So, the essential building blocks of Western music. Doesn’t exactly sound like the easiest topic to be tackling. But the very strength of this topic lies in its reputation, on what it has founded.
However, at its heart it’s no more difficult than basic mathematics, which the entirety of music in the West, theoretically or otherwise, owes its existence to. For even if you are rallying against this highly mathematical logic, you are still composing or performing in reaction to it, and thus you and your art owe to it a debt of some kind, no?
Today we will be dissecting what can initially appear as cruel and confusing logic, scales and the intervals of which they are comprised, hopefully revealing for you what it really is, and helping you assert yourself against it, enabling you to use it to your advantage.
Whether this be in improvisations or in your own compositions, maths can be fun and can be made your own once you have grappled with these very basic facts about it, enabling you to speak on a level with any musician more theoretically knowledgeable or otherwise focused on what makes Western music tick (aside from the musicians whose hearts it contains of course!)
Intervals: The Building Blocks of Western Harmony
As the title so boldly suggests, an interval is indeed what the harmony of Western music is founded upon, and indeed what the harmony of many other cultures is cemented by too. When we talk about an interval, at its most basic we simply mean the gap between two notes, so a larger interval will be synonymous with a larger gap between any two notes that it is describing.
When two pitches are exactly the same, we think of them in unison: there is no gap between them and thus no interval. If we were to hear these two pitches played on the same instrument, both tuned to the exact same pitch in hertz, then we wouldn’t be able to hear any difference aside from perhaps volume.
This is one of the founding tenets of an orchestra, wherein many instruments are doubled up to embolden their volume for larger performance spaces and audiences, and where often many instruments, violins for example, will be playing the exact same melody strengthened by the volume of instruments into a volume of decibels.
It would be quite a feat to compose or otherwise perform a piece of music without intervals. We might even best think of them as the oxygen of Western music. Where Eastern music and philosophy is more defined by the gaps between the sounds and what they mean for the sounds within the piece of music, Western music tends towards a converse approach, wherein the sounds and individual notes are defined by their relationship to each other as opposed to their inherent quality to stand alone.
The Simple Interval
In Western music, a simple interval is one that operates within the space of an octave. If we define an octave as the amount of space between two of the same pitches repeating in a sequence, it ought to be easy to see why the system of measuring intervals is divided in this way.
Each interval has been bestowed a name, so nominated for its relation to the mathematical logic of Western harmony as a whole. When naming an interval, it is common practice to do so in accordance with the rule of considering the relationship between the higher note and the lower note, and not the other way around.
However, this is not to say that the rule hasn’t been broken, countless times in fact, and is equally as interesting and important for the way in which it reveals the seams with which Western classical harmony is woven.
These simple intervals, from one end of the octave to the other, are designated thus:
|Semitones (from other note)||Designated Title|
The arrangement of the intervals in this fashion is indebted to the major scale, upon which it is heavily mapped. There are alternative names, as mentioned above, though this table will provide a firm basis from which to begin understanding these highly vital interval relations.
There are a number of simple rules which we might do best to lay out here, new and useful terminology being emboldened typographically for your consideration:
- To augment an interval, said interval must be perfect or major in the first place and then must be raised by one semitone (one fret on the guitar).
- Likewise, to diminish an interval it must be perfect to begin with and then lowered by one semitone (one fret on the guitar). If an interval is major, it is diminished if it is lowered by two semitones (two frets on the guitar).
- To render an interval minor¸ it must first be a major interval and then will be lowered by one semitone (one fret on the guitar).
If we want to understand why these things are the way they are, we will have to delve quite a lot deeper into the mathematical schematics of Western culture, so for now it is best to simply take these rules as gospel, unless you are so curious as to be unable to contain it.
The Compound Interval
Conversely, the compound interval can be thought of as any interval that stretches over the bounds of an octave. As an octave will repeat the same notes simply at a higher pitch, we can think of these intervals by exactly the same logic as the simple intervals, simply extended higher, usually to designate more expansive chord extensions.
The compound intervals of one octave, when mapped alongside the simple intervals in the octave below, will align like so:
|Semitones (from other note)||Designated Name||Simple Interval Relation|
|13||Minor 9th||Minor 2nd|
|14||Major 9th||Major 2nd|
|15||Minor 10th||Minor 3rd|
|16||Major 10th||Major 3rd|
|17||Perfect 11th||Perfect 4th|
|19||Perfect 12th||Perfect 5th|
|20||Minor 13th||Minor 6th|
|21||Major 13th||Major 6th|
|22||Minor 14th||Minor 7th|
|23||Major 14th||Major 7th|
If these compound intervals follow the exact same logic as their simple interval counterparts, why do we bother to delineate and separate them in this way? Ironically, despite how complex this can initially seem, this is usually for simplicity’s sake.
In music that is inherently harmonically complex and capitalizes on this by using expansive chord extensions, these delineations are the difference between a smaller chord and a larger chord more fitting for the musical situation. Thus, this extended list of harmonic relations becomes a must if you are seeking to quickly communicate with other musicians on the fly about the harmony in a piece of music.
