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The Sound of Music – Part 1 – About Sound

 

 

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… and dancing to it, you may think I will write about. This has been done excessively. I will write about sound, what it is, how it is made, recorded and played back and finally, how we hear it and how it affects us.

Why? Some of you may be interested in what I do when I dust music. For you to understand what I am talking about, I need to give you some basic understanding. Not too deep, I am glad you are still reading and I’d like to keep it this way.

 

All Sound is Vibration

Sound is vibration, sure, of what? The pressure of air changes minutely and locally, above and below the ambient pressure. This up and down is called sound vibration when it occurs in a way that is audible to our ears. It is not like something wobbling fast or rattling of a loose nut on your car.

How is the air pressure changed? With a musical instrument, a voice box… with something that is vibrating mechanically. When something is vibrating, the speed of movement in cycles follows the shape of a sine curve, then creating a sine wave.  The displacement of the object causes air pressure changes, like a fast reciprocating piston.  Did you know that the pistons in your car move 33 times a second when you drive at about 60 km/h?

You may have noticed that I said in the heading: All Sound is Vibration.  Unfortunately, not all sound is music, most sound is noise.  Again, unfortunately, sound of noise propagates the same way as sound of music and in terms of science, physics and the ways of processing it, there is no difference.

Our ears and mind decide what we turn our attention to or what we want to avoid.  Like: “Beauty is in the eye of the beholder”, “Pleasant sound is in the ear of the beholder”.  And we have to accept that some people like the sound of noise.  It will damage their ears…

Allow me to close this discussion with the words of a German folk poet, Wilhelm Busch (not related with the late American president) freely translated:

Your music of choice
At certain hours of the day
By many it may
Be considered as noise.

 

Water and Waves are synonymous

… like air and sound.

On a day, when the water is calm, go to a lake or pond, equipped with some stones of all sizes.  Observe the water, after you have tossed in a medium size stone and “record” the sound it made when it plopped.  Close to the middle the concentric rings are higher than further out and then they fade away and out. Hitting a bell once, would cause the same wave pattern in air.

Repeat the same experiment with a smaller stone, followed by one with a larger stone.  The pop sounds are higher and respectively lower than the one from above.  Again there are concentric circles (as expected).  The difference is, the small stone pattern is smaller in diameter and the ripples are lower and follow each other in a shorter distance.  The large stone pattern is larger and the ripples are higher and further apart.  Hitting a smaller and larger bell would show the same behaviour.

This is the same in air with sound, every observation you made during the water / stone experiment has its equivalent in the air sound system.  You can replace water and waves with air and sound and all observations and occurrences would be identical.  I refer to this image, whenever you want to clarify something in acoustics.  I will return to this later on.

 

Reflecting and Bending of Sound Waves

Sound has a peculiarity.  High pitch sounds are reflected from walls and other obstacles (the reason for echo).  Low pitch sounds flow around and along.  There are physical reasons for this, but I think, explaining here would go beyond the scope of this story.  Let us accept that it is this way.  And those of you who want to know… there is plenty of material on the net.

Echo needs high pitch sounds, like when yodelling.  Our ears and senses use only high pitch sounds for finding out where sound comes from, permitting us to focus on one particular speaker within a group of talking people.  Children have higher voices, so they can make themselves noticed without delay and doubt where they are.  No, I won’t say anything about why women have higher voices.

 

Changing Air Pressure

Take a balloon and blow it up. The pressure inside is higher than ambient. When you let it go, it makes a certain well known sound. This is caused by the mouthpiece of the balloon flopping around, subsequently changing the flow of air being expelled.  The flow of air is interrupted to some degree and let loose again.  A bit less airflow causes lower pressure and an immediately following increase, a bit above the ambient pressure.

classical-guitar-part-names- my version

Picture 1 – Classical Guitar

I would like to give you a more musical example. Guitars have strings, held under tension between the tuning pegs, resting on the nut (the white piece on the top end of the fret board) and the bridge (the other white piece), which is attached to the body of the guitar via the saddle .

Plucking a string makes it vibrate, which is transmitted via bridge and saddle to the soundboard (the top part) of the guitar body. The mechanical vibration causes the volume of air inside the body to change. This variation of air pressure is emitted via the sound hole.

You can feel the vibration of the body with your hand. Skilled players vary the pressure of their plucking hand on the soundboard to change the sound characteristics.

Was this too much detail? As long as you know, it is the minute variation of air pressure that makes the sound, that’s enough.

 

Hearing Range

The hearing range of the human ear is about 40 Hz up to 18 kHz, optimally. The higher frequency reduces drastically with age and is affected by illness. I am 70 years old; my hearing range is still 30 Hz at the bottom end, my higher end is ok till 8 kHz but fizzles out to nothing at around 12 kHz. In a chapter about sound identification, I will return to this fact.

hearing range in loudness

Picture 2 – Human Hearing Range

 

The graph shows lines of equal loudness as perceived by us.  The blue line depicts loudness at a “normal” hearing level as an acceptable equivalent, which does not quite follow the grey line but can be reproduced by sound equipment.

