Is it possible that the harmonic laws of sound and vibration might apply to everything that exists ? Does music really contain a secret code that explains the inner workings of the universe ?

Watch the videos, and read the info below to start your journey into this hidden world ! (no adds or pop up windows).

Watch the videos, and read the info below to start your journey into this hidden world ! (no adds or pop up windows).

## 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.

The Fibonacci Fractal Meditation below is based on these numbers, if you click on the tracks name you can read the very interesting explanation on how this was done in the tracks description on bandcamp.

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

The Fibonacci Fractal Meditation below is based on these numbers, if you click on the tracks name you can read the very interesting explanation on how this was done in the tracks description on bandcamp.

The Fibonacci Series is very closely connected with another series called the "Harmonic Series" which is the basic building block of all musical sounds.

The harmonic series = 1-2-3-4-5-6-7-8-9-10-11-12-13 etc. (freq x 1 - freq x 2 - freq x 3 etc)

While the Fibonacci series = 1-1-2-3-5-8-13 etc. (last 2 numbers added together to get the next one)

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.

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.

The harmonic series = 1-2-3-4-5-6-7-8-9-10-11-12-13 etc. (freq x 1 - freq x 2 - freq x 3 etc)

While the Fibonacci series = 1-1-2-3-5-8-13 etc. (last 2 numbers added together to get the next one)

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.

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:

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 over tones 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. These sounds however can be called "out of tune" and not "proper" musical sounds in relation to the 12 tone scales that we use in the west.

So now you can see that the Fibonacci series and the harmonic series are very closely connected and appear to follow the same harmonic "grid".

So now you can see that the Fibonacci series and the harmonic series are very closely connected and appear to follow the same harmonic "grid".

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 such as bridge construction, industrial energy grid optimization, esoteric sound healing and subatomic particle science.

The following video explains how bridges collapse due to harmonic resonance.

The following video explains how harmonics apply to electricity:

If you look at the numbers at the very start the following video, you will see that the Zipf's law and the harmonic series are really one and the same. If you do an internet search on "Zip's law" it will simply blow your mind how far reaching all of this really is.

Sound however 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)

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:

Below is an image that shows you the harmonic series for 9 and the sum for calculating it, you can replace 9 with any number to calculate its harmonic overtone series in the same way.

Another way to calculate the harmonic series is to add the first frequency (9 in this case) to itself and then to keep adding it to your answer over and over again. So for 9 it would simply be 9 + 9 = 18, 18 + 9 = 27, 27 + 9 = 36… a very similar formula to the Fibonacci series.

All of the intervals that we use in music can be found between the harmonics in the harmonic series.

All of the intervals that we use in music can be found between the harmonics in the harmonic series.

The following video explains how our modern day music scales came from the harmonic series in an interesting way.

## Sacred geometry and harmonics

The chart below shows the number of degrees found in each sacred geometry shape when all of its angles are added together,

as you can see sacred geometry and the harmonic overtone series are really one and the same (if you use the degrees as Hz).

180-360-540-720-900-1080 = The harmonic overtone series of 180 Hz (regular polygons) (180 x 1 - 180 x 2 - 180 x 3 etc)

360-720-1080-1440-1800-2160 = The harmonic overtone series of 360 Hz (flower of life) (360 x 1 - 360 x 2 - 360 x 3 etc

as you can see sacred geometry and the harmonic overtone series are really one and the same (if you use the degrees as Hz).

180-360-540-720-900-1080 = The harmonic overtone series of 180 Hz (regular polygons) (180 x 1 - 180 x 2 - 180 x 3 etc)

360-720-1080-1440-1800-2160 = The harmonic overtone series of 360 Hz (flower of life) (360 x 1 - 360 x 2 - 360 x 3 etc

In the following music video, you can hear the above numbers as sound frequencies. In this way you can hear that geometry really is "frozen harmonics".

The following video makes the connection between the harmonic series and the regular polygons quite clear.

## Harmonic series music

Here is some music that was made using a VST synthesizer called "Omnisphere". It uses single note recordings of real sounds that you can then play across the whole keyboard, it can also have each individual note adjusted to exact Hz frequencies and so can play any scale that you like.

In this music each note has been re-tuned to play harmonics 16 to 32. 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 the same as the intervals between the overtones inside each note really works, creating fractal harmonies and "sonic geometry" that seems 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 it is with proper harmonic tuning.

In this music each note has been re-tuned to play harmonics 16 to 32. 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 the same as the intervals between the overtones inside each note really works, creating fractal harmonies and "sonic geometry" that seems 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 it is with proper harmonic tuning.

## the pythagorean scale

The Pythagorean scale is another very interesting scale. It is made by repeating a pure harmonic 5th (slightly different to a 5th on a normal piano) 11 times and then lowering each tone by octaves (C to C or D to D etc) to make a 12 tone music scale.

You can work out frequencies for this scale by multiplying any starting frequency by 3 eleven times and then using octaves to get them all into a single octave. Multiplying a frequency by 3 is the same as raising it by a pure fifth + one octave, since each note is played over many octaves however these octaves with the fifths make no difference to the final scale.

The chart below works in frequency x 3 from left to right, and octaves of these up and down. As you can see, starting with 1 Hz makes for some very interesting numbers / frequencies.

