment. If you have any questions, leave them as a comment and I’ll respond as soon as I can. To stay up to date wth new posts, please subscribe.
This post is one of a 2-part series of free basic music theory lessons on my blog, musictheoryde-mystified.com. You can see the complete list here. Please feel welcome to make a comment or ask a question.
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.
A to C# is a major 3rd
How To Name An Interval:
Write the lower note of the interval in the ruler as the root note and add the notes of the major key.
Now flatten the 2nd, 3rd, 6th and 7th note for the *minor as indicated by the red arrows.
Next, look in the ruler for the upper note of the interval.
The interval name is made up of the quality; major, minor or both (=perfect), and the degree.
In the above example, A-C# is a major 3rd (= 4 semitones).
Similarly, A-C is a minor 3rd (= 3 semitones), A-D is a perfect 4th (= 5 semitones), etc.
1st, 4th, 5th and 8th are perfect-type intervals.
2nd, 3rd, 6th and 7th are major/minor type intervals, depending on which scale the upper note is in.
As well as the octave, we’ve already met three intervals:
Minor 3rd (3 semitones to the 3rd letter) – the interval between the root notes of relative major and minor keys.
Perfect 5th (7 semitones to the 5th letter) – the interval from any key to the next key in the cycle of 5ths.
Perfect 4th (5 semitones to the 4th letter)- the interval from any key to the previous key in the cycle of 5ths.
An Interval Name Is Based On The Lower Note
All the examples so far assume that A is the lower note of the interval, hence we’ve used A scales for our ruler. If we want to measure an interval with a different lower note we want the interval ruler to start on that note. For example, to name the interval from G to E we would need G scales and to name the interval from Bb to Db we would need Bb scales.
G-E
E is the 6th note of G major, so G – E is a major 6th (9 semitones).
Bb-Db
Db is the 3rd note of Bb minor, so Bb – Db is a minor 3rd (3 semitones).
By now you’ll see why I was so keen on learning key signatures of major scales: knowing them makes this process a lot quicker than having to work it out on the fly! Every time we look at the interval between a pair of notes with a different lower note, we need to use a different scale for our interval ruler.
At least by using the interval ruler we only need to learn the major scale, as we can flatten the 2nd, 3rd, 6th and 7th to find the *minor (phrygian mode).
Try These…
Name the following major, minor and perfect intervals:
F-Bb
F-E
F-Db
G-B
G-D
G-F
Bb-G
Answers at the end of this post.
Interval Names In Reverse: finding the upper note
So far we’ve named an existing interval. Now let’s recreate an interval from its name. We’ll pick a note to be our lower note and name the higher note based on the interval name.
For instance, let’s find the note that’s a minor 6th above E.
First we’ll create our interval ruler on E. We’ll start with E major. The key signature of E major is 4 sharps: F#, C#, G# and D#, so the scale of E major is E, F#, G#, A, B, C#, D#, E.
Now we’ll write E *minor below it by flattening the 2nd, 3rd, 6th and 7th notes.
Next we look for the interval, in this case a minor 6th. Minor 6th means the upper note is the 6th note of the minor built on the lower note, so we look for the 6th note of E *minor on our interval ruler.
Minor 6th above E
An interval name means:
The higher note of the interval is the …th (degree name) note of the … (major or minor or both) scale built on the lower note.
Saying it in this way may help to remember how interval names work.
Try These…
Find the upper note in the following major, minor or perfect intervals:
a minor 3rd above C
a major 6th above C
a minor 2nd above E
a perfect 4th above E
a minor 7th above E
a major 2nd above Eb
a major 7th above Eb
Interval Names As Scale Degrees
The different notes of a scale are called degrees. So far I have used the note’s position in the scale to indicate the degree, such as 3rd or 5th. We can refine this by calling the third note of a major scale the major 3rd, the 5th note of either scale the perfect 5th and so on.
If you found this post helpful, please feel welcome to like, share or leave a comment. If you have any questions, leave them as a comment and I’ll respond as soon as I can. To stay up to date wth new posts, please subscribe.
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.
The chromatic scale
The chromatic scale is made up of every one of the 12 musical note pitches, each 1 semitone apart from the next. It is the parent of all modes (…except in cultures with more than 12 note pitches per octave…).