Using it as a reference it shows, that sound at 63 Hz must be 25 dB louder to be considered equally loud as a sound at 1 kHz.  At the upper end, 16 kHz the sound must be only 5 dB louder.

The lower hearing sensitivity (green line), from which upwards we can hear sound.   The red line indicates the sound, or rather noise level at which sound becomes painful and damaging to the ear.

You can also see that our hearing sensitivity is frequency dependent.  At normal hearing level (blue line) the lowest frequency we can hear is about 50 Hz, while our best hearing is around 3 kHz.  That’s why whistles are the best warning signals.

 

Damping

I would like to encourage you to a small experiment. If you have a drum, use it. If not, get a pot and place it on you laps. Also find something to bang the pot. Then, bang it, listen and observe. Then I would like you to put your other hand onto the pot (or drum skin). The sound is muffled.

The degree of muffling (damping) changes with the change of pressure your hand applies or how much of your hand rests on the pot (or drum skin).

Damping can be caused by modifying the instrument (putting your hand on it and other items being attached) or by the room it is played in. That’s why you have an opera singer’s voice in the bathroom (no dampening) and not in your living room (carpet, curtains, furniture, other people).

 

The Measure of Sound

Hertz

In the diagram you see a simplified sound wave of a pure sine wave The wave between the arrows is called a period (one up and down, crossing the median line once). The number of periods per second is called frequency, measured in periods per second.

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Picture 2 – Sine wave and period

The unit of measure for frequency is Hertz, abbreviated Hz, 1000 Hz are called kilo Hertz, kHz, a thousand times more, mega Hertz, MHz, and after that, giga Hertz, GHz. Heinrich Hertz is the name of a scientist who contributed much in this field, electromagnetic waves. We may come back to those later, maybe.

Decibel

The dimension for loudness of sound (sound level or sometimes noise level) is a bit more difficult to explain. First of all, the unit is called decibel, abbreviated dB (mostly pronounced: d b).  The unit is named after Alexander Bell, someone who made a lot of money out of the inventions of others.

How this gave him the esteem of those scientists whose names are honoured by naming a unit of measure after them, I don’t know. May this be as it is: “deci” means: a tenth of a Bel… for some reason they dropped one ‘L’.

Simply : it expresses the ratio between two levels of energy, in our case air pressure. One is the maximum pressure caused by the sound wave, the other is the ambient pressure. Simply, the higher the dB the louder the sound.

One thing to note is:

Sound is perceived as being twice as loud when the increase of sound pressure is 6 dB. 12 dB would be four times as loud, 18 dB would be eight times louder.

The next paragraph is only for those who asked: Why?

The dB value equals the decimal logarithm of the ratio of two pressures.   P1 stands for ambient pressure, P2 for the absolute pressure (not the variation, ∆P) caused by the sound source. You are asking why again? The human perception of sound increase almost follows the decimal logarithm of the physical increase of sound intensity. This is the reason for choosing such an odd way of measuring and calculating. I warned you. The formula is

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Back for all again.

 Attenuation

Attenuation is an other characteristic of acoustics with decibel as unit of measure.  It is a value, which describes the degree to which the travel of sound is reduced.  We can say, the less dense a material is, the higher is its attenuation.  Air has a high attenuation, porous materials with enclosed air or gas bubbles are used for sound insulation.

The opposite value, is called sound conductivity.  It describes how well sound is transmitted in a material.  Metals are good sound transmitters.  Remember the old cowboys and Indians movies?  Why did they put their ears onto the railway track?  Because the sound of the approaching train could be heard on the metal track, long before they were noticeable through air.

A little Summary

So far we know:

  1. Frequency is speed of pressure variation, measured in Hertz
  2. High pitch sound (treble) has a high frequency, low pitch sounds (bass) have low frequencies
  3. Loudness of sound, attenuation and conductivity are measured in decibel.
  4. Attenuation is the reluctance of material to transport sound, sound conductivity is the opposite
  5. High frequency sound waves are reflected, low once bend

 

Writing and Reading Music

Composers, when they write down music they use tonal scales and musicians can read all this and translate it to make a specific sound on their instruments. For high sounds, they use small instruments for deep sounds, big instruments, like violin and double bass.

Don’t ask me why. Not that I don’t know it, but this would take us too far away from where I want to get. We can have a special page on this topic.

