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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 minor intervals are minor 2nd, minor 3rd, minor 6th and minor 7th. There are a few ways we can learn to sing these intervals.
Phrygian mode
The minor intervals are based on the phrygian mode. The phrygian mode is not easy to sing!
Most people aren’t used to starting a scale with a minor 2nd (1 semitone). However, if you listen to early music or traditional folk genres, you may be able to sing it.
Give it a try if you like. Don’t worry if you find it hard because there are easier options below.
If you can sing this scale, you can teach yourself the minor intervals by counting scale notes in the phrygian mode, just as we did for major intervals in the previous lesson. If not, read on…
Natural Minor
The next option is to sing the natural minor scale. That works for all except the minor 2nd, 1 semitone. See below for how to learn to sing a minor 2nd.
Most people find this much easier to sing than the phrygian mode. Again, the best way to find out is to try it.
Try It…
If you can comfortably sing the natural minor scale without following the video, you can use it to find the minor 3rd, minor 6th and minor 7th. Learn to sing the minor 2nd separately (see later in this post).
Example: minor 7th by singing the minor scale
Major Scale
The final method, outlined below, is to start to sing a major scale. To sing a minor 2nd, 3rd, 6th or 7th, drop down by 1 semitone from the major to find the equivalent minor interval, much like the interval ruler in 16. Interval names 1: major, minor and perfect intervals.
This method is great when you want to name an interval that you hear, because at first you won’t know whether it’s major or minor.
Rather than having to try both major and minor scales, just sing the major scale. If the major scale overshoots the upper note of the interval it’s probably a minor interval. (There is one exception to this but we’ll leave that until Part 2 of this course).
This requires one trick; the ability to sing 1 semitone below a note. This may seem hard, but I’m sure you can already do it without even realising it…
How To Sing 1 Semitone Up Or Down
Try This…
Sing the first 4 (or the last 4) notes of a major scale.
Now go back and forth between the last two notes you sang – that’s 1 semitone.
Feel how close together these last two notes are, almost squeezed together… Remember that feeling when you want to sing two notes 1 semitone apart.
Does it remind you of something? Start slowly and speed it up… The theme of the all-time classic movie, Jaws…
Now you’ve sung 1 semitone up and down a few times, reverse it. Sing down before going up (start on the higher note if you like). Below we have 1 semitone as a minor 2nd on C, first upwards, then downwards. Focus on keeping the two notes squeezed tightly together.
After a little while, you‘ll be able to sing a semitone up or down down by itself.
How To Sing Minor Intervals By Singing The Major Scale
For a minor 2nd, learn to sing 1 semitone up as outlined above.
For other intervals, sing the major scale indicated by the degree of the interval name (3rd, 6th or 7th).
Sing down 1 semitone.
Repeat this a few times.
Now just sing the first and last note as an interval.
Repeat a few times. Build up to being able to sing it by yourself, without the video.
Once you’ve sung a few intervals, try to sing the in-between scale notes more quickly and quietly, until they’re just a thought.
Try These…
Minor 2nd by singing the major scale
Sing the first bar again while you listen to the 2nd bar.
This is just a semitone up rather than down, as we learnt earlier.
Minor 3rd by singing the major scale
NOTE: For this and the following intervals, repeat the 3rd bar while listening to the 4th bar.
Minor 6th by singing the major scale
Minor 7th by singing the major scale
How To Name An Interval That You Hear
Identify the lower and higher note of the interval and sing them.
While listening to the interval, start to sing the major scale of the lower note, counting degrees (note numbers).
If it’s a major or perfect interval, you’ll find the upper note and have the answer.
If it’s a minor interval, at some point you’ll be too high. As soon as you notice this, sing 1 semitone below your last note. If you’re still too high, you went too far up the major scale and you should start again.
You may need to repeat this a few times until you feel sure that your upper note matches the upper note of the interval.
Try These…
Name the following intervals:
Answers at the end of this post.
NOTE: There is one interval we haven’t covered in the last two lessons, an interval of 6 semitones, often called a tritone (we’ll learn its proper interval name in Part 2 of this course). It’s a bit harder to sing than the other intervals and isn’t all that common so we’ll leave that one out for now.
