The Perfection of the Perfect Fifth

The question of the perfect fifth has been simmering in my mind for some time now. It started when we started investigating chord substitutions on Song Talk Radio in 2016. For that show, I looked at the Circle of Fifths as a great tool for making chord choices when writing a song. The Circle of Fifths describes tonal and chord centre relationships within the 12-note equal temperment scale we use in Western music. The most common cadence in songwriting or composing is a V – I (e.g. G-major to C-major in the key of C-major).

People, especially musicians, say that music is a universal language. This part of the question came to me when my older brother decided to learn how to play guitar, never having studied music in the past. He asked me if the scales we use and notes we use are based in anything scientifically true. So, think back to your math and science classes, we’re about to nerd out…

It’s all about the ratios

Let’s start with the most basic of tonal relationships: the octave. The octave to any note, as we know, is the same note name, either higher or lower. We can represent a note visually by a single frequency (nerd alert: this is a basic representation of a fundamental frequency, ignoring the harmonics that make up most sounds):

And its octave above is a note that is twice the frequency (purple line):

Notice how the black line (base octave) completes one cycle for every two cycles of the purple line (octave above) – a ratio of 1:2. The cycles intersect frequently and in a clear, simple pattern. This is why two notes, an octave apart, sound the most harmonious and pleasing. Regardless of the specific tuning standard (the vast majority of us use the A4=440 Hz standard), or what your base note is, this relative relationship holds true.

Now let’s introduce the next simple ratio – the 2:3 ratio. Incidentally, 1:2 and 2:3 are within the first few ratios of the Fibonacci Sequence, which commonly shows up in physical natural patterns. The green line represents a note one fifth above (V note) the black line’s note (I note). For example, if the black line is a C, the green line is the G above.

Again, notice how for every 2 cycles of the I note, there are 3 cycles of the V note – a 2:3 ratio. The lines intersect, but in a slightly more complex way than the 2:1 octave ratio. This introduces a sense of musical harmony as we know it. The perfect fourth, which you get if you go counter-clockwise on the circle of fifths, is perhaps equally “perfect” with a 3:4 frequency ratio.

In Western music, the rest of the major scale is created by going up a fifth five times, and down a fifth one time. Starting on C, we follow with G, D, A, E, and B. Going a fifth down, we get F. Rearrange them all in order and we get C, D, E, F, G, A, B – the heptatonic major scale.

In western music, look at the two most commonly used scales: the major and minor scales. The fourth and fifth are among the common notes between them.

Degree I II III IV V VI VII
Major scale 1 2 3 4 5 6 7
Minor Scale 1 2 b3 4 5 b6 b7

The Fifth will hold us together

When you start exploring the frequency ratios for major and minor thirds, sixths, and seconds, the ratios become more complex, and the consonance of octaves and perfect fourths and fifth shifts gradually to dissonance. Composer Howard Goodall, in his excellent podcast, BBC Radio 3’s Story of Music in Fifty Pieces, describes the shift in Western music from writing exclusively with perfect fourths, perfect fifths, and octaves into using thirds and triads in 15th century Europe.  Goodall talks about this development as  a fundamental pivot point that forever defined all of western music to follow.

While scales differ between styles of music (e.g. blues scale) or cultures, the perfect fifth remains predominantly consistent. For example, the drone used in East Indian instruments (e.g. tambura) is often expressed as a fundamental note and its perfect fifth played together. Add the octave and you’ve got a power chord.

Many other scales used the world over often use flattened or sharpened seconds, thirds, fourths, sixths and sevenths, but usually maintain the same perfect fifth.

Degree I II III IV V VI VII
Dorian mode 1 2 b3 4 5 6 b7
Gypsy scale 1 2 b3 #4 5 b6 b7
Hirajoshi scale 1 3 #4 5 7
Ukrainian Dorian scale 1 2 b3 #4 5 6 b7

A songwriting challenge

In songwriting, like any art form, expression comes from tension and release and the contrast between them. When looking at harmony, this contrast is referred to as consonance and dissonance. The perfect fourths and fifths are very consanant, thirds only slightly more dissonant, and seconds and sevenths even more so. Then there’s chromatic alterations and the relationships between chords. It’s up to us as songwriters to balance tension and release, and harmony is a fundamental component of a song.

In the future, I’d like to try writing a song in a major key that never uses a major V or major IV chord. I imagine this would sound fairly tense and result in a chord progression that is very unresolved. As mentioned above, the V-I cadence is likely the most heard figure in western music, and always emotes a resolved feeling of finality. To avoid its use would certainly impart a feeling of tension and lack of resolution.


Thanks to my composer / songwriter friend Frank Horvat for his review of this article.

2 comments

  1. bro says:

    Wow I inspired this? That’s awesome. I only understood up to “In Western music, the rest of the major scale is created by going up a fifth six times, and down a fifth one time.” Everything up to that point was logical and progressing on pyhsics of sound and now suddenly we decide to go up six times and down one? Seems arbitrary – why six up and one down? It remains a mystery to me…

    On a more positive note I’m up to 98% mastery on Seven Nation Army. A few more bars and I should have the whole song down. And only 2.5 years to achieve that! : )

  2. Neel Modi
    Neel Modi says:

    Yes, it does seem arbitrary to make the major scale that way, and in part it is, to decide upon 7 notes, but that doesn’t change the fact that all the notes are based on a progression of perfect fifths. So while arbitrary, it also does seem a natural and logical decision to make. This is where the article shifts from science to culture, as both things play in part in the historical development of music.

    And awesome you’ve made excellent progress on Seven Nation Army! Keep it up!

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