Engaging regularly with practice like the one linked below will enable you to communicate in this way quickly and instantaneously with other musicians, so rapidly that you won’t even think about it. Thus, I would encourage you to engage with it and train your ears as well as your fingers.
Scales: Traditional to Pentatonic
Now that we’ve covered the essential building blocks of western harmony, we can have a closer look at what these foundational components build, contributing as they do to the overall equilibrium of Western harmony.
The Major Scale
Sometimes referred to as a diatonic scale and just as often as Ionian, this scale can be most simply thought of as the foundational representation of intervallic sequences, up or down. It is an eight note sequence comprised of, from the root note, all the perfect and major semitones.
Taking the example of the C major scale, we can view these interval relations like so, all of which correspond to their relationship with the root C:
- C (perfect unison)
- D (major 2nd)
- E (major 3rd)
- F (perfect 4th)
- G (perfect 5th)
- A (major 6th)
- B (major 7th)
- C (perfect octave)
If we have the root note of a key, we can just as easily construct the major scale using a formula, which in its own way speaks to the relationship between the notes within the scale and their root:
|Interval in Steps from Previous (frets)||Half (one)||Whole (two)||Whole (two)||Half (one)||Whole (two)||Whole (two)||Whole (two)|
The Minor Scale
This scale also has other names by which it is referred, such as the Aeolian mode, as well as being also a diatonic scale. It can more simply be defined by its relationship with its relative major scale, which if we work from the root is always three frets up, where we will find the root of the relative major.
If we think of the minor scale as the sixth permutation of the major scale, we can see that each minor scale starts on the sixth note of its relative major scale. This would be better illustrated with an example, this time in D minor:
- D (perfect unison)
- E (major 2nd)
- F (minor 3rd)
- G (perfect 4th)
- A (perfect 5th)
- Bb (minor 6th)
- C (minor 7th)
- D (perfect octave)
Like its sibling the major scale, we too can think of the minor scale in terms of a formula, especially seeing as these two scales are so related as to have relatives amongst themselves. The relative major of D minor is F major, so if we lay out the F major scale in two octaves and emboldened the D minor hidden within, you will more obviously see their alignment:
F – G – A – Bb – C – D – E – F – G – A – Bb – C – D – E – F
If we were to think of all of this formulaically, the D minor scale would look something like this:
|Interval in Steps from Previous (frets)||Whole (two)||Whole (two)||Half (one)||Whole (two)||Whole (two)||Half (one)||Whole (two)|
In relation to these other scales, a pentatonic, whether major or minor, is simply one that has five scale degrees instead of seven. This makes it perfect for those seeking a more simple and sparse approach to composition and improvising, in which you might add something more of yourself, through expressiveness or otherwise.
The major pentatonic is the exact same as its major scale compatriot, simply having had its 4th and 7ths removed. The same goes for the minor pentatonic, though this time with the removal of its 2nd and minor 6th.
As previously, this would be better illustrated with an example, first in Bb major:
- Bb (perfect unison)
- C (major 2nd)
- D (major 3rd)
- F (perfect 5th)
- G (major 6th)
- Bb (perfect octave)
And then, we can see these tones reflected exactly in the mirror image of its minor pentatonic relative, G minor:
- G (perfect unison)
- Bb (minor 3rd)
- C (perfect 4th)
- D (perfect 5th)
- F (minor 7th)
- G (perfect octave)
For those more inclined to figure these things out formulaically, I will do so in the table below with the same key Bb major, wherein each half is swallowed by its adjoining whole:
|Interval in Steps from Previous (frets)||Whole Half (three)||Whole (two)||Whole (two)||Whole Half (three)||Whole (two)|
And the same can be seen in its mirror image, the relative G minor pentatonic:
|Interval in Steps from Previous (frets)||Whole (two)||Whole Half (three)||Whole (two)||Whole (two)||Whole Half (three)|
So, hopefully with a bit of your own intuition and involvement you are well on your way to grappling with this very vital foundational stepping stone for Western harmony as a whole.
This is by no means an exhaustive list, and I would strongly encourage anyone still interested to explore further scales, some of which can get incredibly experimental, inhabiting the fringes of harmony and pitch, lurking in the gaps between traditional tones.
FAQs Scales Intervals
This will depend on the type of scale. A typical, traditional scale tends to involve seven scale degrees, and thus seven intervals between the tonic and these degrees.
These are seven in number beginning with the tonic and ending in the octave of this same tonic, they read as thus: perfect unison, major 2nd, major 3rd, perfect 4th, perfect 5th, major 6th, major 7th, and perfect octave.
This will largely depend on which order they are played in, but they are almost always referred to with regard to their relation to the adjoining note. Looking at it purely theoretically, we would ascend and descend in order of pitch, though there is also in theory no limit to the combinations we might achieve with these very same notes.
An interval is a way to measure the gap between two notes, higher or lower. A scale, however, is a series of notes in a given key, inherently comprised of these intervallic relations by default of being build from ascending and descending note relations.