The universe may seem infinitely complicated, but everything in it actually seems to follows some very simple patterns.

These patterns are easier to understand when using sound or vibration as a medium, so on this page I have compiled a series of videos, audio and images to reveal as much of this possible.

These patterns are easier to understand when using sound or vibration as a medium, so on this page I have compiled a series of videos, audio and images to reveal as much of this possible.

## Nature by numbers

The number series shown in the beginning of the above video (1-1-2-3-5-8-13 etc) is known as the "Fibonacci Series",

in this series you will find that "golden ratio" which makes the spiral in the sunflowers seeds etc.

in this series you will find that "golden ratio" which makes the spiral in the sunflowers seeds etc.

The Fibonacci Fractal Meditation below is built on the numbers 1-2-3-5-8. These numbers are too low to be used as Hz based musical tones so in this track they have all been raised by 6 octaves, multiplying each one by 2 six times to get these 5 frequencies:

64-128-192-320-512. (Hz) This is still a Fibonacci series because you can still add the last two numbers together to get the next one, only now they are within hearing range and can be played as audio tones. It is really odd how they make such a perfect musical chord...

64-128-192-320-512. (Hz) This is still a Fibonacci series because you can still add the last two numbers together to get the next one, only now they are within hearing range and can be played as audio tones. It is really odd how they make such a perfect musical chord...

The Fibonacci Series is very closely connected with another series called the "Harmonic Series" which is the basic building block of all musical sounds. If you compare the 2 sets of numbers you will see that the harmonic series really contains the entire Fibonacci series, and that all of the Fibonacci numbers are also pure harmonic overtones of the starting number in their series. The harmonic series = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16... while the Fibonacci makes a perfect overlay:

So now you can see that the Fibonacci series (natural forms) and the harmonic series (sound vibration) are very closely connected and appear to follow the same "grid".

Remember that both of these series can be started with any number, measurement or frequency. For example the harmonic series could be written as: 10-20-30-40-50-60-70-80-90-100-110-120-130 etc and the Fibonacci series as: 10-10-20-30-50-80-130 etc.

**1**,**2**,**3**, 4,**5**, 6, 7,**8**, 9, 10, 11, 12,**13**, 14, 15, 16...

So now you can see that the Fibonacci series (natural forms) and the harmonic series (sound vibration) are very closely connected and appear to follow the same "grid".

Remember that both of these series can be started with any number, measurement or frequency. For example the harmonic series could be written as: 10-20-30-40-50-60-70-80-90-100-110-120-130 etc and the Fibonacci series as: 10-10-20-30-50-80-130 etc.

## harmonic series

The best way to understand harmonics is to hear them for your self:

On a piano the octave is exactly the same as the octave in the harmonic series, the fifth is also very close. Some of the other intervals are not exactly the same though. The fact that a vibrating piano string can stimulate a harmonic of the same note in another string even though it is slightly out of tune tells us something. It tells us that sound frequencies do not have to be exact to be effective.

Here is a video made with a micro-tunable guitar illustrating some the slightly different intervals very well. Take note that although they do sound / vibrate differently, from a creative perspective they are pretty much still the same interval that do express about the same emotion.

Here is a video made with a micro-tunable guitar illustrating some the slightly different intervals very well. Take note that although they do sound / vibrate differently, from a creative perspective they are pretty much still the same interval that do express about the same emotion.

Below are some spectrum analyser images of the note C played with various commonly used musical sounds. The tone on the far left is the main fundamental frequency of C while the higher tones to the right are its harmonic overtones. You can see that the intervals between the harmonics are the same but that the volumes are different, it is these variations in the volume of each overtone that make each instrument sound unique. If you play a higher or lower note on the same instrument then the whole structure simply moves to the left or right (on the spectrum analyser). This is because the intervals between the harmonics are fixed and never change in relation to the fundamental frequency. The fundamental frequency and all of the overtones are a type of sound called a sine wave, this is the only type of sound that has no overtones of it's own.