I know, I am side tracking again, but there is an interesting bit I would like to add:

In the total tonal scale (hearing range) there are seven levels of C. When notes are written in the score, their location indicates, which one is meant. To indicate, which C we mean when we talk or write about it, we add an index, like C1 and the next one higher C2. The step or interval between one note and the same note higher up (for example C1 and C2) is called an octave.  This means eight note steps in between, like in octo-pus.

 

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Picture 3 – Harmonic and Sub-Harmonic

 

Now the interesting part: the frequency of a note one octave higher is double of the starting note. For example, the famous tone A4, the tone of the tuning fork, is 440 Hz, the one above A5 is 880 Hz and the one below A3 is 220 Hz.

I find this fascinating. Our musical forefathers worked out the octave scale long before we knew anything about frequencies and sound waves. It shows how close the human physiology is connected with sound (and light).

 

 

 

 

Back to the main topic.

 

Overtones or Harmonics

Or, perhaps I haven’t sidetracked at all. Let me see what’s next. When we hear a sound, how do we recognise, which particular instrument plays it? The characteristic sound of a violin, a trumpet, an oboe or flute?

Heard of overtones or harmonics? Both words mean the same. They are notes or sounds of frequencies, which are multiples (2 – 3 – 4 – 5) of the note, which is played, the fundamental note. Not only those who are an octave apart (1 –2 – 4 –8 –16).  This is what harmonics or harmonic frequencies are. Those below the fundamental note, established through clean fractions (1/2… 1/3… 1/4… etc.) are often called sub-harmonics.

Harmonics effect (superimpose) the fundamental tone (note or frequency) and that’s how we know, which instrument is playing the tone. Each instrument has its particular, unique wave pattern (spectrum) of harmonics. It’s called timbre. (Even musical instruments made from metal have timbre). There can be over ten harmonics in the characteristic spectrum of an instrument.

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Picture 4 – Trumpet with Harmonics

The picture shows the fundamental tone G5 = 784 Hz played on a trumpet. That’s what is says. However in the graph  it shows more as G#5 = 830 Hz. Just a minor detail to make sure you are not getting confused. You can see the harmonic spectrum including the sub-harmonics.

Of the left side of the graph you may read the word acoustic impedance. Don’t worry. It’s proportional with the sound level.

 

 

 

Here are a few more harmonic spectra of other instruments.

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Picture 5 – Flute and Harmonics

 

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Picture 6 – Violin and Harmonics

 

 

 

 

 

 

A modern Application

The knowledge of the above inspired musically inclined engineers (like me) to think about creating the sound and particular spectra of instruments.  They knew, mathematically, it can be done (like in picture-9), however, making it in reality, that was the real challenge.  Since this machine would create the sound of an instrument synthetically, they called it a synthesiser, obviously.

They took an old organ, chopped off the strings and pipes and placed a series of sine wave generators on top of it.  Pressing a key on the keyboard would initiate the sound wave of a particular fundamental note.  The spectrum (various amplitudes of harmonics and sub-harmonics) had been pre-set on the various sine wave generators (the boxes above the keyboards).   For each instrument was dedicated to one keyboard and about 5 wave generators.  The synthesiser in picture-7 shows two finger keyboards on one pedal board, thus, it could play three instruments simultaneously.

early synth 6

Picture 7 – Early Synthesiser

 

Modern synthesisers have many more registers (number of possible instruments) and if that is not enough, they record the sound on a hard-drive, and add more instruments to it and synchronise them all later.

And it sort of worked, it inspired us youngsters significantly to make us feel excited.  One of the earliest record released on Germany was called: “Barock-Revolution oder die seltsamen Abendteuer des J.S. Bach im Land der Elektronen” or “Baroque Revolution or the Unusual Adventures of J.S. Bach in the Land of Electrons.” offering some of his most famous organ pieces.

The American original was called: “Switched on Bach”

 

I had only just started with my studies (aged 20) and I remember saving up for some time to buy one.  The cost of an LP then would have been the equivalent of around $50, today.  A bus ticket was 20 cts, then.

early synth record Baroque Rev German cover

Picture 8 – My first LP of synthesised music

I was wrapped and believed a new era of music had started.  I also was a regular hippie.  Not a real one, they were in drugs, long hair and being dressed in a particular way.  All those dreams and believes have fallen into the crevice of the past.

Music had been in my life already, seeing the artist and engineer combined inspired me to focus on acoustics in my field of study.

Today, I have turned completely away from synthesised music.  Adding dancing to my group of passions, my musical sensitivity has deepened and I found, there was and is the most important, essential ingredient missing: the spirit.  In real music, it has been put in there during the many hours of composing, rehearsing and performing, thus being influenced by the musician’s spirit and having absorbed their energy and feelings.

This is missing, it cannot be analysed, synthesised and reproduced by a computer.  As a dancer, it is the spirit of the music that moves me, not my brain.  When there is no spirit, I don’t feel inspired… in-spiritus = fill with spirit.