When these frequencies are arranged correctly, you get your standard Pythagorean scale written in Hz. The image below shows only one octave, which is repeated above and below to make the full scale (the bottom 432 Hz "A" is really the first A of the next octave).

What is very interesting is that the pentagram, which was one of the Pythagorean's favorite symbols actually contains the entire code needed to make this scale. If you use the degrees in it's angles as Hz, you get one octave + one fifth. 36 Hz to 72 Hz is an octave, and 72 Hz to 108 Hz is a fifth. These are the first three harmonics of the harmonic series based on 36 Hz, you can also find them in the stack of fifths chart above.

This scale is known to sound out of tune in some keys while sounding better than normal equal temperament tuning in others,

for this reason many people consider it to be unacceptable for most music making. I however like the way it is very pure in the root key (A minor), and then goes a bit off in parts of the song returning to pure harmony for each main "chorus" part. The track below " Sunday Afternoon" was made using this scale.

for this reason many people consider it to be unacceptable for most music making. I however like the way it is very pure in the root key (A minor), and then goes a bit off in parts of the song returning to pure harmony for each main "chorus" part. The track below " Sunday Afternoon" was made using this scale.

This track is made using a variation of the Pythagorean scale that has been adjusted to sound better in more keys.

Click on the image below to download a free tuning file pack for this adjusted scale. (for vst synths and Logic) from the files section in my Facebook group: (Feel free to join the group !) The image below also shows you how the scale was made: 2 stacks of pure fifths with one compressed fifth in the middle.

## Just intonation

Another type of scale that is also of interest is called a "just intonation" scale, just intonation scales are made using ratios of a single reference pitch or root frequency. If you do not understand how ratios work, I will explain them in a simple way: The ratio for D in the next chart is 9/8, this means that the frequency for D is the root frequency (C) multiplied by 9 and divided by 8, all the ratios in the scale work in the same way just with different numbers.

When talking ratios you don't need to specify the Hz frequencies, a person using the ratios can decide for themselves what frequency to use as a root (unison / perfect prime in chart below). Then they can use the ratios to calculate the rest of the frequencies from that one. The scale below is a good example of a ratio based just intonation scale. If you want to try this scale, click the image below, follow the link to my facebook group and look under "files".

When talking ratios you don't need to specify the Hz frequencies, a person using the ratios can decide for themselves what frequency to use as a root (unison / perfect prime in chart below). Then they can use the ratios to calculate the rest of the frequencies from that one. The scale below is a good example of a ratio based just intonation scale. If you want to try this scale, click the image below, follow the link to my facebook group and look under "files".

The following track was made using the above just intonation scale and it's nice small ratios:

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. Small ratios sound better because they represent spaces between harmonics that are closer to the fundamental of the harmonic series. You can find the true "harmonic series position" of any ratio based interval by finding the two numbers in it's ratio in the harmonic series.

The basic rule is that intervals found closer to the fundamental sound better, while intervals found further away don't sound as good. This rule reveals the harmonic order of all ratio based intervals: The 2/1 octave is the most harmonic, then the 3/2 fifth, then the 4/3 fourth, then then 5/4 major third, then the 6/5 minor third and so on.

All music really originates in the harmonic series, even the normal 12 tone equal temperament scale is based on this. So, even with "normal" music, the basic intervals (octave, fifth, fourth, major and minor third) still follow the same order of "harmoniousness". This fact was known as far back as ancient Greece, where the octave, fifth and fourth were considered to be the best intervals. It can be applied to all aspects of music, including song structure, poly-rhythms, key changes and even in the order of notes in a melody.

Things get more complex and less linear above the sixth harmonic, where harmonics 7, 11 and 13 and ratios containing them for example tend to sound quite odd. The reason for this is because higher octaves of 7, 11 and 13 don't share harmonics with higher octaves of numbers like 1, 2, 3, 4, 5, 6, 8 and 9.

All music really originates in the harmonic series, even the normal 12 tone equal temperament scale is based on this. So, even with "normal" music, the basic intervals (octave, fifth, fourth, major and minor third) still follow the same order of "harmoniousness". This fact was known as far back as ancient Greece, where the octave, fifth and fourth were considered to be the best intervals. It can be applied to all aspects of music, including song structure, poly-rhythms, key changes and even in the order of notes in a melody.

Things get more complex and less linear above the sixth harmonic, where harmonics 7, 11 and 13 and ratios containing them for example tend to sound quite odd. The reason for this is because higher octaves of 7, 11 and 13 don't share harmonics with higher octaves of numbers like 1, 2, 3, 4, 5, 6, 8 and 9.

## Mathemagical music Production

If you want to know more about all of this or even make you own music tuned to these frequencies and ratios, then I would recommend reading the new second edition of "Mathemagical Music Production".

Click image below for Kindle and paperback editions:

Click image below for Kindle and paperback editions:

## Mathemagical Music Scales

If you enjoy "Mathemagical Music Production", then you will also like "Mathemagical Music Scales". This book focuses on micro-tuning and ancient mathematics, outlining a tuning system that makes for some very harmonic music, and also mirrors the elegant mathematics found in the Mayan calender, the Hindu Yugas, the Sumerian kings lists, sacred geometry, the ratios between the Sun, Earth and Moon and a few other strange things.

Click the image below for the Kindle version:

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