Without these intervals the sound will just be a noise, for it to be a musical tone it needs to have this exact arrangement of overtones that you see mirrored in all of the sounds above. Some sounds like certain stringed instruments can distort the harmonic series slightly making the intervals a bit too big, while other sounds like bells and gamelans have there own strange and completely unique overtones not in this "classic" overtone series. Many metallic sounds can actually be called "out of tune" and not "proper" musical sounds in relation to the 12 tone scales that we use in the west. Any producer who has tried to tune a church bell sample to their music will know that it can be hard. If you tune the root note of the bell to match your track, you will often find that a loud higher harmonic is a bit off. Tune the harmonic to match your track and the root note goes out of tune.

With digital sound synthesis you can arrange computer generated sine waves according to the harmonic series to create sounds, the next video shows you how the classic synthesizer wave forms are made in this way:

If you look at the numbers at about 0:50 in the following video, you will see that the Zipf's law and the harmonic series are really one and the same. If you look near the end of the "overtones, harmonics and additive synthesis" video above, you will see that the sawtooth waves harmonics follow this law not only in frequency as all sounds do, but also in amplitude.

Anything that oscillates or vibrates has a fundamental frequency and harmonic overtones. Sound, light, atoms, orbits, electric currents and rotating machines are all vibrations which is why you find these same harmonics intervals playing important roles in many seemingly unrelated fields.

Quantum physics is all about waves, and everything is made from quantum stuff.

The following video explains how bridges collapse due to harmonic resonance. In it you can clearly see the bridge wobbling at 1/2 or one octave of the length of the middle part of the bridge.

The following video explains how harmonics apply to electricity. This video is quite long and boring, but you can skip to 7 minutes to see just the important part if you are really interested in this:

Sound is the best way to experience and so truly understand how harmonics work. This is because sound is vibration that is within the human hearing range, and so it can be perceived and experienced directly. A good place to hear the harmonic series is in the sound of a mono-chord or overtone chanting, both of these sound generation methods amplify the harmonics of the fundamental pitch so that you can hear them as a very familiar melody.

Here is a video with mono-chord and overtone chanting at the same time: (this man is a master of overtones)

Here is a video with mono-chord and overtone chanting at the same time: (this man is a master of overtones)

## Cymatics and geometry

When you see a cymatics video of a metal plate with sand or water being vibrated with sound, you will see that amazing patterns are made by certain frequencies. If the frequency is swept upwards, the patterns will jump out at certain points. These get more complex with higher frequencies and simpler with lower ones.

It is important to remember that the patterns do not happen with certain frequencies because they are special, they happen because those frequencies are the same as the root pitch and harmonics of the plate or drop of water itself. If you were to hit a metal plate or use a violin bow on it from various angles, you would be able to make it ring these same tones.

So to really understand cymatics you need to remove the vibrating plate, as its size and shape influence the patterns in the sand or water too much. The short video below called “Shape oscillation of a levitated drop in an acoustic ﬁeld” is the purest form of cymatics I have seen. In this video they have taken a transducer and aimed it at a reflector so that the sound bounces back at it. This creates a standing wave with pockets of high and low air pressure that are fixed in place and don’t move at all. When this happens you can place small objects or drops of water in these pockets and they will float in the air! This is good for cymatics, as now you only need to worry about the resonant frequency of the water drop itself, and not its container as well.

In the video they play the fundamental frequency of the drop of water, and it flattens into a disk. Then they play the first harmonic (octave) of this pitch and it becomes elongated, like a sausage. This sausage, however, is oscillating. The ends move together and the sides move apart, forming new ends so that it was like a “plus symbol” but with only one line visible at a time, at the peak of each oscillation. When they play the third harmonic the water forms a triangle, also oscillating with another one so that both together would be a Star of David, but only one was fully formed at a time.

