Music

The Mozart Effect – Hype and Reality

The idea that music can make you smarter became very popular in the mid-nineties under the name “Mozart effect” and has remained popular ever since. The hype began with the publication of Rauscher et al. (1993) in the journal Nature. The researchers discovered that participants who were exposed to the aforementioned Mozart sonata performed better on the Stanford-Binet IQ test than those who listened to verbal relaxation instructions or sat in silence.

This revelation caused armies of mothers and fathers to storm the CD stores and bombard their children with Mozart music. One US governor ordered the distribution of Mozart CD’s by hospitals to all mothers following the birth of a child. Not surprisingly, marketers eagerly joined the fun (with increasingly ridiculous claims about the effect of music on intelligence) to profit from the newly-found “get-smart-quick” scheme. What got lost in the hype however was the fact that Rauscher et al. never found or claimed that exposure to Mozart would increase your IQ in general. Neither did they claim that the performance on an IQ test is a reliable indicator of how smart a person is. All they demonstrated was that exposure to an enjoyable musical piece led to a temporary (< 15 minutes) increase in spatial reasoning ability, not more, not less. Despite that, the study suffered the fate all studies are bound to suffer when they fall into the hands of the tabloid media, politicians and marketers: the results get distorted and blown out of proportion.

By the way: I wonder if mothers and fathers would have been just as eager to expose their children to Mozart had they known about some of the less flattering pieces written by the brilliant composer, among them the canon in B-flat major titled “Leck mich im Arsch” (which translates to “Kiss my Ass”) and the scatological canon “Bona Nox!” which includes the rather unsophisticated line “shit in your bed and make it burst”. These are just two examples of the many obscene and sometimes even pornographic pieces the party animal Mozart wrote for boozy nights with his friends. One can picture the young composer and his companions sitting in a flat in Vienna singing obscene songs after downing a few bottles of wine while concerned mothers cover their children’s ears, cursing the young generation and their vile music. That’s the side of Mozart you won’t get to hear in orchestral concerts.

But back to the topic. So whatever happened to the Mozart effect? Hype aside, is there anything to it? The thorough 1999 meta-analysis of Mozart effect studies by Chabris came to the conclusion that the popularized version of the effect is most certainly incorrect. Listening to Mozart, while no doubt a very enjoyable and stimulating experience, does not permanently raise your IQ or make you more intelligent. However, said meta analysis, as well as the 2002 Husain et al. study described above, did find a small cognitive enhancement resulting from exposure to Mozart’s sonata. The explanation of the enhancement turned out to be somewhat sobering though.

In the original study, Rauscher et al. proposed that Mozart’s music is able to prime spatial abilities in a direct manner because of similarities in neural activation. Further discussion and experiments showed that such a direct link is rather unlikely though, especially in light of the results of Nantais and Schellenberg (1999). In this study participants performed a spatial reasoning task after either listening to Mozart’s sonata or hearing a narrated story. When the reasoning task was completed, the participants were asked which of the two, Mozart’s piece or the story, they preferred. The result: participants who preferred the sonata performed better on the spatial reasoning task after listening to the piece and participants who preferred the story performed better on the test after hearing the story. However, participants who listened to Mozart’s music and stated that they would have preferred the story instead did not show the cognitive improvement. Overall the researchers found no benefit in the Mozart condition. All of the above implies that the enhancement in performance is a result of exposure to a preferred stimulus rather than a direct link between Mozart and cognition. It seems that the Mozart effect is just a small part of a broader psychological phenomenon that goes a little something like this: experiencing a preferred stimulus, be it a musical piece, a narrated story or a funny comic book, has a positive effect on arousal and mood and this in turn enhances cognitive abilities.

This was an extract from my Kindle e-book Curiosities of the Mind. Check it out if you interested in learning more about the psychological effects of music as well as other common psychological effects such as the false consensus bias, the placebo effect, the chameleon effect, …

Decibel – A Short And Simple Explanation

A way of expressing a quantity in relative terms is to do the ratio with respect to a reference value. This helps to put a quantity into perspective. For example, in mechanics the acceleration is often expressed in relation to the gravitational acceleration. Instead of saying the acceleration is 22 m/s² (which is hard to relate to unless you know mechanics), we can also say the acceleration is 22 / 9.81 ≈ 2.2 times the gravitational acceleration or simply 2.2 g’s (which is much easier to comprehend).

The decibel (dB) is also a general way of expressing a quantity in relative terms, sort of a “logarithmic ratio”. And just like the ratio, it is not a physical unit or limited to any field such as mechanics, audio, etc … You can express any quantity in decibels. For example, if we take the reference value to be the gravitational acceleration, the acceleration 22 m/s² corresponds to 3.5 dB.

To calculate the decibel value L of a quantity x relative to the reference value x(0), we can use this formula:

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In acoustics the decibel is used to express the sound pressure level (SPL), measured in Pascal = Pa, using the threshold of hearing (0.00002 Pa) as reference. However, in this case a factor of twenty instead of ten is used. The change in factor is a result of inputting the squares of the pressure values rather than the linear values.

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The sound coming from a stun grenade peaks at a sound pressure level of around 15,000 Pa. In decibel terms this is:

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which is way past the threshold of pain that is around 63.2 Pa (130 dB). Here are some typical values to keep in mind:

0 dB → Threshold of Hearing
20 dB → Whispering
60 dB → Normal Conversation
80 dB → Vacuum Cleaner
110 dB → Front Row at Rock Concert
130 dB → Threshold of Pain
160 dB → Bursting Eardrums

Why use the decibel at all? Isn’t the ratio good enough for putting a quantity into perspective? The ratio works fine as long as the quantity doesn’t go over many order of magnitudes. This is the case for the speeds or accelerations that we encounter in our daily lives. But when a quantity varies significantly and spans many orders of magnitude (which is what the SPL does), the decibel is much more handy and relatable.

