A blog about music theory demystified. Music theory and notation made simple. A holistic approach to understanding music theory. Free basic music theory lessons. Online music theory books.
Hi, I’m Erik Kowarski. Welcome to my blog! At any time, please feel free to comment. If you find my posts useful, please like and share them. You can also subscribe so you’ll be notified of new posts. To go straight to the latest post, scroll down.
In this blog I try where possible to look at music, or at least Western music, as a whole, rather than in terms of a specific genre; to explore the underlying principles and learn by observation rather than by a set of rules.
The posts are grouped into categories. On the Posts page there is a list of individual posts within each category, oldest first. This is particularly useful for Basic Music Theory Lessons as they should be done in numerical order.
Basic Music Theory Lessons is a 2-part course designed for beginners and self-taught musicians. Using clear explanations rather than rules it focuses on theory that applies broadly, across all genres. The emphasis is on learning by listening and observation.
The lessons can be done as a course, in small modules or as individual lessons.
If you’re a beginner, Basic Music Theory Lessons are the posts for you. Nothing is assumed, everything is explained from scratch. There are plenty of illustrations, audio clips and mini movies as well as practical tips and exercises. Every major point is backed by examples you can hear.
If you have a question, please post it as a comment and I will reply when I can.
Beginner’s Tips and Hacks
Beginner’s Tips offers some handy hacks and tips as well as lists for quick reference.
Music Theory De-mystified
Music Theory De-mystified, aka The De-mystified Files, is a series of brief investigations into what makes music theory tick. A very basic understanding of music theory is assumed, such as note names, key signatures and basic interval names. Although I still endeavour to explain related background information, the posts would get too long and with too many detours if I followed every back story. Instead, I try to look at one unusual aspect of music theory and provide some context.
Musicianship
A list of all posts which contain musicianship/ear training exercises. These include timing, rhythm, singing scales, pitching intervals, recognising notes in a triad and more.
Musings
Musings is a forum for discussion. The posts are my personal thoughts and observations- you might agree or disagree with my views. I would love to receive your comments.
The Interval-Singing Project
A survey looking for different intervals used at the start of popular songs in various genres. The aim is to build a database of familiar songs containing each interval, as a learning aid for singing intervals. The database will be available free to subscribers.
The Theory Of Practice
Tips on practice technique.
Please like and share my posts. If you have any questions, please leave them as a comment and I’ll reply as soon as I can.
The course consists of two parts of around 20 short lessons each, covering all the basics, from note names, scales and basic rhythms to chords.
Lessons can be done individually, in modules of just a few lessons at a time, or as a complete course. Most lessons only take around 10 minutes to read and, for lessons that include exercises, less than an hour to complete.
Music Theory De-mystified Free Basic Music Theory Course starts from scratch. It assumes nothing. The theory taught applies to all genres and styles: it is equally relevant to popular and classical music.
Hear it and see it for yourself!
There is an emphasis on listening and understanding. Lessons are amply illustrated with audio and diagrams as well as music notation.
No rules, just explanations. Descriptions are clear and concise and every major point is demonstrated: no need to take it on faith.
Lessons contain clear How-to sections complete with examples and exercises.
Lessons on scales, intervals, timing and rhythm include practical exercises designed to develop basic musicianship skills.
Music Theory De-mystified also contains various related posts including a growing series of tips and hacks as well as investigative articles about how music works.
An octave is 12 semitones. However, half an octave is 7 semitones – and the other half is 5 semitones!
How is this so? Surely half of 12 equals 6?
Frequencies
Each note pitch produces a repeating sound wave. Lower notes produce longer waves which repeat more slowly, whereas higher notes produce shorter waves which repeat more quickly. The speed at which a sound wave repeats is it’s frequency, measured in Hz (Hertz). 1 Hz = 1 wave cycle per second.
Composite Wave
When two (or more) notes are played together, their sound waves combine to form a composite wave. This wave also has a frequency. Playing two notes produces three!!!
The frequency of this combination wave is also a note. For example, below is an interval of a major 3rd.
Consonant intervals (intervals that sound musical) have frequencies which are closely related. The composite wave’s frequency is an octave of one of the two notes that make up the interval.