And so they go on. Each harmonic’s shape has the same amount of sides as its sequence number; 1 = circle, 2 = sausage, 3 = triangle, 4 = square, 5 = pentagon and so on. Obviously cymatics made using metal plates and other objects are just showing you complex versions of these basic shapes, made so by the extra factors being brought in by the objects’ physical properties.

So to really understand cymatics you need to remove the vibrating plate, as its size and shape influence the patterns in the sand or water too much. The short video below called “Shape oscillation of a levitated drop in an acoustic ﬁeld” is the purest form of cymatics I have seen. In this video they have taken a transducer and aimed it at a reflector so that the sound bounces back at it. This creates a standing wave with pockets of high and low air pressure that are fixed in place and don’t move at all. When this happens you can place small objects or drops of water in these pockets and they will float in the air! This is good for cymatics, as now you only need to worry about the resonant frequency of the water drop itself, and not its container as well.

In the video they play the fundamental frequency of the drop of water, and it flattens into a disk. Then they play the first harmonic (octave) of this pitch and it becomes elongated, like a sausage. This sausage, however, is oscillating. The ends move together and the sides move apart, forming new ends so that it was like a “plus symbol” but with only one line visible at a time, at the peak of each oscillation. When they play the third harmonic the water forms a triangle, also oscillating with another one so that both together would be a Star of David, but only one was fully formed at a time.

And so they go on. Each harmonic’s shape has the same amount of sides as its sequence number; 1 = circle, 2 = sausage, 3 = triangle, 4 = square, 5 = pentagon and so on. Obviously cymatics made using metal plates and other objects are just showing you complex versions of these basic shapes, made so by the extra factors being brought in by the objects’ physical properties.

And so, the harmonic series can be directly linked to geometry. You can learn more about this on the next page of this site.

## Harmonic series music

Here is some music that was made using a VST synthesizer called "Omnisphere 2". It can have each individual note adjusted to exact Hz frequencies and so can play any scale that you like. In this music it has been re-tuned to play only notes from the harmonic series.

The voice sounds are real human voices with nice natural harmonics, you can hear these harmonics ringing like bells and playing "ghost" melodies that are perfectly in tune with the actual chords and melodies. Having the intervals between the notes exactly the same as the intervals between the overtones inside each note really works. Tuning music like this creates fractal harmonies that seem to have a very calming and balancing effect on people. While this does work with normal equal temperament tuning, it is not nearly as accurate or as powerful as with proper harmonic tuning.

The voice sounds are real human voices with nice natural harmonics, you can hear these harmonics ringing like bells and playing "ghost" melodies that are perfectly in tune with the actual chords and melodies. Having the intervals between the notes exactly the same as the intervals between the overtones inside each note really works. Tuning music like this creates fractal harmonies that seem to have a very calming and balancing effect on people. While this does work with normal equal temperament tuning, it is not nearly as accurate or as powerful as with proper harmonic tuning.

## Just intonation

Another type of scale made from the harmonic series is called a "just intonation" scale, just intonation scales are made using ratios. These ratios can be said to represent the spaces found between harmonics in the harmonic series. For example the 9/8 whole tone (see image below) is found between harmonics 8 and 9, while a 6/5 minor third is found between harmonics 5 and 6.

Ratios with small numbers always sound better than ones with larger numbers (a ratio of 6/5 sounds better than one of 11/8). This is why the sweetest just intonation scales are made with smallest possible ratios. This is so because small ratios represent spaces between harmonics that are closer to the fundamental of the harmonic series, which would also be the root key of the music being played with the scale.

Here is some music made using the above just intonation scale. You may notice that it sounds smoother, but not that different to normal equal temperament tuning. This is because equal temperament was based on this, it was the best approximation of this scale possible with equal divisions of an octave. This scale actually is called a "5 limit just intonation" scale because all of its ratios contain only regular numbers with prime factors no higher than 5.

As you can see, the harmonic series does seem to be the source of a lot of interesting things. If you want to learn more about this, you can find more pages on this website. You can also ask a question or using the contact form below.

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