Apart from some largely academic genres such as serial music, chromatic scales are mainly used as musical effects, such as the rapid chromatic passages used to build tension and drama in film music.
As a key, the chromatic scale has no inherent tonality: there’s no way to tell the root note from any other note. That’s not to say that you can’t nominate a root note, just that it requires a lot of effort to make that root note felt in a piece.
I don’t mean that it has no musical character, either. It does, but it’s a very nebulous one…
Modes
A mode is the pattern of intervals that determines which of the 12 different note pitches within an octave are used to produce a scale/key. Apart from the chromatic scale and the “whole tone scale” (6 notes within an octave, with 2 semitones between each note and the next), modes have an irregular pattern to their interval structure. As long as the root note is highlighted from time to time this irregularity allows a mode’s unique character to permeate the character of the music.
Diatonic Modes
The traditional Western modes, such as ionian (major) and aeolian (minor), are made up of one- and two-semitone intervals. Such modes are called diatonic modes; modes whose scales only have two different size intervals between their notes.
Just to be confusing, they’re also called heptatonic modes, meaning that they have 7 different notes within an octave. The traditional modes are all made up of 7 different notes, where the eighth note is the octave of the first.
A mode doesn’t innately have these limits. For example, the harmonic minor (discussed later in this course) still has 7 notes but one of its intervals is 3 semitones, that between the 6th and 7th notes of the scale. Other modes have a different number of notes per octave, such as pentatonic (5-note) modes and the blues mode. Some modes even use one or more different notes ascending and descending. The melodic minor works like that, as do some Indian modes.
However, the most common modes in most Western genres are the traditional Western modes which evolved out of the Renaissance era.
Although often associated with period music and traditional folk music, some modes, such as the myxolydian mode, are commonly used in a variety of other genres. Jazz goes even further by using relative modes as an approach to improvising around extended chords.
What Are The Traditional Modes?
Let’s have a look at the natural notes for two octaves. Each note can be the root note of a diatonic mode (yeah, I wouldn’t worry about the “heptatonic” bit, it seldom crops up in conversation…).
The traditional Western modes
Look at the notes for an octave, starting on each note in turn. Each root note produces a different pattern: a different mode.
We can compare their interval structure by lining them up underneath each other.
Each different mode has a unique quality that greatly influences the overall character of music played in that mode.
You can hear this, even by just playing a scale.
You can also teach yourself a new mode just by reading and playing the notes of the scale.
If you play by ear, follow its pattern of intervals on your instrument by counting semitones.
Below is a scale of each mode starting on A, so we can compare their character..
A aeolian (natural minor)
A locrian
A ionian (major)
A dorian
A phrygian
A lydian
A myxolydian
The character of each mode is easy to identify in a melody. Have a listen to this short, simple melody played in each of the modes…
Simple melody in A aeolian (natural minor)
Simple melody in A locrian
Simple melody in A ionian (major)
Simple melody in A dorian
Simple melody in A phrygian
Simple melody in A lydian
Simple melody in A myxolydian
Modes And Key Signatures
The way in which key signatures are used for modes other than major or minor depends on genre and school. There are two approaches: like major/like minor or the mode’s actual key signature.
Like Major or Like Minor
Classical musicians are brought up on a strict diet of major and minor (as well as two variations of the minor, melodic minor and harmonic minor). A classically trained player is only going to look for two possible root notes when interpreting a key signature. Music in a less familiar mode would be hard to interpret on first reading; the root note would seem to conflict with the key signature.
The most important notes of a scale are the root note and the note 7 semitones above the root note, called a perfect 5th (don’t worry about the interval name, we’ll look at interval names soon). The perfect 5th helps stabilise the root note.
There is one other important note, the 3rd note. One reason the 3rd is important is because it’s the most significant difference between major and minor. In the major mode the 3rd note is 4 semitones above the root note and in the minor it’s 3 semitones above the root note.
We can categorise the other modes as being “like major” or “like minor”, based on the 3rd note.
Below is a list of the modes staring on A, grouped in “like major” or “like minor”. The note in the other modes that differs from the major or minor is highlighted.