Dissonant (musically unpleasant) intervals such as a semitone or a tritone (augmented 4th/diminished 5th) have frequencies that are not closely related. As a result it takes many cycles of each note before they meet up to produce one cycle of the composite. The composite wave has a low frequency unrelated to either note which, if below our ability to detect pressure waves as continuous sound, can be felt as a disturbance known as beats or beating.
When two notes are an octave apart, their sounds match so well together that we think of them more as being in different registers rather than as completely different notes. Notes which are whole octaves apart are considered to be different versions of the same note, to the extent that they share the same name.
When two notes are an octave apart, the upper note is 2x the frequency of the lower note. For example, if A = 440 Hz then the next A an octave higher is 880 Hz.
The composite wave is 440 Hz, the same as the lower note.
Half An Octave
Half an octave is half-way between the frequencies of the two notes. In the above example, half an octave is half-way between 440 Hz and 880 Hz, which is 660 Hz.
660 Hz is E, 7 semitones above A 440 Hz.
Two Halves
A to E, the lower half of the octave, is 7 semitones
E to A, the upper half of the octave, is 5 semitones
Let’s look at the composite wave’s frequency of each half.
The interval between A 440 Hz and E 660 Hz has a frequency ratio of 3:2. That is, it tales 3 cycles of E and 2 cycles of A to form the composite wave. The composite’s frequency is 220 Hz, the A an octave below the played note A 440. This reinforces the lower note of the interval, making it stronger.
The interval between E 660 Hz and A 880 Hz has a frequency ratio of 4:3. The composite’s frequency is also 220 Hz, which is 2 octaves below the played note A 880. This reinforces the upper note of the interval, making it stronger.
In other words, the upper half of an octave, a perfect 4th, behaves upside down compared to the lower half, a perfect 5th.
In a perfect 5th, the lower note is stronger
In a perfect 4th, the upper note is stronger
Perfect 5ths and perfect 4ths are literally inversions of each other!
Half An Octave In Scales And Melodies
In a scale, the 5th note, the note half an octave above the root note, is called the dominant. The dominant has a double function:
The half-octave point is as far away from the root note as you can get
It is also a strong supporter of the root note, as seen by the composite wave examples
The dominant provides a polar opposite point allowing melodies to venture away from the root note and to return from.
This is easily demonstrated in the most simple melody of all, the scale. By splitting it in two, we can see that the first half of the scale leads away from the root note and towards the dominant and the second half of the scale leads from the dominant up to (the octave of) the root note.
In the example below I’ll use the major scale but it works equally well for the melodic minor.
Perfect 5ths And Perfect 4ths In Chords
The presence of a a perfect 5th or perfect 4th in a chord helps us to identify the root note. The root note will be the lower note of a perfect 5th/the upper note of a perfect 4th.
If a chord contains more than one perfect 5th (or perfect 4th), the chord has more than one possible root note and its interpretation is determined by the musical context.
For example, the notes A C E G could be seen as either
Am7 an A minor chord; A C E, plus a minor 7th; G, or
C6 a C major chord; C E G, plus a major 6th; A
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.
Intonation is the ability to play in tune. When we compare one note to another, how do we decide whether they sound in tune?
If the two notes are in unison and played together, the answer is easy. They’re in tune when they match. When two unison notes played together are in tune, their frequencies match and they sound like one louder note.
When they’re slightly different, two notes produce a difference frequency which we can hear as anything from a slow, swishing pulse to a more rapid, tremolo-like effect known as beating or beats. For more, including an audio example, please visit The Secret To Tuning: How To Tune An Instrument To A Reference Note.
If the notes are not in unison, how you play in tune depends on the context.
Playing In Tune
First, let me state the obvious. Fixed pitch instruments such as keyboards are unable to adjust their pitch on the fly. Playing in tune is entirely dependent on how well and how recently the instrument has been tuned. We’ll look at how they are tuned later in this post.
Two Types Of Intervals
An interval is the pitch difference between two notes.
When two notes are played one after the other, as in a melody, it is called a melodic (horizontal) interval.
When two notes are played together, either on a polyphonic instrument or on two instruments, it is called a harmonic (vertical) interval.
Other than solo melodies, music consists of both melodic and harmonic intervals. Melodic intervals make up the flow of a part as you move through time and harmonic intervals are the parts interacting at any given moment, such as a melody note with a bass note or the notes of a chord with each other.