 

A larger Summary

We have seen:

  1. All instruments have their own identifying spectrum composed of harmonics giving each instrument its individual timbre.
  2. Harmonics are multiples or clean fractions of the fundamental note.
  3. Harmonics above the fundamental note are just called harmonics, those below are often called sub-harmonics
  4. Instruments can have up to ten harmonics, including sub-harmonics.
  5. Allow me to add a little bit more: the spectrum of an instrument is not constant for all the notes it can play. A low note causes a slightly different timbre to a high note. Composers know this and they use it to combine all the instruments of an orchestra into one sound.

 

Applying our Knowledge

The next diagram brings it all together.  On the left side you see the fundamental tone and 6 levels of harmonics.  On the right, the upper diagram shows what the sine waves look like individually and the lower diagram shows how they add up (superimpose) to a singular sound-wave. The sound-wave of one instrument.

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Picture 9 – Sine waves of fundamental tone and harmonics and their superimposition

There is no need for you to know, how this works.  For those who want to know, there is ample of material on the web under the topic: adding or superimposing of waves, in this case, sine waves.  This is how a synthesiser operates.

 

Interference

In everyday language, interference is something we don’t like.  In acoustics it happens all the time as soon as there are two or more sound sources.  Like the stone falling in water causes concentric waves, so do most sound sources.  When you throw stones into water, you can observe how the waves approach each other and mingle.  In acoustics this is called interference and what we observe, an interference pattern.

interfering waves

Picture 10 – Interference Pattern

 

The picture shows the waves of the two sound sources.  This is called an interference pattern.  Waves go up and down, having crests and troughs.  When two crests meet, they add to each other, the same at troughs.  When the sounds are of the same frequency, then we end up with double the loudness.

Imagine, what such a pattern would look when a whole orchestra is playing…

 

 

When two sound sources emit different sounds then it looks like this:

interfering sine pattern

Picture 11 – Interference Pattern of two different sounds

The black and red are the sine waves of two different instruments, you can see the two sine wave with different lengths or periods; the amplitude (height) could be different, too.  The blue interference line is the sum of the red and black line.

Since all sound waves are sine waves, all interference lines are sums of sine waves, even they don’t look like it.  Have a look at picture-9, the diagram at the bottom and picture-13, all made up from sine waves, unbelievable.

Therefore, it is possible to mathematically analyse interference waves and calculate their initial sine wave components.  I talk about this later in the part about what I do when I dust.  Just to finish this off, this process is called Fourier Analysis, after an important French mathematician and physicist.

 

When you now add up all the instruments of an orchestra, a sound-wave may look like this:

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Picture 12 – 14 seconds of the beautiful Tango Marejada played by Carlos Di Sarli and his orchestra

You don’t recognise it? These are 14 seconds (from 59” to 1’13”) of the beautiful Tango Marejada played by Carlos Di Sarli and his orchestra. The whole piece is 2’39” long, meaning, the complete diagram is about 12 times longer. And this is what I am working with.

Or with the following one, when it gets harder.

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Picture 13 – 0.1 of a second of the beautiful Tango Marejada played by Carlos Di Sarli and his orchestra

This diagram is about 0.1 second long, a section of the same piece as above at around 30″.  On the left you see a quiet section followed by a sudden increase of sound towards the right.  The increase may appear gradual, just remember, the whole diagram depicts only 0.1 of a second.  In my next topic, I will refer to this diagram and will explain more details.

 

Final, short, quintessential Summary

The pinnacle of all sound culminates in interference.

 

Finishing off, for today

The point is, I would like and I will to tell you more about what I am doing, but first I had to introduce you to some fundamentals. I guess, if you have arrived here, you are keen to find out more. I promise, I won’t let you wait for too long.  I am enjoying myself far too much, and I seriously wish, you too.

Finally, I would like to acknowledge those who made the above diagrams available on the Internet, some of them I have modified to suit my purpose.  The last two, are from my own records.

Enjoy

Amadeus Wolfgang

 

You want to hop to the next part, go for it

The Sound of Music – Part 2 – Recording

 

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8 thoughts on “The Sound of Music – Part 1 – About Sound

  1. That is Fantastic Wolfgang, amazing job I wll share with some of my friends. Thank you

  2. Great text! Thank you for sharing. I learned something new while reading. Cheers!

  3. Such a lucid and understandable explanation helps clear away the noise from the melody. Well done Wolfgang A.M.

  4. Very clear and nicely illustrated description of sound fundamentals. Thanks for the refresher course.

    • Hi Robert. The pleasure is all mine… thanks for the comment. I am planning to add two more parts to it, one about recording, playback and what happens to the sound wave. The last one will be about what I am doing with it when I am dusting. I love good sound.

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