In the first part of this series, I analyzed the magic of the major scale, using math and physics. I used the C major scale as an example.
My results were:
· C (fundamental) to C (octave) shows the best resonance
· C to F & C to G show great resonance
· C to E & C to A show good resonance
· C to D & C to B have resonance but much less than the other notes on the major scale.
The previous article has the methodology to reach this conclusion. If this “minor scale” article moves a little too fast for you, I recommend reading the “major scale” article first.
So what is the Minor Scale?
My musical experience is that the two scales create two different moods. When I play a simple major scale or chord on my son’s piano, I get bright, joyful sound. But when I switch a minor scale or chord, I get a somber, serious sound.
The table below shows the notes of C major and C minor scale.
In summary, the major and minor scales have four notes the same. Three notes have been changed by adjusting to the next lowest frequency. And that little change creates the change in mood of the music.
I am also amazed at how the use of the sharps and flats retains the alphabetical order of C-D-E-F-G-A-B-C in both the major and minor scale. And this notation remains the order for all 12 keys! The musicologists of a few centuries ago were amazing thinkers!
Combining C & E♭
The C-D, C-F, and C-G combinations have been already calculated and displayed in my “major scale” article. So I won’t repeat them here. So this article gives my analysis the three different notes, starting with E♭. How does E♭ (311.13 Hz) combine with C (261.63 Hz)?
For this article, I will repeat a bit of the methodology used in the previous article — for the benefits of first-time readers of this series. But these readers may still want to read the first article.
Here is the visual representation of Middle C:
The equation for this graph is y= cosine (r), where r is in radians. 60 radians corresponds to about 0.04 seconds of Middle C’s vibration.
Next is the visual representation for E♭:
This wave has 11 cycles in the 60 radians. E♭ has a little higher frequency than C, so it creates more waves in the same time duration.
The equation for this graph is y= cosine (1.1892 x r), where 1.1892 is the frequency of E♭ divided by the frequency of C (311.12/261.63).
Let’s superimpose C and E♭ into one graph:
The crests of the two curves start at 1. We are looking for when the two crests meet again. We see this at about 31 radians.
The next graph shows the magic a lot better. We add the C and E♭ together:
When the amplitude is 2, the two crests of each frequency meet at same place. Here, it is 31 radians.
Between 0 and 31, there are five crests in the cycle. The next cycle looks like a new cycle will happen at 62 or 63 radians.
Combining C and A♭
Here is the next blend to analyze. This time I will not provide all the interim steps.
The first resonance is 31 radians, which is the same as E♭.
However, there are seven peaks in this cycle, two more than E♭. So I would say the E♭ has better resonance with C than A♭.
In my major scale article, I pointed out there seemed to be some anomalies in the C-E, C-F, and C-A graphs: the cycles did not quite match. I gave some possible reasons, but I’m not sure. I’m seeing a bigger anomaly with these two graphs. Maybe something inherent with the minor notes?
Combining C + B♭
This graph was the most complex of all the note blends analyzed so far.
At about 25 and 31 radians, the crest-to-crest of the two curves almost match, but not quite. Which one is the resonance? If we assume 25, then we should see another cycle at 50 radians. But at 50, this curve is clearly not reaching an amplitude of 2. Likewise, if 31 is the crest-to-crest, we should see another 2 at 62 radians, which does not seem to be happening.
So I’m ruling out 25 and 31 radians as the resonance time for C and B♭. The next crest-to-crest meeting is at 56 radians.
This means there 15 peaks in a cycle.
Because resonant time B♭ is longer with C than E♭ and A♭ and B♭ has more peaks in a cycle, I claim that B♭ is less resonant with C than E♭ and A♭.
Comparing the Minor Scale Notes
Here is my chart for the notes in C minor:
Because I was a rather amateur musician, I didn’t get much experience with music in the minor keys. I suspect the notes with a better resonance are used more in the minor scale. But to get that minor scale feel (sad, somber), one or more of the three “flat” notes must be written into the music. Otherwise, it is a major scale.
Comparing the Differentiating Notes of the Major and Minor Scale
Three of the seven scale notes were replaced to create the minor key. The table below shows how these replacements compare:
Based on these values, I would say that, in terms of resonance with C:
· A has a better resonance than A♭.
· E is slightly better than E♭.
· B and B♭ are of equivalent resonance.
It seems that, collectively, the major notes are a little better at resonating than the minor notes. Yet, all these minor notes are still showing resonance with C.
I noticed the major notes had an even number in “peaks per cycle” and the minor notes had an odd number. Trying to explain this even/odd phenomenon would be above my pay grade in music theory.
The Amazing Slight Difference between Major and Minor
I’m going to bring back my guitar and change from the Key of C to the Key of A.
When I strum the A major chord, my strum puts all these notes together: E-A-E-A-C#-E. I get my happy sound.
To get to the A minor chord, I need only make one little change. Now here is my strum: E-A-E-A-C-E. And now I get the sad sound.
Just think about this. Five strings are playing the same notes in the major and minor chords. One string in the minor chord has a frequency that is only 5% lower than what it plays for the major chord.
One small change in one string makes a such big difference in mood!
What’s Next?
Please don’t assume that I invented any of this science. Whatever you have read in my two articles is at least 300 years old. I had a little fun figuring this out for myself. I hope you learned a few things about basic music theory.
My reason for being on Medium is to promote my alternative democracy. So I am dovetailing the minor scale into this new way.
The two scales will be great models in building this new democracy. If we need inspiration and optimism, we will use resonance similar to the major scale. If there is a setback which requires some fixing, we will use resonance similar to the minor scale. We can communicate good and bad news with resonance. How the message is presented is so important.
The next article of this series will talk about how our current political process presents itself.
Hint: There is not much resonance.
Published on Medium 2023
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