Note that the locrian mode is not in either list! The locrian mode wasn’t used in Western music, or even named, until relatively recently because it lacks the essential ingredient of a perfect 5th. By not having a note 7 semitones above the root note, music written in this mode is elusive. We naturally listen for a root note but we either can’t find it or we’re misled by other possible root notes that do have a perfect 5th but don’t hang around long enough to feel convincing.
It’s VERY hard to make the root note stick in the locrian mode. Modes without a perfect 5th need almost constant reinforcement of the root note in order to be musically stable. One way to achieve this is by having a drone accompaniment, where the root note persists throughout the piece.
Accidentals
For modes which are like major, we use the key signature of the parallel major mode; the major mode on the same root note.
For modes which are like minor, we use the key signature of the parallel minor mode; the minor mode with the same root note.
This requires the use of an accidental. Anyone who’s seen music written in the melodic or harmonic minor will be used to accidentals used in this way.
For example, let’s look at one of the more common modes, the myxolydian mode.
Using only naturals (key signature of 0 sharps/flats), the myxolydian mode starts on G. The actual key signature of G myxolydian is 0 sharps/flats.
The myxolydian mode is like major, so for a ”like major/like minor” key signature we would use the key signature of the major mode on G, G major, which is 1 sharp (F#).
To preserve the intervals of the myxolydian mode we need to flatten the 7th note, the note which differs from the major of the same root note, F# (remember, in the cycle of 5ths, the latest sharp is the 7th note of the scale…).
When we flatten F# we get F natural, so for the first F in every bar that has one, we write a natural sign as an accidental.
*NOTE: An accidental is only written for the first instance of a given note in each bar.
Try These…
Like Major, Like Minor
Write the scale of the following modes for 1 octave ascending using the key signature of its parallel major or minor (the major or minor key with the same root note) and an accidental where required. Base your decision on whether the 3rd note belongs to the parallel major or parallel minor.
NOTE: Accidentals aren’t written as part of the key signature. They must be written beside the first instance of that note in every bar where that note occurs.
A dorian
D lydian
C ionian (trick question… just seeing if you were paying attention)
C myxolydian
B phrygian
F# dorian
Bb myxolydian
Answers at the end of this post.
Actual Key Signature
Players of early music and traditional folk music, as well as a number of other genres, are quite familiar with the traditional modes. Typically, in such genres the actual key signature is used.
In the above example, G myxolydian is written in the key signature of 0 sharps/flats, rather than in the key of G major with F natural as an accidental. It’s cleaner and simpler to read (as long as you interpret the key signature correctly when reading).
When first reading a piece knowing only it’s key signature, you might wonder how to determine the root note of the piece, with so many modes to choose from. The approach is the same as when you’re just looking for major or minor. Look for an obvious note near the start and end of the piece.
Pentatonic modes (5 notes per octave) are quite popular in various genres. Having only 5 notes, we can think of them as a subset of the traditional heptatonic modes that we’ve already looked at.
The most well known of these is the minor pentatonic mode, notes 1, 3, 4, 5 and 7 of the natural minor/aeolian mode. In this instance, we would use the key signature of the “parent” minor key. Other Western pentatonic modes are also subsets of parent modes, so we would use the key signature of the “like major” or “like minor” mode of which it is a subset.
Here are the two most common Western pentatonic modes.
Not all pentatonic modes are related to a parent Western mode. Any combination of 5 notes within an octave can be used as a pentatonic mode.
The Blues Scale
The most common mode in blues is a hexatonic (6-note) mode based on the minor pentatonic, with an extra note added between the 4th and 5th notes. From a notation viewpoint, there is no room in the naming system for the extra note to have its own letter: instead, it is considered an alternative to the 4th or 5th note and should be named according to its use. Either option requires an accidental.
Other Modes
Most musical cultures around the world have a concept of modes, a system of choosing a set of notes within an octave based on a root note and the intervals between its scale notes. Some use different intonation (tuning) systems: such modes can sound unfamiliar to the Western ear. Many are based on the same intonation as Western music, 12-Tone Equal Temperament, yet may have different numbers of notes per octave or notes that differ when ascending or descending. If you wish to experiment, you can create your own mode for a new composition or improvisation.
