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.