Generally, it’s easier to tune to a harmonic interval because, to varying degrees, we can hear the sound waves interact, much like when tuning to unison.
Melodic intervals are easier to tune to if we can clearly recognise the key. One way to do this is to warm up on a scale in the same key as the passage you’re playing.
Two Types Of Intonation
Just Intonation
The earliest forms of music revolved around a single note; the root note or tonic. Other notes flowed towards or away from the tonic so the focus in tuning was on how well the other notes fit the root note.
Any harmonic interval has a “best fit”. Most intervals can be tuned to simple frequency ratios by listening to the difference frequency and adjusting the note so there is no beating effect. The stable sound makes chords extra strong and rich.
So why don’t we use just intonation all the time?
Just intonation is great while tuning to one root note, but over time Western music developed into a more outgoing direction. Rather than stay in one key all the time, melodies ventured from one key to another, exploring the relationships between different keys and chords.
The Problem With Just Intonation
With just intonation, the farther you move away from the original key, the more out of tune the notes sound. What’s more, the semitones aren’t even all the same size!
The simple ratios of just intonation only work while the reference note is that of the key you’re in. To change keys, you need to change the tuning of the notes on the fly…
If you work out the frequency of every note using just intonation, by the time you get back to the starting note the frequency is significantly different!
Equal Temperament
The solution to playing in multiple keys is equal temperament. In equal temperament, the cumulative error over all keys is averaged out. All semitones are musically the same size. In equal temperament music can be played in any key and pieces can travel from key to key with every note sounding equally in tune.
No single interval is perfectly in tune as far as difference frequencies go but the amount is so small that we don’t hear it as beating. The only thing we might notice is a slight softening of the clearest intervals such as perfect 5th which, if anything, adds a sense of warmth.
Equal temperament is perfect for keyboards and other fixed pitch instruments and is widely accepted as the predominant tuning system in Western music.
Tuning On The Fly
Small consorts, in particular string quartets and small vocal ensembles, have a reputation for being able to play perfectly in tune.
This is achieved by combining the best of both worlds. Equal temperament is great for melodic intervals as the music progresses through time, while just intonation can be used to fine tune harmonic intervals to suit a chord at a given moment.
The ultimate guide is your ear. In any key, any note has a best fit. Be responsive to what you hear and you’ll find that best fit.
Feeling a bit nerdy? If you’d like to know a bit more about just intonation and equal temperament, please visit the Shop page for a FREE DOWNLOAD of my e-book, Intonation: From Pythagoras To Equal Temperament.
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.
Have you ever had trouble tuning to another instrument? If so, read on…
In any ensemble, big or small, all the instruments need to be in tune with each other. If not, no matter how skilled the players, the music will not sound musical.
Who Tunes To What?
All the players need to agree on a pitch reference that everyone can tune to. This can be an external source, such as a tuner, or one of the instruments.
If your instrument is tuneable, you can tune a note on your instrument by matching it to the same note on a tuner or other instrument. We do this by listening for a disturbance called beating.
If you have a fixed pitch instrument such as a piano, your instrument becomes the reference and others tune to you.
Note: On fretted string instruments such as guitar or bass, once you’ve tuned one string to an external reference you can play a fretted note on that string as the reference for the next higher string and progressively tune the other strings.
How to Tune To A Reference Note: The Difference Frequency
When two (or more) notes are played together their sound waves combine. This combination wave has a frequency which is the difference between the frequencies of the two notes.
If the two notes are identical, there is no difference frequency. The notes lock together and sound like one louder note.
If your note is almost but not quite the same pitch as the reference note, the individual frequencies take many cycles before they match. This results in a very low (slow) difference frequency. The closer to unison, the lower the difference frequency.
Here is a diagram of 2 notes of nearly the same pitch (blue and green). Up/down represents amplitude. We hear amplitude as volume.
The difference frequency is produced by the overall shape of the composite waveform, shown here in yellow.
Look at the composite (yellow) wave:
where both notes go up or down together, the composite wave is taller/louder
Where they oppose each other, the composite wave is shorter/quieter
If they oppose each other by the same amount, there is silence
Over one cycle, the composite wave gradually shifts from loud to silent (or near-silent) and back, creating a pulse.