Freedom From Modes
The Western modes were originally used as a rigid framework for determining which notes were used in a composition. Over time, as music developed towards the journey through various visiting keys that it largely is today, the use of accidentals became more and more common, to accommodate these temporary keys.
Accidentals are also used for embellishment (ornamentation). Ornaments are treated as effects: an ornament may well use notes outside the key, requiring an accidental. This may extend to chromatic passages involving several accidentals.
The contemporary view is that a key is based on the overall use of the notes of a major or minor key, with the option of sharpening/flattening notes or incorporating other notes as desired.
If you found this post helpful, please feel welcome to like, share or leave a comment. If you have any questions, leave them as a comment and I’ll respond as soon as I can. To stay up to date wth new posts, please subscribe.
This post is one of a 2-part series of free basic music theory lessons on my blog, musictheoryde-mystified.com. You can see the complete list here. Please feel welcome to make a comment or ask a question.
The relationship between two keys is simply how many notes they have in common: the more notes in common, the closer their relationship.
Why do we care? Because this is not just true on paper. Theory reflects reality. Closely related keys actually sound close, musically. They sound compatible.
In the preceding lessons we have already seen two types of key relationships; the cycle of fifths and relative major and minor. Here’s a quick review:
The Cycle Of Fifths
The cycle of fifths is a list of the keys in the order of their key signatures, from every note being a flat through to every note being a sharp. In this list, any two adjacent keys have all but one note in common.
The effect of this close relationship is that the music can comfortably and cohesively shift from one key to the other and back.
This is most easily demonstrated with chords. We’ll look at chords in a later post, but for now we can say that a (basic) chord represents a key. Chord names mimic key names, just in a shortened form. A note name by itself implies a major chord/key. If it’s followed by ”m”, it’s a minor chord.
Adjacent keys in the cycle of 5ths can be visited in any order. Here’s a short example in C major with a simple melody and chords. As usual in my posts, the examples are purely for illustration, so they don’t sound as exciting as real compositions…
Here’s an example of a simple melody in C major visiting adjacent keys, as represented here by chords.
A large proportion of music in Western culture in most genres, whether fast or slow, rhythmic or free, accompanied or solo, is based on visiting closely related keys.
To find the next key in the cycle of 5ths, go up to the 5th letter in the key to find the root note, then sharpen the 7th note of the scale (add a sharp or lose a flat).
To find the previous key in the cycle of 5ths, go down to the 5th letter in the key (or up to the 4th letter) to find the root note, then flatten the 4th note of the scale (add a flat or lose a sharp).
You can also use the cycle of 5ths as a list to look up the root note of a key and its latest sharp or flat, or even the complete key signature. An example of this for major scales can be found in 12. Major Keys And The Cycle/Circle Of Fifths. The cycle of 5th for major and minor keys, with key signatures, is shown in The Cycle (circle) of Fifths.
Relative Major And Minor
Next we looked at another close relationship between keys, one where two keys have every note in common: relative major and minor. Having all notes in common, the difference is in which one is the root note. Of course, changing the root note changes the mode, hence the term relative major and minor.
Major and minor have different characters – different tonalities. Moving between one and the other feels a bit like going to an unfamiliar corner of a familiar room; like viewing the scene from a different angle.
Here is a simple melody in C major visiting the relative minor.
To find the relative minor of a major key, go up to the 3rd letter in the key and keep the same key signature (play the same notes starting on the 3rd note).
To find the relative major of a minor key, go down to the 3rd letter in the key and keep the same key signature.
There is a third type of key relationship which we haven’t yet visited; parallel major and minor. This means a major and a minor on the same root note.
The easiest way to see their relationship is by writing one on top of the other, literally parallel.
Here’s an example on C:
In the above graphic we can see that the parallel minor has three notes that are flattened compared to the parallel major, the 3rd, 6th and 7th notes.
Key signature wise, the parallel minor is 3 keys behind the parallel major (anticlockwise).
Parallel major and minor have only four of their seven notes in common so, as far as the cycle of 5ths goes, they’re not that closely related. However, because they share the same root note, their relationship feels closer than that.
Here is a simple melody in C major visiting the parallel minor.
