Composing With Musical Intervals
Intervals are the basis of harmony and harmony is important to us as musicians, composers, and music producers. This article will discuss what intervals are and tips on how to use them in compositions.
A Single Note Holds A Lot Of Information
- We can determine the pitch in both Hertz and in letter name. Is the note an A, or maybe an F#? Does it have a fundamental frequency of 220 Hz, or maybe 370 Hz?
- Which instrument is playing the note? This is defined by its harmonic content. Is the note played on a guitar or piano, is it a sine wave or a sawtooth wave?
- How much emphasis is there on the note? Is the viola playing staccato, pizzicato, legato? Is there an envelope filter on that synth or bass?
More Notes, More Information
But there's not really music in a single note. One way of creating music is to give that note a rhythm. We could create a one-note song with an interesting rhythmic structure. Hmm, I may try that out actually. Or better yet, we could add other notes and start creating melody and harmony!
I like to think of a single note as zero-dimensional. A single point. It has nowhere to go and nothing to relate to. Adding another note to create an interval, or multiple other notes to create a chord brings us to the first dimension. The notes have specific distances (intervals) from one another in both notation and frequency values.
Creating chord progressions or melody lines brings us to the second dimension, where the notes can change as well as the intervals and chords in time.
This is best shown in the piano roll of a digital audio workstation. The Y-axis contains the first dimension mentioned above, whereas the Y+X axes represent the second dimension.
In this example, we have a minor second interval (C relative to B) in the first half, and a major seventh (B relative to C) in the second half. These intervals are considered to be inversions of one another. More on that later!
Let's Define The Intervals
An interval is the distance between two notes. One note (typically the higher note) is referenced against the other (typically the lower note) by the distance between the two. The names of these intervals show up in the names of chords and when spelling out the scale degrees of musical scales.
Here they are with the lower note acting as “1” and the interval as a number above 1. There are 12 notes in the chromatic scale, so there are 12 different intervals we can make within an octave. However, since the major scale has only 7 notes, there are only 7 numbers and thus 5 alterations to those numbers (# or♭):
A Note On Enharmonic Equivalents
The interval degrees (the numbers 1-7) listed above are common names for the intervals, but they are not the only names for those intervals. For example, the tritone interval can be referred to as an augmented fourth or a diminished fifth. It can even be called double-sharp third or triple-flat sixth in extreme scenarios. This all depends on the scale, and the number of notes the interval in question comes after the 1.
Let's revisit the table above based on the note C:
Now let's look at “flipping” these intervals to see what happens. This idea of flipping intervals was first put into words for me by the great Victor Wooten in his book The Music Lesson. There's a passage in which he encourages us to play two notes: one note with a second note one halftone above. This creates a minor second interval and is very dissonant. In this example, the notes are B and the C immediately above it.
Then he urges us to raise the first note an octave. Now that the first note is higher, we will use the original second note (now lower) to describe an interval of a major seventh. It's not nearly as dissonant now! In this example, the notes are C and the B nearly an octave above.
So what's the deal? Why do the two sets of intervals sound so different? They are the same two notes after all.
Yes, the notes are the same, but the distance between them is different. If we take the lowest note in each example, we have B – C (a minor second interval) in the first example and C – B (a major seventh) in the second example. A major seventh interval is less dissonant than a minor second interval. But why is that?
The Ratio Between Fundamental Frequencies
It has to do mainly with the ratio of fundamental frequencies. Much like we can identify instruments by the frequencies and amplitudes of their upper harmonics, we can tell which note is being played by its fundamental frequency (the first harmonic).
What Is A Fundamental Frequency?
Here is a sine wave playing E with a fundamental frequency of ~82 Hz. The sine wave is special in that it has no additional harmonics above the fundamental. So all we get in a perfect sine wave is the fundamental frequency.
Here's a sawtooth wave playing E 82 Hz (the fundamental frequency 82 Hz, the same as the sine wave above). Every harmonic is created from this waveform, meaning that every multiple of 82 is represented. And These harmonics decrease by 6 dB/octave.
And here's a guitar playing E with a fundamental frequency of 82 Hz. Notice that the second harmonic is much louder than the first harmonic. This is characteristic of a guitar sound. This guitar track was already recorded from an amplifier through a microphone, so those two pieces of equipment will ‘colour' the sound and slightly change the frequency response.
Upper Harmonics Aside
It's the first harmonic or fundamental frequency we are most concerned about when thinking about how the intervals sound, especially when the interval notes are played by the same instrument.
There is a ratio between the frequencies of the two notes that make up an interval.
Here are the ideal ratios of the intervals found in Western music theory (note that these are “ideal” and only very close approximations to what the actual ratios are):
A simpler ratio means the interval is more consonant (less dissonant), and a more complex ratio creates an interval that is more dissonant (less consonant). All the intervals have their spot in music and I encourage you to discover which ones you like using in your music.
So a ratio of 1:1 is as consonant as we can get, followed by 2:1 and all the other octaves. The next is the interval of a perfect fifth, with a ratio of 3:2; then a fourth (4:3); followed by a major third (5:4) and so on.