Beating
We can hear the difference frequency as a pulse known as beating or beats. When both notes match, there is no pulse. When they’re almost in tune, there’s a slow, gentle pulse, maybe only 1 or 2 Hz (times per second).
As you tune your note away from the reference, the pulse becomes faster and the beating effect becomes more noticeable. This happens quite quickly, so make gradual adjustments!
Note: once the pulse is faster than 20 Hz we can’t hear the individual beats anymore. Instead, we start to hear two distinctly different notes. By now we’ve gone way too far…
Tuning the other way, as you get closer to matching the reference, the pulse slows down, then disappears when you’re in tune.
Example
Here is an example using 2 synthesiser notes, starting off in unison. After a couple of seconds, one note drifts flat, then back to unison, then sharp, before returning back to unison. I have chosen this sound because, like an organ, the notes don’t decay.
In the above example, the note is only just over a quarter of a semitone out at the furthest points. By then we can hear that the note sounds distinctly out of tune.
Sharp Or Flat? Listen For The Beats
Note that the beating effect is the same whether your note is slightly sharp or slightly flat. The beating only indicates how far you’re out: faster means further out, slower means closer.
Method
As you adjust your note, listen to the beating. Is it getting faster or slower?
If the beating becomes faster, you’re getting farther out of tune. Change the direction of your adjustment; tune the other way.
If the beating becomes slower, you’re getting closer to being in tune. Keep going. When the beating is slow, adjust more carefully.
When the beating is gone, the two notes will sound as one. Even with an electronic tuner, where the timbre of the reference is nothing like your instrument, the notes will feel like they’ve locked together.
If you’re not sure whether you’re sharp or flat, keep going in the same direction! Sooner or later it will either lock in because it’s in tune or the beating will have become fast and obvious enough to tell you that you’ve gone too far and you need to turn around.
Make slow, gradual adjustments as you listen.
Above all, don’t panic! If you make random adjustments you may end up tuning to a different note altogether, or you may end up going back and forth without ever reaching the note.
Stay calm, listen for the beating and stick to the method outlined above.
Plucked Strings Take Note
Beating is more noticeable when the notes sustain well. On many acoustic plucked string instruments, notes don’t sustain for long before they fade away.
One solution to this is to play repeated notes; each note long enough to hear the beating but not so long that they die down. For an acoustic guitar, once every 3 or 4 seconds should work. Instruments with a small body and nylon strings, such as the ukulele, have less sustain and you will need to play more frequent, louder notes in order to hear the beating clearly.
What Note Do We Tune To?
It doesn’t really matter what the note is, as long as everyone agrees. Different instruments find certain notes easier to play than others. Ideally, the note used for tuning is an easy note for all involved.
A 440 – Concert Pitch
It’s possible for a keyboard or tuner to play different notes for different instruments to tune to. However, the tuning process is much quicker and more straightforward if everyone tunes to the same note. This is particularly true for large ensembles such as orchestras.
The closest to a universal tuning standard is A 440 Hz, or just A 440, also known as concert pitch.
Lower instruments can match A in a lower octave. Beating works when tuning notes at different octaves just as it does in unison.
Are Instruments Always Tuned To Concert Pitch?
The short answer is no.
Over the centuries the tuning reference has varied considerably, both above and below the current 440Hz. Some ensembles specialising in period music will use the appropriate pitch reference for the era.
More generally, apart from digital instruments, fixed pitch instruments don’t stay perfectly in tune forever and may end up sharp or flat overall. All other players will need to tune by ear to make sure they are in tune with that instrument.
As long as everyone tunes to a common reference, it doesn’t matter whether it’s in concert pitch or not.
Note: Beating can also be heard when other consonant intervals like a perfect 5th or perfect 4th are out of tune. You can tune to these intervals in the same way as tuning to unison.
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.
Two classic examples of the Jimi Hendrix chord and why calling it an augmented 9th chord makes no sense.
Preface
Theory should reflect how we hear music. If the theory doesn’t reflect what you hear, it’s wrong.
In the case of the Hendrix chord, applying formal jazz theory to a more organic genre such as blues doesn’t add up.