Another Shortcut
Here’s another way to remember a few keys you don’t know…
Major to Parallel Minor
If you know the key signature of a major key then the minor on the same root note, the parallel minor, is 3 keys backward (anticlockwise) in the cycle of 5ths.
If you know the notes in the scale rather than the key signature, such as when playing by ear, flatten the 3rd, 6th and 7th notes. You’ll get the same result.
Minor to Parallel Major
If you know the key signature of a minor key, the major on the same root note is 3 keys forward (clockwise) in the cycle of 5ths.
If you know the notes in the scale, sharpen the 3rd, 6th and 7th notes.
Examples
Major to parallel minor
We know C major has no sharps or flats, so C minor has 3 flats (Bb, Eb, Ab)
Minor to parallel major
We know A minor has no sharps or flats, so A major has 3 sharps (F#, C#, G#)
Nothing In Common Is Still Something
On the far side of the relationship spectrum, two keys can have no notes in common. This is achieved by sharpening or flattening the root note and thus, every note. Musically, it’s a complete reset. Moving between two such unrelated keys can sound anywhere from refreshing to dramatic or mysterious.
In the case of C major, 0 sharps/flats, sharpening everything gives us C# major, 7 sharps.
Similarly, flattening everything gives us Cb major, 7 flats.
To sharpen everything, go forward (clockwise) 7 keys in the cycle of 5ths. All flats become naturals and all naturals become sharps. Every note is played 1 semitone higher than before.
To flatten everything, go backward (anticlockwise) 7 keys in the cycle of 5ths. All sharps become naturals and all naturals become flats. Every note is played 1 semitone lower than before.
Flattening D major (2 sharps) results in Db major (5 flats). All naturals become flats and all sharps become naturals.
Note: there is a practical limit to how many sharps or flats we can have. If there are more than 7, one or more notes in the scale will have a double sharp or double flat. These exist but are only used when necessary, usually as an accidental rather than as part of a key signature. For keys, it’s generally easier to respell (rename) the root note and avoid the issue.
If there are more than 7 sharps or flats, respell the root note. The key signature will go from lots of sharps to a few flats or from lots of flats to a few sharps.
For example, you probably remember by now that G major has 1 sharp, F#.
If we sharpen everything we get G# major, with 8 sharps. All the naturals are sharps and F is a double sharp.
However, G# is the same pitch as Ab. Ab major only has 4 flats so it’s much easier to read and doesn’t require a double anything.
Knowing G major does help you find Gb major though. By flattening everything we go from 1 sharp to 6 flats, no doubles there.
From The Known To The Unknown
Use your knowledge of key relationships to help learn the key signatures of more keys. Start with a couple of common or easy to remember keys and with a little thought, you’ll soon know most of them. At the same time you’ll become more familiar with the idea of keys being related to each other.
For instance, just by knowing C major (0 sharps/flats) you can quickly find its parallel minor, C minor (3 flats), 3 keys back in the cycle of fifths or flatten the 3rd, 6th and 7th notes.
You can also find C# major and Cb major by sharpening or flattening everything, as we’ve seen above.
From C minor you can find C# minor (sharpen everything: 3 flats becomes 4 sharps). Or you can find C# minor from C# major using parallel major to minor.
From C minor you can also find Eb major (still 3 flats), using relative minor to major (count up to the 3rd note in the key).
Similarly, from C# minor, using relative minor to major, you can find E major (4 sharps). Or you can find E major by sharpening everything in Eb Major (3 flats becomes 4 sharps).
We know A minor already, but if you forgot, you could find that from C major using relative major to minor (count down to the 3rd scale note, keeping the same key signature, 0 sharps/flats).
That’s 8 keys and key signatures just from remembering one key!
And I could keep going: From E major you can find E minor and so on… Not to mention using the cycle of 5ths to find the next key (add 1 sharp or lose 1 flat) or previous key (add 1 flat or lose 1 sharp), and then their relative minors or majors, etc.
Try this yourself with another common key like A minor or G major.
Try These…
Test your ability to think in key relationships! Name the following keys and list either their notes as a scale or their key signatures:
A major has 3 sharps; F#, C#, G#. What is the next key in the cycle of fifths after A major?