Coming Soon! The Interval-Singing Project
The interval-singing project is survey of well-known songs in many genres, each of which starts with a specific interval. For each genre I hope to collect song titles to cover each interval.
Instead of having to learn intervals from scratch, students will be able to draw on their own knowledge, needing only to remember which song represents which interval.
Anyone who subscribes to my blog will have access to the database at no cost.
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.
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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 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.
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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 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.
If you’re looking for the quick answer, scroll down to the summary.
A scale is both a sequence of note pitches you can play by itself as a simple melody (usually for practice) and the basis of a piece of music.
In 1 Note Names, Semitones and Octaves, we saw that there are 12 different musical note pitches within an octave, each 1 semitone apart. We also saw that there are only 7 letters used to name music. On a musical stave there are also only 7 pitch positions per octave, one for each letter.
This is because most music in Western culture is usually made up using only 7 of the 12 notes at a time, the eighth note being the octave (hence the name “octave”). Such a selection of notes is called a scale. The first note of a scale is the reference note for music written in that scale.
Note: It is possible for a scale to have more or less than 7 notes (such as the 5-note pentatonic blues scale) but the vast majority of music in Western culture, both historically and in modern times, is based on 7-note (heptatonic) scales.
How Far Apart Are Scale Notes?
For 7 notes to make up an octave (12 semitones), the notes can’t all be spaced evenly. Most of the notes are 2 semitones apart, but there are two pairs which are only 1 semitone apart. For example, let’s look at the naturals; the notes that have just a letter as their name.
The naturals from A to A with note spacing in semitones
C major
Although the notes are named starting on A, C is the starting point for the most common scale of all, C major. We’ll talk about major and minor shortly, but for now, let’s look at the notes starting on C.
The naturals from C to C with note spacing in semitones
C major is made up of the naturals starting on C. We can see that C to D is 2 semitones, as is D to E, then E to F is only 1 semitone, etc. This is quite easy to see on a piano keyboard, as the named notes are the white keys and the others, the black keys. The interval from one key to the next is 1 semitone, whether between adjacent white keys or between a white key and an adjacent black key. (The staggered layout of a piano’s keys is for practical reasons- so one hand can span an octave).
Note: In scales, the intervals marked as 2 semitones are usually called a “tone” rather than “2 semitones”. Other schools use the terms ”steps” and ”half-steps” for the 2- and 1-semitone intervals between the notes of a scale.
In this blog I will always name intervals by semitones or by their musical interval name. For my reasons, see A Story Of Tones And Semitones.
The Root Note
When we play a scale, we usually emphasise the first and last note, in this case, C, by playing those notes louder, longer or both. Playing a scale in this way helps us feel that the starting/ending note is the home note and that the other notes either lead away from that note or towards it.
The first note of a scale is called the root note or tonic and it is the most important note in a scale. The root note represents home in a musical journey and the start of the pattern of intervals from note to note that defines the scale.
Modes
Let’s play a scale using only the naturals, from C to C and back.
Now let’s play the same notes but starting on a different root note, such as A. We’ll play A to A and back.
Sure, one was slightly higher than the other, but did you notice a difference in character/flavour/mood? Have another listen…
… (I’ll wait)…
This difference in character is even more noticeable in a real piece than just a scale.
Now let’s compare the spacing of the notes.
Notice the difference in the order of the 2’s and 1’s in relation to the root note? It is this pattern that determines the scale’s character.
The pattern of intervals that determine the note spacing of a scale is called a mode. When using just the naturals, each time we start on a different note, the pattern of note spacing is different. There are 7 different naturals, each of which is the root note of a mode. Of the 7 modes produced, six are quite common in various genres and one, the one starting on B, is seldom used (but that’s the subject of another post).
Earlier on, I called the first scale, starting on C, C major. The term major refers to the mode. Major is the most commonly used mode in modern Western music, hence the name. The one on A is called A natural minor or just A minor for short. Minor scales are usually used in a slightly different way to major in that there are two popular variations on the natural minor. We’ll look at how these variations are used in part 2 of this course so for now we’ll use the natural minor as our minor example.