Warning: if you are about to sit a formal music theory exam and you’re asked to describe this chord, call it an augmented 9th chord! Exams are set by academics; they’ll want the answer that they teach.
The Hendrix Chord
You may have heard of the Jimi Hendrix Chord or the augmented 9th chord, E7(#9).
To the disapproval of many academics, this chord is also informally known as a 10th chord. I believe this is a more plausible name than augmented 9th. To me, it is a 7th chord with both a major and a minor 3rd.
Chord Symbol vs Chord Function
Let me say at the outset that I’m not advocating that the Hendrix chord be called E10. This is an informal symbol, mainly in use among musicians without formal training.
E7(#9) is the official, accepted name for this chord. The many thousands of musicians who were brought up reading chord charts will be familiar with this symbol and will instinctively play the right chord.
Many chords have several possible interpretations, depending on the context. The function of a chord is significant for analysis.
However, when reading, it’s more convenient to see the most commonly used version of the chord name each time, regardless of the context.
Personally I think the name was incorrect in the first place; it makes no sense to me, but there’s no point in my trying to deny that the Hendrix chord is formally always written E7(#9). My music notation software won’t even recognise the symbol E10!
More properly it could be named as a polytonal chord, Em over E. However, there’s no easy way to type this symbol so it’s mainly used in handwritten chord charts and music publishing apps.
My argument is that even though it’s called an augmented 9th chord, we should treat the Hendrix chord as a 7th chord with both a major and a minor 3rd.
What Key Are We In?
Rather than worry about chord names, let’s look at how the Hendrix chord is commonly used.
The classic use of this chord is on guitar, in the key of E major, as the root (tonic) chord with an added D and G at the top. The order of the notes, from low to high, is E G# D G. In this classic guitar chord shape, the 5th, B, is left out.
Aside: in a root position 7th chord it’s not uncommon to leave the 5th out to reduce clutter, especially if closely voiced. No B is no big deal…
G or F Double-sharp? That Is the Question
I note that some major sources, including the Fender website, name the highest note G even though they call the chord an augmented 9th chord. If it truly is an augmented 9th, it should be called F double-sharp. More on this later…
Purple Haze
The ultimate example of this chord in use is the Jimi Hendrix song that made the chord famous, Purple Haze.
Forgive the cheesy sounds used here- it’s all about the notes 🙂
What Key Are We Really In?
What is the key? If you look at the melody, it’s in E minor, not E major. G natural is a prominent note in the melody.
In the Hendrix chord it’s the major 3rd, G#, that’s dissonant against the melody, not the minor 3rd, G. To acknowledge that G belongs to the melody, as it does, it should be called G, not F##.
Blue Note
The Hendrix chord is functionally both a major and a minor chord. I suppose you could respell the note G# as Ab, a diminished 4th, to reflect the tension between it and G, but I personally think it amounts to a blue note. After all, this chord is very much the domain of blues.
Blues songs are often described as having variable 3rd and 7th notes yet they are considered as being in a major key. I think that most blues melodies are in a minor key but are accompanied by major chords (usually as dominant 7ths, but that doesn’t stop them from being major chords). The interaction between the minor 3rd in the melody and the major 3rd in the chord is what creates that variable quality; that grungy, ambivalent bluesy character.
If you don’t believe me, try singing Purple Haze with a major 3rd and 7th.
Very different! Nothing like the character of the original.
If you think it might be in the myxolydian mode, sing the major 3rd and keep the minor 7th.
The riff sounds better but the melody still sounds wrong!
Now sing it with a definite minor 3rd and minor 7th – sounds about right, I reckon.
The note G is a prominent note in the melody. It’s a main note (a chord note), not a passing note. Surely a chord note that sounds the same as a prominent melody note should be acknowledged as a regular chord note, not as an augmented anything!
A Chord With Both 3rds
I’m not trying to say that G#, the major 3rd, isn’t also a chord note. The Hendrix chord is simply one that contains the 3rd of both the melody’s key and the chord progression’s key.
G Major Chord
The chord that follows is a G major chord. The riff after the verse also contains a G major chord, as a 1st inversion triad: B D G, B D G.
In E minor, G major is a closely related chord: it’s the relative major, a perfectly normal chord to visit.