Bb major has 2 flats; Bb, Eb. What is the previous key in the cycle of fifths before Bb major?
D major has 2 sharps; F#, C#. What is the relative minor of D major?
D minor has 1 flat; Bb. What is the relative major of D minor?
E major has 4 sharps; F#, C#, G#, D#. What is the parallel minor of E major?
F# minor has 3 sharps; F#, C#, G#. What is the parallel major of F# minor?
You worked out the key of D minor. Now sharpen it.
G major gas 1 sharp; F#. What is the key of Gb major?
Answers at the end of this post.
Key Relationships Are Real
Being able to work out key signatures by using the various key relationships not only helps you with the odd unfamiliar key but it also reinforces your understanding of these relationships. As mentioned earlier, key relationships aren’t just musical arithmetic, they are real: when listening, you can hear the connection between related keys.
Try This…
For any key, the next and previous keys in the cycle of 5ths and their relative minors or majors are the most closely related. Choose a key whose key signature (or scale notes) you remember and work out these closely related keys.
If you play chords, try changing between the chords of these keys. If you play melodies, play their scales or triads. Either way, you’ll find that you can mix them up into any order and they will feel like they belong together.
(Sib simple chord sequence as chords, then triads, then as rapid scales)
You can also use closely related keys to work your way progressively to a distant key without really noticing, such as in the classic chord progression of Jimmy Hendrix’s Hey Joe, a cascading sequence of forward steps in the cycle of 5ths. In that song, the surprise comes when the sequence resets at the start of the next line: only then can you hear how far from home you ended up…
(Sib Hey Joe progression in scales and chords with repeat)
Note: we’ll investigate chords and triads later in this course.
If you play by ear, you can use any of the methods above to find how to play the scales of related keys. All you need to remember is the name of the key.
If you found this post helpful, please feel welcome to like, share or leave a comment. If you have any questions, leave them as a comment and I’ll respond as soon as I can. To stay up to date wth new posts, please subscribe.
Many musicians are put off learning music theory, either because they believe it will destroy their creativity or because they’ve had some traditional music theory lessons and found them confusing or irrelevant.
My goal is to empower musicians with the tools to control their musical environment: to introduce enough basic musical language to be able to discuss and understand the basic principles which underpin the vast majority of Western music, and how to use these principles effectively in playing and creating music, regardless of genre or style.
Who is this course for?
This is a course for people with little or no music theory background, both complete beginners in music and players who have learned by ear. It is also suitable for students who have studied traditional music theory courses and want to gain some more understanding.
Creative musicians especially will benefit from the insights of this course, as the principles behind music theory are the tools for controlling the direction and scope of your musical creation, be it composition or improvisation.
This course is primarily written for adults and older children.
What grade does this course teach?
I haven’t exactly followed the grade system of any country or school. The information is the same but sometimes it is presented in a different order, making it hard to draw a comparison.
Not every single musical term covered in the grade system is covered here. In traditional theory courses there is an abundence of terminology, some of which is quite cumbersome and potentially distracts from understanding. I do, however, use all the key musical terms taught in such courses.
The focus of my course is to demonstrate how the concepts and underlying principles of music theory affect the music we play and create, and to help to understand these principles, rather than teaching them as a set of rules. Nonetheless, the information itself is the same as in any traditional music theory course.
Is this a course or a reference?
This is a structured course in basic music theory. Beginners should start with the first lesson and do the lessons in their numerical sequence.
Each lesson is clearly defined and easy to follow, with detailed explanations as well as bullet points, examples (many as mini-movies) and illustrations. There are even a few exercises at the end of most lessons, which I highly recommend.
I play by ear. Is this course relevant to me?
I strongly encourage musicians who play by ear to gain the many benefits of the language of music, such as note names, basic music notation etc. However, all musicians, no matter how they learn, should become acquainted with scales, keys and chords, particularly when working with other musicians in regular ensembles such as bands.
I have written those lessons which cover these major topics, as well as lessons on musicianship (such as basic timing), with players who learn by ear kept in mind.
Major points are demonstrated by audio and illustrations with text notation as well as mini-movies of notation with audio. Explanations and exercises cover both written and practical bases to learning.
