Intervals and Scale Degrees
Today I’m taking a break from the modes series and writing a post on intervals and scale degrees. Although intervals are kind of ‘boring’ as far as theory goes (not ‘cool’ like modes or fancy jazz harmony) they do form the basis of everything in Western music. They are some of the fundamental stepping stones to a deeper understanding and appreciation of the music we play and love (I’ll get back to fun modes stuff next week ).
What are Intervals?
An interval is simply the distance between two notes. For instance what is the distance between C and F? Or G and A#? Well that’s what we’re going to find out (and more). Intervals can be melodic if the two notes are played successively, or they can be harmonic if the notes are played together.
Tones and Semitones
The most basic intervals in music are tones and semitones (whole-steps and half-steps for those in the U.S.). A semitone is a distance of one fret or one key on a piano.
A tone is twice the interval of a semitone, and is a distance of two frets on the guitar and two keys on the piano.
So to answer the questions at the start of the page, what is the distance between C and F?
As you can see, C and F are five keys apart, telling us that they are five semitones apart (don’t count the C but count every other key from C to F including the black keys).
What about G and A#? Well they are three keys apart which means they are three semitones apart.
All of the more complex intervals, such as a minor third or an augmented fourth, are simply combinations of multiple tones and semitones.
Intervals are designated a quality and a number. For example, a “major 6th” is an interval of a 6th and its quality is major. First we are going to have a look at the number component of interval names, before looking at the quality component.
The number of an interval comes from the number of letters (note names) that separate two notes. For example, C and D are two letter notes apart and is therefore an interval of a second. F and A would be an interval of a third since they are three notes apart. C and A are six letters apart and is therefore an interval of a sixth.
As we’ve learned in reading the notes part 1 a D# and an Eb are the same pitch. However it’s important to realise that, although a C to a D# is the interval of a second, a C to Eb is an interval of a third. What is important here is how many letter names apart the notes are.
C and D, C and Db, and C and D#, are all intervals of a second, as they are all two letters apart. Interval quality is what sets them apart from each other. For instance C to D is called a perfect second, C to Db is a minor second and C to D# is an augmented second. A major second requires a distance of two semitones, a minor second requires a distance of one semitone, and a augmented second requires a distance of three semitones.
This table below lays out all common intervals with their name and distance in semitones. I don’t expect you to go through this table and try to memorise it by rote. Instead I suggest that you print it off for later (or better yet, save paper by just bookmarking the page in your browser). That way you’ve got the table for reference when you need it.
Also the table might seem hard to digest right away so here are a few pointers to make it easier.
- Augmented intervals are one semitone larger than a perfect or major interval Diminished intervals are one semitone smaller than a perfect or minor interval
- Major intervals are one semitone larger than minor intervals
- Minor intervals are one semitone smaller than major intervals
- Fourths, fifths, unisons and octaves are never major or minor – but they can be perfect
- Seconds, thirds, sixth and sevenths are never perfect – but they can be minor and major
Also, it’s worth noting is that any interval can be augmented or diminished.
|Interval Name||Common Abbreviation(s)||Number of Semitones||Example|
|Interval Quality||Interval Number|
|Perfect||Unison||P1||0||C to C|
|Minor||Second||m2, b2||1||C to Db|
|Major||Second||2, M2, ♮2||2||C to D|
|Augmented||Second||#2, +2||3||C to D#|
|Minor||Third||m3, b3||3||C to Eb|
|Major||Third||3, M3, ♮3||4||C to E|
|Perfect||Fourth||4, P4, ♮4||5||C to F|
|Augmented||Fourth||#4, +4||6||C to F#|
|Diminished||Fifth||b5||6||C to Gb|
|Perfect||Fifth||5, P5, ♮5||7||C to G|
|Augmented||Fifth||#5, +5||8||C to G#|
|Minor||Sixth||m6, b6||8||C to Ab|
|Major||Sixth||6, M6, ♮6||9||C to A|
|Diminished||Seventh||bb7||9||C to Bbb|
|Minor||Seventh||m7, b7||10||C to Bb|
|Major||Seventh||7, M7, ♮7||11||C to B|
|Perfect||Octave||8, P8, 8ve||12||C to C|
(Astute readers will notice that I missed a few intervals from the table – such as ‘augmented sixths’, ‘diminished octaves’ etc. Although these intervals exist in theory, in reality they are hardly ever needed, so I thought it best to limit the table to the more common intervals. Besides, if you do get to such an advanced level of theory that you do find yourself using augmented sixths then you should already have enough musical knowledge to figure it out by yourself )
Complementary intervals have the same letter names but occur in the opposite direction. For instance C to E is a third (three letter names), however, E to C is a sixth (six letter names). Complementary intervals have some interesting characteristics, such as:
- The complement to a minor interval is major – i.e. minor becomes major
- The complement to a major interval is minor – i.e. major becomes minor
- The complement to a perfect interval is perfect – i.e. perfect remains perfect
- The complement to a diminished interval is augmented – i.e. diminished becomes augmented
- The complement to an augmented interval is diminished – i.e. augmented becomes diminished
- Adding the numerical value of two complementary intervals always adds up to nine
- C to E is a major third. The complementary interval is E to C which is a minor sixth (major has changed to minor, and three plus six equals nine)
- C to A is a major sixth. Its complement, A to C, is a minor third (minor becomes major, and 6+3=9)
- C to G is a perfect fifth. Its complement, G to C, is a perfect fourth (perfect interval remains perfect, 5+4=9)
- C to G# is an augmented fifth. Its complement, G# to C, is a diminished fourth (augmented becomes diminished, 5+4=9)
- C to C can be an octave, or a unison. Octaves and unisons are both perfect intervals (perfect remains perfect) and their numerical values add up to nine (8+1=9)
We can also use the interval nomenclature (major third, augmented fourth etc) and their abbreviations to label the degrees of scales. Note how the root is usually marked with an R, as opposed to P1 which we use for intervals.
For instance, here is a C major scale with the notes labelled according to their degree.
Similarly, say we flatten the seventh and third degrees. We can use the lowercase m’s or b’s to represent the minor seventh and minor third.
|Notes||C||D||Eb||F||G||A||Bb||C||Scale Degree||R||2||b3 or m3||4||5||6||b7 or m7||8|
Being able to label scale degrees this way means that, we can easily refer to particular notes in a scale of chord. For instance: “I’ll play the root and the fifth, you play the third and the sixth on top of that”, or “Gimme an F major chord but put a #4 and a ninth on top or colour”.
Beyond the Octave
So far we’ve only looked at intervals and scale degrees within the confines of an octave, however occasionally (and especially when studying chord theory) its necessary to be familiar with intervals greater than an octave. Of course, by going beyond the octave we end up creating extra labels for notes which already have a label. For instance a 9th and a 2nd are the same note (but an octave apart), as are the 10th and the 3rd, the 11th and the 4th, the 5th and the 12th, and the 6th and the 13th.
Of all of these possible ‘extra’ intervals/scale degrees only a few are particularly common – such as the 9th, 11th and 13th – so it’s probably worth becoming familiar with those first, rather than trying to learn everything at once. Also, the qualities of augmented, diminished, major, minor and perfect, apply to these upper octave scale degrees, exactly the same as they were applied to the lower octaves.