G major is less closely related to E major: it isn’t even built on a note in the key of E major. Yet, when we hear the song, it effortlessly fits in. This supports E minor rather than E major as the key of this song.
Taxman
Another classic song featuring the Hendrix chord, this time in D, is Taxman by the Beatles.
For the sake of comparison, I have transposed Taxman to E (up 2 semitones).
The melody pointedly avoids the 3rd during the E7(#9) chord but in the next line, as a passing note over a D chord, there is a G natural, suggesting E minor as the key. The D chord is also more closely related to E minor than E major.
Blues Mode
D is soon followed by A, which seems to contradict my argument by being closer to E major than E minor. This brings to mind a common feature of blues songs.
Blues melodies often miss out the 6th note of the scale (Purple haze is like this). When the 6th is included, it tends to be a major 6th, to fit the subdominant chord, the one calm moment in blues.
In E major that’s the note C#, the 3rd of an A major chord.
Given a minor 3rd and a minor 7th, a scale with a major 6th is the dorian mode. Here is E dorian:
E dorian
What Came First? The Chicken Or the Egg?
I’m no historian but I suspect that African American slaves were singing the blues long before they had access to a guitar. The accompaniment came later.
The dorian mode is a common mode for blues melodies. Superimpose this with major chords based on the major (ionian) mode and we have the blues effect.
G Chord
Just before the final solo, Taxman eventually goes to a G chord, again favouring E dorian as the Key. Both D and G are chords whose root notes aren’t in the scale of E major…
Again, the melody is more minor than major and it is the contrast with the major third in the chord that creates the grungy, bluesey character.
Summary
In a nutshell, blues often combines a minor or dorian melody with major chords. The chords often include an added minor 7th (dominant 7th chords).
The Hendrix chord is a 7th chord with both major and minor thirds, highlighting the character of blues music.
In its classic form, the Hendrix chord is used as the tonic chord in E
Blues melodies are more minor than major. They are often in the dorian mode
Because the minor 3rd of the Hendrix chord belongs to the melody, the chord must use the melody note’s name. In E that’s G, not F##
The grungy, dissonant character of blues is due to the ambiguity of the 3rd and 7th notes of the scale, which feel like they’re somewhere between major and minor
This ambiguity is created by contrasting the minor 3rd and 7th of the melody with the major 3rd of the tonic and dominant chords
The Hendrix chord combines both the 3rd of the melody and the 3rd of the major chord which accompanies it, so both notes are 3rds: one from the melody’s mode and one from the key of the chord
Postscript: Root Note Power in Chords
There’s another reason the note G shouldn’t be called F double-sharp.
The core notes of a chord are the 1st and the perfect 5th. The 5th reinforces the root note, helping us to hear what the root note is. The 5th literally blends in to the root note to make it stronger.
Any pair of notes a perfect 5th apart point to a possible root note.
The inversion of a perfect 5th is a perfect 4th. Whereas in a perfect 5th, the higher note blends in to the lower note, in a perfect 4th, the lower note blends in to the higher note.
Maybe It’s a G Chord
In the key of E, the top two notes of the Hendrix chord, low to high, are D and G. That’s a perfect 4th, pointing to the upper note, G, as a possible root note.
If the notes were D and F##, the interval between them would be an augmented 3rd, presumably an interval with a degree of tension, in the context in which it’s used. For an example of the valid use of an augmented interval name, please visit Sleight of Ear: the effect of musical context on perception.
This is clearly not the case. When you listen to the chord, the top two notes sound clear and stable, as you would expect from a perfect 4th.
I’m not trying to suggest that G is the real root note: the chord’s voicing strongly favours E (If it was, G# would be respelled as Ab and the chord would be called G6 add b9).
However, the fact that both notes are voiced high in the chord doesn’t prevent them from being noticed as a stable (perfect) interval. If anything, being in the same octave, they’re even more recognisable. You can hear them clearly, as an overlay to E major: a hint of G major.
Furthermore, both G and D are reinforced by belonging to the melody.
E10 is part E major and part E minor. It can also be seen as part E major and part G major. If the note B wasn’t left out of the classic guitar chord shape, the chord would contain a complete G major triad! Just like the riff in Purple Haze…
Controversy Corner is a category in which I like to present a sometimes controversial perspective that doesn’t necessarily represent orthodox music theory. These are my own thoughts and observations. Whether you agree or disagree, I’d love to read your thoughts as comments.
