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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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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?
These three terms are often confused. They refer to the same subject but in different ways.
Scale
A scale is a series of (usually 7) consecutive note pitches finishing an octave above the first note.
The series can be extended over several octaves and is either played in ascending or descending order.
The first (and last) note of a scale is called the root note or tonic.
Mode
A mode is the pattern of intervals between the notes of a scale.
The pattern is based on the first note of the scale, the root note.
Western modes are made up of an irregular combination of (usually 1 and 2 semitone) intervals. This gives each mode a unique character called its tonality.
Key
A key is the use of the notes and tonality of a scale in a piece.
A piece is “in a key” when it uses the notes of a scale in such a way that the tonality of its mode is apparent overall when listening/playing.
Tonality
Tonality is the unique character of a mode, common to all keys in that mode.
The tonality of a mode is simply indicated by the mode’s name.
We should learn to recognise the tonality of the more common modes, both in a scale of that mode and in music written/played in that mode.
Names Of Scales And Keys
Scales and keys have the same names. They are named as the name of the root note followed by the name of the mode. For example:
the major scale on C is called C major.
Music using the notes of C major is in the key of C major.
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 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.