The most dissonant intervals are the tritone (25:18), minor second (16:15), and major seventh (15:8).
An instrument's range is largely defined by the fundamental frequencies it can produce.
To learn more about how fundamental frequencies relate to note values, check out my article Fundamental Frequencies Of Musical Notes In A=432 & A=440 Hz.
The Intervals
Intervals can be used for many reasons in music, and I'll share some common uses of intervals in my writing:
Perfect Unison
I'll use perfect unison when I'm layering melody lines. Oftentimes I'll layer a guitar line with a piano or synthesizer to help give the melody more texture.
Minor Second
I use the minor second to portray a dissonant, spooky, unnerving aesthetic. I really like the minor second for adding a lot of tension in my music. The minor second is the inversion of a major seventh.
Major Second
I use the major second a lot an octave up (It could be referred to as a major ninth). In fact, the intervals played on guitar in the song ‘Did Jerry Do That?!' are all major second (ninth) intervals.
I find the major second interval really wants to resolve but it doesn't sound awfully dissonant. The major second is the inversion of the minor seventh.
Minor Third
Minor third intervals are used a lot in music when building chords. It's the first interval of a minor chord. It's common to think of the minor third as being sad, but I personally only hear the sadness when we build the minor triad (adding the fifth on top of this interval).
The minor third doesn't feel a strong urge to resolve anywhere. The minor third is the inversion of the major sixth.
Major Third
The first interval of major chords, the major third, typically sounds happy. Once again, this is especially so in a major triad (with the fifth added). The major third is the inversion of the minor sixth.
Perfect Fourth
I love the ambiguity of the perfect fourth. It has a nice ratio (4:3) so it's fairly consonant. There's not a lot of tension but it doesn't feel resolved either, giving a unique sound of floating in no man's land. The perfect fourth is the inversion of the perfect fifth.
Tritone
The tritone is possibly my favourite interval. The diminished fifth can sound evil and gnarly, and the augmented fourth can sound really bright. I particularly like the tritone interval in the context of Lydian (augmented fourth). The tritone is the inversion of itself.
Perfect Fifth
The interval with the most stability with a ratio of 3:2. The fifth is in the major and minor triads. I like using the fifth and root in the lower register of the piano and proceeding to play modal notes in the upper register (given that the mode in question has a perfect fifth). The perfect fifth is the inversion of the perfect fourth.
Minor Sixth
I usually think of a minor sixth as a major third inverted. It does sound different though. It's unstable and sounds to me like it wants to resolve back to the fifth. The minor sixth is the inversion of the major third.
Major Sixth
I usually think of the major sixth as a minor third inverted, except that it's kind of unstable in that voicing. The major sixth is the inversion of the minor third.
Minor Seventh
The minor seventh interval sounds to me like a dominant chord without the third and the fifth. It sounds tense and it wants to resolve to its tonic chord. Of course, many chords feature a minor seventh, but the interval always seems to outline a dominant chord to my ears. The minor seventh is the inversion of the major second.
Major Seventh
The major seventh is a dissonant interval with a ratio of 15:8. I don't usually use this interval by itself, although it sounds lovely as part of the major seventh chord. The major seventh is the inversion of the minor second.
I Can Only Offer You My Experience
The above points are how I like to think of the intervals. Again, I encourage you to make up your own opinions on the intervals.
Perhaps a minor second is too dissonant for your musical palette and you'd prefer to stick to more consonant intervals in your composing.
Maybe consonant intervals are a bit boring for your taste and you want to explore dissonance in your writing.
Training your ear to know these intervals is a great way to start using them effectively and on purpose in compositional work! I certainly never thought I'd use as many minor seconds as I do in my professional compositions and scoring!
Here are some ideas to think about when composing with musical intervals:
- When harmonizing a note or melody with certain intervals, consider how they sound inverted.
- How can you use dissonance in your music? The minor second, trione, and major seventh can be used to great effect!
- What scale or mode are you writing in and which intervals can you exploit to really solidify your position in that scale/mode? The augmented fourth/tritone in Lydian, for example.
- Use more consonance in the low end (where the difference in frequency is smaller between intervals) and save the more dissonant intervals for the high end (where the difference in frequency is greater between intervals).
- Stack multiple perfect fourth intervals to create quartal chords to really give a sense of ambiguity.
- Use perfect fourths to give a sense of ambiguity or as an inversion for the perfect fifth.
- Stack multiple minor thirds to create diminished triads and full-diminished seventh chords.
- Stack multiple major thirds to create augmented chords.
Conclusion
All harmony includes intervals of some kind. Chords are often the basis of harmony, but stepping away from full chords and into intervals can be a creative challenge for musicians. I'd invite you to practice hearing the different intervals and using them in your own music.
Toned Ear is a great resource for training your ears to hear different intervals. Try their quiz or check out their app!
Do you have a favourite interval or a great use for one that I haven't mentioned?
As always, thanks for reading and for your support.