Don’t discard those worn-out Christmas carols! While they’re still fresh, they make a great educational tool for children (and others) to learn intervals.
By associating a song you already know with an interval, you can immediately sing that interval.
Here’s an incomplete list of Christmas carols whose opening interval starts with various intervals.
Any other suggestions?
Minor 2nd ascending
I’m Dreaming Of A White Christmas
Minor 2nd descending
Joy To The World (the first line is a complete major scale descending)
Major 2nd ascending
Silent Night
Ding Dong Merrily On High
Major 2nd descending
Deck the halls
Minor 3rd ascending
Jingle Bells (chorus)
Major 3rd ascending
While Shepherds Watched Their Flocks By Night
Perfect 4th ascending
We Wish You A Merry Christmas
Away In A Manger
12 Days of Christmas
Perfect 4th descending
O Come All Ye Faithful
Perfect 5th ascending
God Rest Ye Merry Gentlemen
Major 6th ascending
The Holly And The Ivy
Octave ascending
The Christmas Song (chestnuts roasting on an open fire)
You can also learn to sing intervals by singing scales. For more, please visit:
This post is the last 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.
Major and minor triads form the basis of many other chords. Of these, by far the most well-known is the dominant 7th chord.
What’s a Dominant 7th Chord?
A dominant 7th is a major chord with an added minor 7th. It is so named because it is most popularly used as the chord on the dominant of the home key.
In C major, the chord on the dominant is G: G B D. Add a minor 7th, F, and we get G B D F.
It sounds a bit less solid than a plain major chord. Have a listen…
Triad
A triad is a chord whose content is made up of intervals of a 3rd (it doesn’t mean the chord has 3 notes). The extra note follows this pattern so a dominant 7th chord is a triad.
Although it has a 7th, we can still include the octave. Like any chord, the notes can be played in any pitch order and any of the notes can be doubled at other octaves. In the above example the notes were spread over 2 octaves for clarity.
7th Chords
Dominant 7th chords are often just called 7th chords or 7 chords. This can be confusing because there are also other types of 7th chords. However, broadly speaking, dominant 7ths are the most common. Unless specifically stated otherwise, it’s quite likely that a 7th chord would be a dominant 7th.
Chord Symbol
The main part of the chord is a major triad, indicated by the name of the root note. The minor 7th is written as a suffix after the chord name, the number 7.
Tritone
The dominant 7th chord contains a diminished 5th, an interval of 6 semitones, between the 3rd and 7th notes.
A 6-semitone interval is commonly called a tritone. A tritone is a dissonant interval. When you hear two notes 6 semitones apart, neither note supports the other.
Adding this effect to a major chord makes the chord less stable. Since the 3rd is embedded in the major chord, it’s the 7th that feels unstable. When we hear it, we want it to move.
Usage
A dominant 7th chord is most commonly used as a way to arrive in the home key at the conclusion of a phrase; V7 – I, or V7 – i if the piece is in a minor key.
There’s nothing wrong with using a plain major chord on the dominant but the instability of the 7th helps the chord to “tip over” on to the tonic, giving a satisfying sense of arrival at home.
Here the F in the G7 chord happily drops to E, which belongs to the tonic chord, C.
Tension and Resolution
In the above example, without the 7th, the chord change is a bit static; both chords feel quite stable.
By adding the minor 7th, F, the tritone between the 3rd and 7th adds tension to the dominant chord. The listener is left with a sense of wanting to leave the unstable dominant and arrive solidly at home.
This arrival is called resolution. Tension and resolution is the main driving force in Western music. Dominant 7th chords are used in this way in many genres, old and new.
The dominant 7th can similarly be used on the tonic as a “pretend dominant” to lead away from a no-longer stable home to the subdominant, I – I7 – IV, and onwards…
You could say, if you want a chord to move along, make it a dominant 7th.
The Dominant 7th And The Chords Of The Major Scale
Remember the chords of the major scale from B20. The 6 Most Useful Chords In Any Major Key? That funny chord on the leading note turns out to be the top three notes of the dominant 7th chord. It’s a dominant 7th without the root note!
