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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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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…
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 straight to the summary (but you’ll miss all the fun…)
A scale is the combination of a root note and a mode. It’s even named that way. C major means C is the root note and major (Ionian) is the mode. The same for A minor: A is the root note and minor (Aeolian) is the mode.
In 8. What Is A Scale? we saw that a scale is a selection of (typically 7) notes within an octave, and that our sense of tonality depends on knowing which of these notes is the root note. In a piece that has a clear tonality the notes are organised so that the root note (tonic) is highlighted, especially near the beginning and end.
We also discovered that the reason the root note is so important in allowing us to hear the musical character is because typical Western scales have uneven intervals from note to note. Changing the root note effectively changes the pattern, changing the mode and thus its character.
Scales On Different Root Notes
If you know the character of the mode, you can sing a scale in that mode. As long as it’s within your range, you can sing that scale starting on any note (without even knowing what that note is!). As long as you don’t change the mode it will sound the same, just higher or lower.
The same is true for writing music. You can write a scale on any note. Here’s how it works:
Let’s look at the the major mode, which naturally starts on C. C major is made up of only the naturals.
We can pick any other note as the root note and build a major scale on that. All we need to do is make sure we stick to the major mode, the pattern of intervals from note to note that matches C major, or else we’ll change its character.
Let’s say we want D major. If we just started on D and used the same notes we would have a different pattern of intervals – a different mode – a different character.
It would sound like this:
This scale has quite a different character to C major.
Instead, we use the same pattern of intervals as C major, write D as the root note and then, working from left to right, count the number of semitones from each note to the next to work out the other notes. This will involve using one or more sharps or flats.
The 2nd note should be 2 semitones higher. 2 semitones above D is E.
The 3rd note is 2 semitones higher than E. F is 1 semitone higher than E and G is 3 semitones higher so we want the note in between. This could either be called F# (F+1) or Gb (G-1). What should we call it? We’ll come back to that shortly. We can put in both for now.
The 4th note is just 1 semitone further which is plain old G, and so on until the 7th note, 2 semitones above the 6th note, B. Again we have 2 options, C# or Db, and again we’ll write in both for now.
And, of course, the 8th note, 1 semitone above the 7th, should be exactly the same as the first, as it is the octave.
OK, time to look at what we’ve got… If we choose Gb for the 3rd note we have Gb AND G but no F, whereas if we call the 3rd note F# we have one F and one G. The same goes for the 7th note: Db uses the same name as the root note but a different sign, whereas C# allows one C and one D.
Now that we’ve worked out the notes in D major, let’s have a listen.
Now compare it to C major. The character should be the same, even though one scale is a little higher than the other…
The Note Naming Rule
For scales, there is one simple rule: the next note in a scale should have the next letter in its name.
Each note in a scale must have its own letter.
There’s a good reason for this: there are 7 note names, 7 notes in a scale and 7 pitch positions per octave on a stave.
Music notation is very visual. We can see the notes climb and descend as the melody itself climbs and descends. As we can see from the two versions of D major below, if two different notes in a scale share the same note name there are two different pitches sharing the same place on the stave and needing constant accidentals (sharps/flats/naturals) to show which is which. There is also one unused position, leaving a gap in the visual that we don’t hear.
Below is D major as notes on a stave showing both sets of note naming options. Try to read the notes while you listen. Which one is more visual (and less cluttered)?
Note: We can make a scale look even less cluttered by using a key signature. We’ll look at key signatures in the next lesson.
How to find the notes of a scale
Now that we know how to work out what notes we need to write a major scale starting on D instead of C, we can do so for any mode and any root note.
As the most common modes are major and minor, let’s find the notes for some other major and minor scales.
Choose a mode, e.g. major or minor.
Write the note that you want to build the scale on as the 1st note (root note).
Working from left to right, count how many semitones to the next note. Where there are two names for the same note, choose the name using the letter after the previous note.
(safety check: if you’ve added it up right, the 8th note’s name should be exactly the same as the first).
TIP: Learn the patterns that make up the major and minor modes (I think of them as phone numbers).
Major .2.2.1.2.2.2.1.
Minor .2.1.2.2.1.2.2.
Example: D minor
Have a go…
Here’s the answer…
OK, this one’s minor and has a flat. Pure fluke! There is no connection between being major or minor and having sharps or flats.
Try These…
Grab some paper and a pencil and try a few more… Bb major, A major, C minor, F# minor.
Answers at the bottom of this post. Here’s what a blank major and minor look like:
Practical Tip
Pick a major or minor scale that’s easy to play on your instrument, find its notes and doodle around with those notes. Just in one octave will do for a start, then try 2 octaves worth – it’s more fun. As long as you highlight the root note every now and again, for instance by making it long or strong, you should be able to feel the tonality of the mode you’ve chosen, or at least keep coming back to it if the music goes elsewhere. For a bit more on how to highlight the root note, visit How Can We Tell What Key We’re In?
Summary
A scale is a combination of a root note and a mode.
The root note is the first note of the mode.
A mode is a set of (usually 1 and 2 semitone) intervals from note to note adding up to an octave. The most common modes are major and minor. Of these, only C major and A minor have no sharps or flats.
Due to the irregular pattern of intervals from note to note, each mode has a unique musical character.
To make a scale on a different root note, choose the mode with the character that you want, e.g. major or minor, and write in the note you want to be the root note.
To find names for the other notes, start with the root note and count 1 or 2 semitones to the next note, according to the mode. Write the 2nd note in, count semitones to the 3rd note and so on, all the way to the octave.
Each note of a scale should have its own letter. Work from left to right, using the next letter each time, as you go.
This post is one of a growing series of free basic music theory lessons on my blog, musictheoryde-mystified.com. You can see the complete list here.
Please feel welcome to like, comment or to share this post. If you have any questions, pleased leave them as a comment and I will respond as soon as I can. If you enjoy my posts and would like to be kept up to date, please subscribe.
In kindergarten and early primary school, children are taught scales as having steps and half-steps, or tones and semitones (T and S). This naming conveys that between one scale note and the next is always “one” something (tone or semitone, step or half step), indicating that these notes are consecutive in the scale despite their different size.
This is great for very young minds but doesn’t reflect how intervals are measured and described in general use.
The smallest unit of musical pitch (in Western culture) is 1 semitone. The semitone is a basic unit, like a millimetre. (Smaller units exist but they measure expression such as vibrato or micro-tuning rather than musical notes). Larger intervals are measured in semitones, not tones and semitones. We say an octave is 12 semitones, not 6 tones or 5 tones and 2 semitones.
(Personally I find that calling 2 semitones a tone is confusing, given that a “tone” is also the American name for a note as well as a word for timbre.)
I never refer to “tones” as an interval size in any of my writing. For scales, I write 2 or 1 (semitones) instead of T or S.
Please feel welcome to share this post or make a comment.
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.
