Musical Tuning Frequencies

Imagine being stuck in a room where there is a cacophony of incongruous noises coming from everywhere around you!

This would be a chaotic mixture of sound, not very harmonious and perhaps quite disturbing.

However what would be the difference if all the sounds were somehow “in tune” with each other and much more melodic?

This is the general theory of getting musical instruments in harmony with each other, i.e. tuned to the same frequency.

It’s all about getting the musical frequencies in the correct balance, in order to create an organised sound experience known as ‘music’.

Have you ever thought about the intervals between different notes, specifically on musical instruments?

Freqencies in all life is measured in Hertz (Hz) and is how often per second, something oscillates or vibrates.

You may have seen or used an oscilliscope (favourite in TV dramas) where there is a waveform on a screen, up and down. Each cycle is 1 Hz.

Some frequencies and relationships are much more ‘musical’ than others, which provides a basis for music as we know it.

 

WHAT ARE MUSICAL NOTE FREQUENCIES?

When a piano string vibrates, it vibrates at a very specific frequency related to its length and tension, and by changing the tension we can choose exactly what frequency each string vibrates at – the same principle applies to all musical instruments.

So depending on what frequency is used for the A4 note, all the notes on a piano have a specific frequency. For example, if A4 is tuned to 440 Hz, this is how some of the other keys would correspond :-

A1 = 55Hz C2 = 65.4 Hz F2 = 87.3 Hz G2 = 98 Hz
A2 = 110 Hz C3 = 130.8 Hz F3 = 174.6 Hz G3 = 196 Hz
A3 = 220 Hz C4 = 261.6 Hz F4 = 349.2 Hz G4 = 392 Hz
A4 = 440 Hz C5 = 523.2 Hz F5 = 698.4 Hz G5 = 784 Hz

Music is all about the organisation of different sounds and frequencies to make something pleasant, arranged, composed and interesting for our ears.

Every musical note has a fundamental frequency (or pitch), but, in reality, it’s virtually impossible to create a single frequency at any one time.

If you hit three, five or eight piano notes at the same time, then you are generating perhaps hundreds of frequencies all at once. And when you scale this up to a full band or orchestra, we see that thousands of different frequencies are being created at any single moment.

If these frequencies are controlled and organised by skilled and knowledgeable musicians, the resultant sounds can create incredible and fascinating experiences for us to hear.

As humans, we can hear sound vibrations between 20 Hz and 20,000 Hz,enough to contain all of the different sounds in the most common music forms.

 

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UNDERSTANDING FREQUENCIES IN AUDIO AND MUSIC

There are a number of mathematical associations between musical pitch and frequency, which define the tuning and arrangement of most western music.

One of the simplest mathematical relationships to identify is that octave notes are always seen when the frequency doubles.

Looking back at the piano chart image, we see that the C2 note has a frequency of 65.4 Hz and this frequency doubles at the next C note (C3) which is at 130.8 Hz (65.4 * 2 = 130.8).

The frequency doubles again at C4 which is 261.6 Hz, and you can see that all octaves of all notes occur when the frequency doubles.

The list below shows the A note octave frequencies.

A1 = 55 Hz
A2 = 110 Hz
A3 = 220 Hz
A4 = 440 Hz
A5 = 880 Hz
A6 = 1760 Hz (incidently yards in a mile!)

 

HARMONICS OF MUSICAL SOUNDS

It’s an incredible phenomenon of physics, but strings and bars vibrate with perfect harmonic overtones.

This means that the main fundamental frequency of a string or bar is joined by many other frequencies that are harmonically related, which results in a beautiful rich tone that is much more ‘musical’ than a single frequency all on its own.

The additional overtones are, by a chance of physics, at perfect multiples of the fundamental frequency, so a string tuned to A at 110 Hz also vibrates at harmonics of 220 Hz, 330 Hz, 440 Hz and so on.

This acoustics fact is what makes string and tuned percussion instruments so musical sounding. In fact, the same principle applies to the vibration frequencies on woodwind and brass instruments too!

 

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HOW ARE MUSICAL FREQUENCIES CALCULATED?

The most common musical tuning system is the ‘equal temperament’ system.

We need to set a ‘standard relative pitch’ which defines the frequency that a particular note will be chosen to have.

Usually, we say that note A4 has a frequency of 440.0 Hz, which allows all other musical frequencies to be defined relative to that particular note.

Some composers choose to move this datum pitch a little and tune their instruments with A4 set to, say, 432 Hz, but most popular and classical music stick to the A4=440 Hz norm.

We now need to calculate the frequencies of all 12 notes within an octave, giving each and ‘equal’ spacing.

Because an octave relates to a doubling of the frequency, it’s not possible to use a linear scale and simply divide the octave band by 12 to find the frequencies of each note.

The interval between two notes (or semitones) needs to be a number which when multiplied by itself 12 times gives a perfect octave (i.e. double). This therefore gives us the following equation to find the frequency multiplier for semitone intervals:

Semitone musical interval = 2 ^ (1/12) = 1.059463094 i.e. 1.0595 ^ 12 = 2

We can now calculate the frequency values for the semitones in a given octave range, as listed below for the range A4 – A5. Note that each time we go up a semitone, the frequency increases by 1.0595 times.

A4 = 440.0 Hz
Bb4 = 466.2 Hz
B4 = 493.9 Hz
C5 = 523.3 Hz
C#5 = 554.4 Hz
D5 = 587.3 Hz
Eb5 = 622.3 Hz
E5 = 659.3 Hz
F5 = 698.5 Hz
F#5 = 740.0 Hz
G5 = 784.0 Hz
G#5 = 830.6 Hz
A5 = 880.0 Hz

 

MUSICAL INTERVALS

Musical intervals define the relationships between frequencies in a musical scale. Looking at this on the piano keyboard, we see from C to C there are 12 semitones (i.e. 12 piano keys), but a major scale has only 8 notes, those being C-D-E-F-G-A-B-C for the scale of C major.

The list below shows the frequency differences between each of these notes, which are all musically and mathematically related to the root or first note in the scale. For example we call the third note in the major scale the major 3rd and the 5th is the fifth note in the scale, which is G in the scale of C major.

1st = 1.00
2nd = 1.12
3rd = 1.26
4th = 1.33
5th = 1.50
6th = 1.68
7th = 1.89
8th = 2.00

 

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SOLFEGGIO FREQUENCIES

The Solfeggio frequencies make up a 6-tone music scale, which was first used in religious music of the 10th century.

Music tuned to the frequency of this scale is known to have healing properties and promote better wellbeing.

Evidence of these frequencies existed as far back as early Biblical times.

 

THE MEANING BEHIND THE SOLFEGGIO FREQUENCIES

So, what makes this scale so significant that it’s still being talked about and used hundreds of years later?

There’s the musical, historical, and religious importance mentioned above. But these frequencies are also said to have healing attributes.

 

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