Aside: As a chord in its own right it’s known as a diminished triad. It’s a minor chord with a flattened 5th… but that’s a subject for my upcoming intermediate theory short course…
Other Uses
The dominant 7th chord can be used as a chord in its own right, purely for its character. In blues, for example, it’s quite common to play all the chords as dominant 7ths.
if you play a chord instrument, try replacing the major chords in any simple piece with dominant 7ths; it lends a bluesy quality to almost anything.
Dominant 7th In Minor Keys
The harmonic minor allows the dominant chord to be a major chord in a minor key, so the majority of pieces in minor keys also have a dominant 7th chord.
In the harmonic minor, the dominant 7th chord is the same as in the major key of that root note. For example, the dominant 7th of both C major and C minor is G7; the dominant 7th of both F major and F minor is C7.
How To Find The Notes of a Dominant 7th Chord
A dominant 7th chord is a major chord with an added minor 7th. It is made up of the 1st, Major 3rd, perfect 5th and minor 7th of the key it represents.
The 7th note is a minor 3rd above the 5th note of the chord. You can find it by counting 2 letters up from the 5th.
If the chord is on the dominant of the overall key, the 7th is a scale note, so you won’t need to count semitones. Otherwise, make sure it’s 3 semitones above the 5th.
Method 2
The 7th note is also a major 2nd below the octave. It’s the letter below the octave.
Again, if the chord is on the dominant of the overall key, the 7th is a scale note. You have the answer. Otherwise, make sure it’s 2 semitones below the octave.
Try These…
1
As text, list the content (the different notes) of the following dominant 7th chords:
D7
A7
Bb7
Eb7
E7
2
Name the dominant 7th chord in the following keys:
D major
D minor
A minor
Bb major
C minor
Answers at the end of this post.
Inversions
A dominant 7th chord has 4 different notes, so there are 4 possible inversions: root position plus 1st, 2nd and 3rd inversion. The chord is in 3rd inversion when the 7th is the lowest note.
Having the 7th in the bass lends even more weight to the instability of the chord. It’s often used in the bass as part of a “bass run”, to help a chord move on to the next chord.
The dominant 7th is just one common example of the many different chords which are based on major or minor triads.
Congratulations!
You have now completed the Music Theory De-mystified Basic Music Theory Course! I hope you enjoyed it and that you find it useful.
You now have a working knowledge of time signatures and basic rhythms, music notation, scales and keys, intervals and interval names, major and minor chords and chord symbols.
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This course is part 2 of a two-part course in basic music theory and includes elements of notation and musicianship.
Part 2 is made up of 21 lessons of about 30 minutes duration. This amounts to one semester at one lesson per week or a 6-week course at one lesson every two days.
Although each lesson is self-contained, the lessons are designed to run in numerical order.
Lessons are grouped in modules of just a few lessons. You don’t need to commit to the full course; just work though one module at a time.
Requirements
Part 2 assumes that you have completed Part 1 of this course or have an equivalent understanding of the following:
basic music notation
counting in bars and beats
simple time
scales, keys and key signatures
major, minor and perfect intervals
Although Part 2 includes music notation, like Part 1, musicians who play by ear are well catered for with plenty of audio, video, text and illustrations.
Recommended Additional Resources
This is primarily a music theory course. The notation exercises included are far from comprehensive and may be supplemented by music reading, beginner music theory workbooks and transcription exercises.
The musicianship/ear training exercises in this course are also far from comprehensive. I have focused on the most generally useful skills for this course. There are a number of dedicated musicianship courses available to further develop these skills.
Outcomes
An Understanding Of The Following Musical Concepts
Syncopation in simple time
Compound time
Triplets in simple time
Swing notation
Anacrusis (upbeat)
Harmonic minor scale
Melodic minor scale
Augmented and diminished intervals
Inversion of intervals
Major and minor triads
Modal (open/power) chords
Inversions of triads
Doubling
Relative chord names
The chords of the major scale
Dominant 7th chords
Musicianship Skills
Tap or play syncopated rhythms in simple time down to semiquavers
Tap or play simple rhythms in compound time down to semiquavers
Count in for an anacrusis
Sing major and minor triads in all inversions
Recognise and name major and minor triads in all inversions
Recognise notes that belong to a major or minor chord and sing them in your octave