The major and natural minor modes are also known by Greek names based on modes in the renaissance era. Major = Ionian mode. Natural minor = Aeolian mode.
What About Keys?
You’re more likely to hear people talk in terms of keys rather than scales and modes. A key is simply the notes of a scale when they are rearranged to make music.
For instance, any music which is based on the scale of C major is in the key of C major.
The major or minor (or any mode, for that matter) can be made to start on any root note. The major mode on D is called D major. The minor mode on F is called F minor. We’ll look at how this works in coming posts..
Scales and melodies
We can tell the difference between C major and A minor when we play the scale because we’re emphasising the root note – by playing it first, last and longer than the other notes. Furthermore we can hear the progression of ascending or descending notes arrive on the root note. But how can we recognise the mode when the notes are all mixed up in a melody?
It’s all about being able to recognise the root note.
Melodies rely on a range of techniques to highlight the root note including those I’ve just mentioned. A melody isn’t a random selection of notes. The structure of the phrases that make up a melody and the relative length and strength of notes all contribute to our ability to recognise the root note as home. Some of these techniques are mentioned in a little more detail in How Can We Tell Which Key We’re In?
Summary
A scale is a selection of (usually 7) pitches within an octave, which form the basic pitch elements of a piece. The notes can be played at any octave.
The root note or tonic is the first note of the scale and the reference/ home note for music written using that scale.
The interval spacing of the notes of a scale is called a mode. The most common modes are called major and minor.
Each mode imparts a unique character to the music because of its unique combination of 1 and 2 semitone intervals from note to note.
We can hear the character of the mode because the music is written in such a way as to highlight the root note. For some examples, visit How Can We Tell Which Key We’re In?
This post is one of a growing series of free basic music theory lessons on my blog, musictheoryde-mystified.com. You can see the complete list here.
Please feel welcome to like, comment or to share this post. If you have any questions, pleased leave them as a comment and I will respond as soon as I can. If you enjoy my posts and would like to be kept up to date, please subscribe.
Much of the content is based on my upcoming music theory reference, Music Theory De-mystified, which is currently planned for release as an e-book by the end of 2023.
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.
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Every musician discovers early on that octaves are special.
Notes which are one or more octaves apart have the same note name – that in itself means a lot. Furthermore, changing octaves feels more like changing voice or register than going to a different note.
Why is this so?
When we play a note, a sound wave is produced. Each pitch produces a wave which vibrates at a certain frequency: the higher the pitch, the higher (greater) the frequency.
The frequency is measured in cycles (vibrations) per second, called Hertz, Hz for short. You may have heard of A440, the frequency tuners are calibrated to. 440 means 440 Hz. A440 vibrates 440 times per second.
Playing a note an octave higher doubles the frequency: an octave above A 440 Hz is A 880 Hz. As the frequency gets higher, the length of the wave becomes shorter, so double the frequency is half the wave length.
When we play these two notes together, the higher note’s sound wave fits exactly twice inside the lower note’s sound wave. No other combination of two notes has such a direct relationship between their sound waves as an octave. This perfect fit is why the higher note of an octave sounds like it fits inside the lower note: because it literally does.
Graph showing the sound waves of two notes an octave apart such as A440 and A880. Twice the frequency = half the wavelength
Low and high octaves are large and small versions of each other. A musical part can be played at a different octave without introducing any new notes: it will still fit all chords and other parts equally well.
Please feel welcome to post a comment or ask a question.
*Graphics taken from Music Theory De-mystified, my upcoming music theory book, due to be released late 2022.
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.
If note names mean nothing to you, start here…
In my posts:
A PIECE is any musical work.
A PART is one instrument’s component of a piece.
An ENSEMBLE is any combination of instruments collaborating to perform a piece, be it one person singing and playing, a band, choir or orchestra.
Note names
Most musicians are familiar with the note names A to G. After G comes A again and the pattern continues repeating from the lowest pitches to the highest.
A B C D E F G A B C etc.
Over the audible pitch range there are many A’s, many B’s and so on.
From one A to the next is an octave, as is from any letter to the next instance of the same letter.
