Natural Laws of Music and Tuning

Many questions come my way concerning tuning. This includes the big question, "are certain frequencies good/bad for us?" As I began to ponder these questions, a few realities came my way about how music works. Here are a few key points:

Although I've addressed questions of this nature before, I'm looking at the concept from a different angle in this article. That angle is... natural laws of music have a system of consonance AND dissonance built into them. NO system of tuning is perfectly in tune. Why not? Because the natural laws of harmonics show that some sympathetic pitches above the fundamental frequency are out of tune. Let me explain further...

Figure 1 shows the harmonic series based on the fundamental frequency of C. It's the lowest C on the piano. We hear the notes above the fundamental as "sympathetic vibrations" that "color" the fundamental frequency. Each instrument, voice, power tool, animal, etc. has its own "voice print" with varying strengths/weaknesses of the pitches above the fundamental. 

Notice that above Figure 1, there are plus and minus signs next to certain pitches? That means those notes are naturally out of tune. Sympathetic vibrations stay the same despite temperament. What changes? The number of cents listed in Figure 1 for the out-of-tune notes will vary in any given temperament. We adjust for temperament. Natural laws stay constant. 

In my video (below) on the ancient solfeggio frequencies. I provide several pictures showing a variety of temperaments used during the Renaissance into the Baroque period when the keyboards were first invented. Each performer had a specific method of tuning based on which intervals/chords they wanted to sound more dissonant than others. Think about it... Bach wrote tension into his music through the use of slight out-of-tuneness in certain sections of the music! This creates a tension-release effect that brings balance to music. In one of my earliest blog posts, I include a video where Bradley Lehman figured out how to tune the harpsichord (for his doctoral dissertation) according to Bach's preference of "modified meantone" tuning. CLICK HERE to watch Lehman demonstrate how temperaments affect different key signatures. In THIS VIDEO, Lehmen specifically goes over how he figured out Bach's tuning preferences for the Well-Tempered Clavier. 

By the Baroque era, musicians wanted "variety of color" in the music. They did this through some notes being more in tune than others. When an interval is slightly out of tune, it "colors" the sound with a minimal amount of dissonance (like a binaural beat). This actually adds a certain fullness to the music through the tension/release process. 

Below are two videos with great demonstrations about the musical harmonic series and how we've used it since music began. Assaff Weisman held a TED Talk in New York (video on the right), opening his presentation with the video on the left where Bobby McFerrin engages the audience in naturally sing within the musical harmonic series.

How Do Harmonic Laws Affect Our Music?

There's been a campaign for quite some time within certain circles that puts fear into people concerning the A=440 concert pitch, equal temperament, and that we've strayed from how the ancients tuned. If this was true, then Bobby McFerrin would not have been able to get the crowd at the World Science Festival to naturally sing the pentatonic scale. 

In this musical "mis-campaign," we're told that we're tuning incorrectly and that our music is out of tune when it didn't used to be. They say Hitler retuned our music to the A=440 concert pitch to cause harm. We're also told that the ancient solfeggio frequencies (first discovered by Joseph Puleo in the 1970's) are the original musical scale invented by Guido of Arezzo sometime around 1,000 AD. I won't go into the ancient solfeggio frequencies here because I address that in several other blog posts, along with the Healing Solfeggio Frequencies video below. In my informational video, I show you how Puleo's frequencies can't possibly fit within the natural laws of music. That being said, if you INTEND them to be healing for you, please use them. Just know the historical facts behind them are inaccurate. All I'm saying here is the numbers 369, 417, 528, etc. are frequencies but they may be more important in another discipline other than music.  

Now.. back to the harmonic laws of music. Harmonic laws affect our music in a big way. Out of tune notes are BUILT into the harmonic series. Therefore, some notes are expected to be out of tune. This brings balance to music because it's impossible to always have everything in tune. In the Natural Laws of Music and Tuning video below, I demonstrate how ALL temperaments are out of tune.

NEWSFLASH!!! The natural scale of Just Temperament is out of tune, too. Some intervals are perfectly in tune (pure) while others are too wide or too narrow. In equal temperament, the octave is the only interval that's perfectly in tune. In Just temperament, the Pefect Octave, Perfect 4th, and Perfect 5th are in tune (pure). All other intervals have varying distances between notes. In equal temperament, the distance between every note is exactly the same. Some are closer to being in tune in equal temperament than they are in Just temperament and vice versa. To understand what this sounds like, CLICK HERE to watch a great video on the problems with temperament and tuning. The presentation was created by Created by Elam Rotem and Johannes Keller. They pretty much demonstrate what I've presented in this article. 

The point here is that NO temperment or tuning is perfectly in tune. Therefore, there wasn't one tuning system that worked better than another. Our first introduction to tuning problems came with the invention of keyboard instruments and fretted lutes. From that point onward, music became more complicated (just like cell phone upgrades) and required different tuning practices in order for music to sound pleasing to the ear. I go into greater detail about that in the Healing Solfeggio Frequencies video below. 

Natural Laws and Solfeggio Frequency Informational Videos

You'll notice in my videos above, I show lots of pictures through PowerPoint presentations. Feel free to screenshot any of those slides for your own use. However, if you share them with others, please say where they came from. All the pictures that aren't mine have the copyright information on them. 

NOTE: In both of the videos, I state that equal temperament wasn't invented until the 1800's. That's partially true only because up until that time, tuning was done by ear. A musician with a good ear could have tuned a keyboard or fretted instrument quite close (but not exactly) to equal temperament prior to the industrial revolution. 

Conclusion

As a professional classical musician my entire adult life, I've always known that tuning is a problem. It doesn't matter what ensemble I play with, there are tuning problems. Although I knew it, something didn't register until people started asking more in-depth questions. Out-of-tuneness is part of the natural laws of harmonics. I don't understand why that is because it has to do with physics and that's not my area of expertise. We'll leave that to the physicists reading this to give me a crash course on musical physics.

Music is inherently in-tune as well as inherently out-of-tune. Like other laws within nature, a balancing act holds these laws together. A pendulum sways from left to right but always passes through the middle. Can you image if the pendulum stayed on either the right side or left but never swung back the other direction? There would be no balance. Musical laws require a balance within the tuning systems that we've used over time. Yes, Pythagorean and just temperaments fit closely with natural tuning because they follow harmonic laws. However, most early temperaments work when playing in keys up through two sharps or flats. Bach didn't want to be stuck to only playing in four or five keys so he created a system that worked for his music. Other composers did the same. Let's look at a modern comparison...

Now, imagine how musicians got tired of the hassles of retuning keyboard instruments in the middle of a concert when they wanted to perform in keys with lots of sharps and flats? Equal temperament (not the WELL temperament Bach used) was a welcome relief from tuning nightmares for musicians just like you can now send text messages with a full keyboard on your phone instead of using a number pad for letters.

When it comes to healing music, don't be concerned about any of the details of what concert pitch is used, what specific frequencies are in the music, etc.. Choose music that feels good to you. If you're concerned about the musical intent, listen carefully to the lyrics. For instrumental music, listen with your intuition. INTENT is a major factor in what healing music will work for you. 

With that, if you've not yet had a chance to purchase any of my healing music, be sure to listen to SAMPLES HERE. Or, purchase through iTunes (now Apple Music?).

Del Hungerford, October 2023