Tag: frequency domain

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Frequency Domain Analysis pt. III I-V-vi-IV progression

Since I’ve already covered frequency content of scales and chords in the previous two posts, I’d like to move on to common chord progressions, and what better chord progression than the I-V-vi-IV progression that is literally everywhere (The Axis of Awesome even made a song about how common this progression is, titled the four chord song). What’s even more, there’s an entire wikipedia article for popular songs containing this progression. From the list, basically every song ever uses this progression.

This progression involves the I (tonic), V (dominant), vi (submediant), and IV (subdominant) scale degrees; in the key of C major this corresponds to C – G – Am – F.

Now, it probably makes things a little prettier to visualize it in terms of a logarithmic vertical axis, since musical pitch is exponential.

When we look at pitch with a logarithmic vertical axis it just looks exactly the same as things would if all we did was plot the number of intervals in a linear fashion. Finally, it may be beneficial to look at the progression in terms of pitch names.

There you have it, the most common chord progression in western music!

Get The Code

If you’re interested in checking out any of the super hacky code I’ve written for this, check out my github repo.

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Frequency Domain Pitches Pt. II

In part one I discussed frequency content of the standard chromatic and C Major diatonic scales. I’d like to move forward by discussing the frequency content of the C class of chords on piano.

Chords With Root Note C

If we take a look at the various C Chords in terms of frequency content, and format our plots such that each tick on the vertical axis coincides with the frequency content in semitone intervals, we obtain the following plot:

I’ll probably come back and re-organize this plot as the ordering of chords is a bit crazy since the python script I wrote just iterated through keys in a dictionary… but that’s a whole other story; for now it’s good enough.

From the above plot we can see that we are using A440 concert pitch, as A4 appears as 440 hz, and A5 appears as 880 hz, which is one octave higher.

Let’s take this same plot and change the vertical scale from frequency to number of semitone intervals.

From this plot it’s very easy to see that all of the C chords consist of a root note (in this case middle C), most have a major third as a second note, which is 4 semitones above the root, all the minor notes have a minor third as a second note, which is 3 semitones above the root, and nearly all have a perfect fifth as the third root, which is 7 semitones above the root. All of the numbered chords 7, 9, 11, and 13 have a minor seventh as the fourth note, which is 10 semitones above the root. All chords numbered 9, 11, and 13 have a major ninth as the fifth note, which is 14 semitones above the root, or a perfect octave plus a major second. All chords numbered 11 and 13 have an eleventh as the 6th note, or a perfect octave plus a perfect fourth, which is 17 semitones above the root, and finally both 13 chord have a thirteenth as the 7th note, or a perfect octave plus a major sixth, which is 21 semitones above the root.

Now, there’s one last easy thing we can do, and that’s to show the same plots in terms of the note contents of the chords, again, assuming we are in the fourth octave.