Is this a complete course?
At the time of writing, this course is a work in progress. I regularly add new posts.
Please like and share these lessons and feel free to make comments or ask questions. This is a project driven by passion: it generates no income (unless someone buys my pocket music theory reference, The Tiny Music Theory Book). A little encouragement would help inspire me to keep going.
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.
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.
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.
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.
If you know the key signature of the major scale, it’s easy 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 Major Keys
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.
If you found this post helpful, please feel welcome to like, share or leave a comment. If you have any questions, leave them as a comment and I’ll respond as soon as I can. To stay up to date wth new posts, please subscribe.
This post is one of a 2-part series of free basic music theory lessons on my blog, musictheoryde-mystified.com. You can see the complete list here. Please feel welcome to make a comment or ask a question.
Notes and rests
Music is mostly made up of notes and rests.
A musical note has 5 properties:
Pitch: how high or low a note sounds.
Note length (duration): how long a note sounds for.
Dynamics: how loud or quiet a note is.
Articulation: how the note is expressed, such as an accent (the start of the note is emphasised), staccato (the note is cut off quickly) or legato (the note is played evenly for its full length).
Timbre: the tone colour or texture of a note (warm, bright, honky etc.). Timbre is usually an overall characteristic of an instrument, although players have some control over how to vary it. To a degree, notes can be made to sound warm or bright depending on how they’re played.
Dynamics, articulation and control of timbre all contribute to the expression of a note.
Other effects, such as glissando (sliding pitch), vibrato (wavering pitch) and tremolo (rapidly repeating note) are considered to be effects which are applied to notes. Apart from vibrato, which is considered a form of expression akin to timbre control, they fall under the general category of ornamentation.
A rest is like a silent note: a deliberate, timed silence between notes that forms part of the music.
Music Notation
All these qualities can be indicated in music notation.
Although notation can indicate a great deal of musical information, there is always room for interpretation by the player. Many nuances of performance can only be indicated in a general way: in order to add authenticity to the performance, it is expected that a player has some understanding of what’s appropriate to the genre and style of the music.
By far the most significant qualities of a musical note are pitch and duration.
Notes can be played one after the other, in succession, as in a melody. Notes and rests played in succession also have a rhythm. Several notes can also be played together, producing harmony, such as a chord.
A melody is a series of notes (and rests) in succession. Typically a melody starts in a key, visits various neighbouring keys then comes home.
Harmony is the combining of notes which sound at the same time. The most recognisable use of harmony is in chords, often used to accompany a melody.
Rhythm is the the effect of how notes and rests progress over time. The more obvious rhythms are short and repetitive. Both melodies and chords can have a rhythm. In many ensembles, the underlying rhythm is highlighted by percussion/drums.
Apart from a few small edits, this post in its entirety is taken from my pocket guide to basic music theory, The Tiny Music Theory Book, available exclusively from this site.
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.
Frets on a guitar are placed 1 semitone apart. The 12th fret produces a note one octave above the open (full-length) string.
The Relationship Between Pitch And Frequency
The frequency of a note is the speed at which a sound wave vibrates in order to produce a given pitch. The lower the frequency, the lower the pitch.
The common factor between the pitch of a note and its frequency is the octave. One octave equals 12 semitones, where each semitone sounds the same distance apart as the next, like centimetre or inch markings on a ruler.
An octave is also the frequency ratio of 2:1. Every 12 semitones higher, the frequency doubles. We can look at the relationship between sound waves and what we hear by creating a graph with pitch on one axis and frequency on the other. It would look something like this:
The above frequencies are based on a guitar A string, A = 110Hz.
One octave higher = double the frequency.
Double the frequency = half the wavelength and thus half the string length.
One octave higher than the open (full-length) string is half the string length, half-way from the nut to the saddle.
The next octave higher is half of the remaining string length = 3/4 of the string away from the nut.
In other words, the first half of the string has 12 frets and the next quarter of the string also has 12 frets.
The effect of this relationship is that for every semitone higher in pitch, the frequency increases by a little bit more than the last semitone.
The Relationship Between Frequency And String Length
Frequency and wavelength are inversely related: as one goes up, the other goes down. As the frequency increases, the wavelength, and thus the string length, becomes smaller, a little less so for each semitone.