Octaves
Notes which are an octave (or several octaves) apart enjoy a special relationship. When played together, the higher note blends in to the lower note. If they’re perfectly in tune (that’s for a later post), the higher note blends in so well that it almost merges inside the lower note. Even when played one after the other, what we hear sounds more like a change in register (or voice) than a different note.
Try this on your instrument. If you can play two notes at once or play one and sing the other, the effect will be the clearest, but you can still tell by playing one after the other.
Now try combinations of two different notes, such as A and G or A and C. None feel as closely connected as when they’re an octave apart (or a unison; two notes of exactly the same pitch).
In musical terms, in an ensemble, any part can be played an octave higher or lower without clashing with the other parts. All chords or harmonies will still fit. It is because of this relationship that notes which are octaves apart can, and do, share the same note name.
Intervals
The difference in pitch between one note and another is called an interval. A to the next A, an octave, is an interval, A to G is an interval, F to C is an interval.
Intervals can be measured in octaves and semitones. Each octave is divided into 12 musically equal intervals called semitones. This gives us 12 different notes, the 13th being an octave. The semitone is the centimetre (or inch) of pitch.
On a piano, 1 semitone is the interval between consecutive keys, regardless of the key’s colour.
On a guitar, 1 semitone is the interval from one fret to the next (or from an open string to the first fret).
We started with the letters A to G, followed by A etc. that’s 7 letters, the 8th being the octave of the first (as it happens, octave means 8th). So how do 7 letters add up to 12 semitones?
Not all letters are 1 semitone apart: in fact, most are 2 semitones apart. This is how the letters are spaced:
A . B C . D . E F . G . A 2 1 2 2 1 2 2 = 12
This means that 5 of the 12 different notes (per octave), the ones represented here by dots, have no name.
On a piano keyboard, all the named notes are white keys. You can see when two white keys are 2 semitones apart because there is a black key to represent the so far un-named note between them.
Piano keyboard layout showing naturals for 1 octave
On a guitar, you can find the named notes by starting on an open string, then following the above pattern by skipping a fret for every 2-semitone interval. The dots above represent the frets you skip.
Guitar fingerboard layout, A string, showing naturals for 1 octave
The named notes are called naturals. The un-named notes can be described as being 1 semitone higher or 1 semitone lower than the nearest natural.
Sharps and flats
Any natural can be raised by 1 semitone by adding the sharp symbol, #. Any natural can be lowered by 1 semitone by adding the flat symbol, b.
For instance, the note between A and B could be called A# (A plus 1 semitone) or Bb (B minus 1 semitone).
This may seem confusing: we’ve gone from having no names for some notes to having two names. Fear not. For now, either name will do. The most common note names in general terms are:
A Bb B C C# D Eb E F F# G G# or Ab
Once we look at the notes in the context of a piece of music, the choice of note names will matter but by then it will be quite obvious which names to use. The correct note names for a piece are based on its key, a subject for a future post.
The graphic below shows how any natural can be raised by 1 semitone by adding a sharp or lowered by 1 semitone by adding a flat, resulting in two possible note names for most notes. Notice that even some of the naturals have an alternate name, although their use is relatively uncommon in most keys.
In my next basic post we will look at how note pitches are written on a stave.
Try These…
How many semitones between the following pairs of notes? (count up from the first note until you reach the second note of the pair):
A to C
A to C#
A to E
A to G
Bb to F
B to F
C to A
C# to A
D to Bb
Answers at the end of this post.
This post is one of a growing series of free basic music theory lessons on my blog, musictheoryde-mystified.com. You can see the complete list here.
Please feel welcome to like, comment or to share this post. If you have any questions, pleased leave them as a comment and I will respond as soon as I can. If you enjoy my posts and would like to be kept up to date, please subscribe.
All the naturals (letters) are 2 semitones apart except B to C and E to F, which are 1 semitone apart.
Not only that, but B-F is 6 semitones, whereas every other interval of 5 naturals is 7 semitones apart, such as A-E or C-G. This is important in understanding keys and key signatures.
BCEF is easy to remember because it’s so odd, like a hip-hop band name gone wrong: the BCEF.
So remember BCEF
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.