Strings are effectively half a wave. Higher notes are produced by making the playing part of the string, and thus the wave length, shorter. For each semitone higher, the adjustment is a little less than the previous semitone. The frets mark these positions.
Why do we care? Maybe we don’t need to, but isn’t it nice to know why frets are laid out differently from piano keys?
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.
A plucked guitar string is a good physical representation of half a sound wave.
Sound waves, like ripples in a pond, are wave shaped pulses that travel and spread away from the source. Single frequencies have an evenly-curved shape called a sine wave. A complete wave, from the start to where it begins to repeat, is called a cycle.
One Wave Cycle
Unlike ripples in a pond, a string on a guitar (or any string instrument) is fixed and doesn’t travel. A vibrating string produces half a sine wave at a time, moving gradually upward then downward for each wave cycle. (The full sine wave is twice the length of the string.)
A Guitar (or other stringed instrument) String Is Half A Sine Wave
When you lightly touch the string above the 12th fret (half-way along its length) and pluck the string, we hear a pure sound called a harmonic. By not pressing all the way down, both halves of the string are free to vibrate: only the middle is blocked, allowing a complete sine wave of half the string length.
Guitar String With Octave Harmonic
The sound we hear is exactly one octave above the sound of the open (whole) string.
One octave higher = half the string length.
In other words, one octave higher = half the wavelength.
By the way, you can check the accuracy of a guitar’s intonation by comparing just touching the string at the 12th fret to pressing all the way down at (behind) the 12th fret. The pitch should sound the same.
double the frequency = half the wavelength. As the frequency goes higher, the sound wave becomes shorter.
You can also place a finger lightly over the 5th fret, 1/4 of the string length, and hear a note 2 octaves above the open string, at 4x the frequency.
This is just another way of demonstrating the close relationship that exists between notes one or more octaves apart. The octave is fundamental to how music behaves. It is a universal musical phenomenon, independent of genre or culture.
Even though we don’t think of sound waves when playing or listening, I suspect that we are innately aware of them. We tend to think of bass notes as big and piccolo or tin whistle notes as little…
A power chord is a chord that’s made up of just 2 notes: the root note and the perfect 5th. This chord is also known as a modal chord or open chord.
Many schools of music teach that the most basic chord is a triad (root note, 3rd and 5th) and brush aside the existence of what is, in various genres both traditional and modern, one of the most common types of chords.
“It’s an interval!”
Time and again I will come across the argument that a modal chord (aka power chord) isn’t a chord because a chord needs at least three notes. A two-note chord isn’t a chord, it’s an interval, they say.
First, notes in a chord can be doubled, in unison or any number of octaves. On guitar, for example, modal chords are used extensively in some genres, some even using different tunings to enable more of such chords to be played on all 6 strings.
Which leads me to a point. An interval has ONLY two notes. Add an octave and you have 3 notes, which, surely, is a chord. It’s certainly not just an interval anymore.
Furthermore, even two notes played together as a “chord” become three notes if there is a melody over the chords. A chord is made up of all the notes that occur at a given moment. If it’s a brief moment, it’s called a passing chord (I’m not suggesting that you need to analyse music to that degree… unless you want to…).
Finally, I would argue that even with a single note, such as a drone, and a melody over it, the progression of intervals produced acts like a chord progression, like chords with a note left out.
“It’s a major chord with the 3rd left out!”
Others will describe a modal/power chord as a major chord with the 3rd left out. To me, that’s like saying a major chord is a 7th chord with the 7th left out… it’s creating complexity where there is none. Worse, it’s misleading.
The beauty of a modal chord is that, by not having a 3rd, it can fit the context of either a major chord or a minor chord. A major chord can’t do that, so not having a 3rd gives a modal chord a completely different character to a major chord.
For example, if the melody had the minor 3rd followed by the major 3rd, both would be main notes (chord notes). The same chord would act as minor to accommodate the first note, then major for the second note. This may seem obvious because it is…
Please feel welcome to comment, whether you agree or disagree. Posts in this category are just my thoughts and opinions and I’d love to read yours. This category is a forum for discussion.