Another reason for using the decibel for audio signals is provided by the Weber-Fechner law. It states that a stimulus is perceived in a logarithmic rather than linear fashion. So expressing the SPL in decibels can be regarded as a first approximation to how loud a sound is perceived by a person as opposed to how loud it is from a purely physical point of view.

Note that when combining two or more sound sources, the decibel values are not simply added. Rather, if we combine two sources that are equally loud and in phase, the volume increases by 6 dB (if they are out of phase, it will be less than that). For example, when adding two sources that are at 50 dB, the resulting sound will have a volume of 56 dB (or less).

(This was an excerpt from Audio Effects, Mixing and Mastering. Available for Kindle)

New Release: Audio Effects, Mixing and Mastering (Kindle)

This book is a quick guide to effects, mixing and mastering for beginners using Cubase as its platform. The first chapter highlights the most commonly used effects in audio production such as compressors, limiters, equalizers, reverb, delay, gates and others. You will learn about how they work, when to apply them, the story behind the parameters and what traps you might encounter. The chapter also contains a quick peek into automation and what it can do.

In the second chapter we focus on what constitutes a good mix and how to achieve it using a clear and comprehensible strategy. This is followed by a look at the mastering chain that will help to polish and push a mix. The guide is sprinkled with helpful tips and background information to make the learning experience more vivid. You get all of this for a fair price of $ 3.95.

cover

Table Of Contents:

1. Audio Effects And Automation
1.1. Compressors
1.2. Limiters
1.3. Equalizers
1.4. Reverb and Delay
1.5. Gates
1.6. Chorus
1.7. Other Effects
1.8. Automation

2. Mixing
2.1. The Big Picture
2.2. Mixing Strategy
2.3. Separating Tracks

3. Mastering
3.1. Basic Idea
3.2. Mastering Strategy
3.3. Mid/Side Processing
3.4. Don’t Give Up

4. Appendix
4.1. Calculating Frequencies
4.2. Decibel
4.3. Copyright and Disclaimer
4.4. Request to the Reader

Overtones – What They Are And How To Compute Them

In theory, hitting the middle C on a piano should produce a sound wave with a frequency of 523.25 Hz and nothing else. However, running the resulting audio through a spectrum analyzer, it becomes obvious that there’s much more going on. This is true for all other instruments, from tubas to trumpets, basoons to flutes, contrabasses to violins. Play any note and you’ll get a package of sound waves at different frequencies rather than just one.

First of all: why is that? Let’s focus on stringed instruments. When you plug the string, it goes into its most basic vibration mode: it moves up and down as a whole at a certain frequency f. This is the so called first harmonic (or fundamental). But shortly after that, the nature of the vibration changes and the string enters a second mode: while one half of the string moves up, the other half moves down. This happens naturally and is just part of the string’s dynamics. In this mode, called the second harmonic, the vibration accelerates to a frequency of 2 * f. The story continues in this fashion as other modes of vibration appear: the third harmonic at a frequency 3 * f, the fourth harmonic at 4 * f, and so on.

String Vibrating Modes Overtones

A note is determined by the frequency. As already stated, the middle C on the piano should produce a sound wave with a frequency of 523.25 Hz. And indeed it does produce said sound wave, but it is only the first harmonic. As the string continues to vibrate, all the other harmonics follow, producing overtones. In the picture below you can see which notes you’ll get when playing a C (overtone series):

(The marked notes are only approximates. Taken from http://legacy.earlham.edu)

Quite the package! And note that the major chord is fully included within the first four overtones. So it’s buy a note, get a chord free. And unless you digitally produce a note, there’s no avoiding it. You might wonder why it is that we don’t seem to perceive the additional notes. Well, we do and we don’t. We don’t perceive the overtones consciously because the amplitude, and thus volume, of each harmonic is smaller then the amplitude of the previous one (however, this is a rule of thumb and exceptions are possible, any instrument will emphasize some overtones in particular). But I can assure you that when listening to a digitally produced note, you’ll feel that something’s missing. It will sound bland and cold. So unconsciously, we do perceive and desire the overtones.

If you’re not interested in mathematics, feel free to stop reading now (I hope you enjoyed the post so far). For all others: let’s get down to some mathematical business. The frequency of a note, or rather of its first harmonic, can be computed via:

(1) f(n) = 440 * 2n/12

With n = 0 being the chamber pitch and each step of n one half-tone. For example, from the chamber pitch (note A) to the middle C there are n = 3 half-tone steps (A#, B, C). So the frequency of the middle C is:

f(3) = 440 * 23/12 = 523.25 Hz

As expected. Given a fundamental frequency f = F, corresponding to a half-step-value of n = N, the freqency of the k-th harmonic is just:

(2) f(k) = k * F = k * 440 * 2N/12

Equating (1) and (2), we get a relationship that enables us to identify the musical pitch of any overtone:

440 * 2n/12 = k * 440 * 2N/12

2n/12 = k * 2N/12

n/12 * ln(2) = ln(k) + N/12 * ln(2)

n/12 = ln(k)/ln(2) + N/12

(3) n – N = 12 * ln(k) / ln(2) ≈ 17.31 * ln(k)

The equation results in this table:

k

n – N (rounded)

1 0
2 12
3 19
4 24
5 28

And so on. How does this tell us where the overtones are? Read it like this:

  • The first harmonic (k = 1) is zero half-steps from the fundamental (n-N = 0). So far, so duh.
  • The second harmonic (k = 2) is twelve half-steps, or one octave, from the fundamental (n-N = 12).
  • The third harmonic (k = 3) is nineteen half-steps, or one octave and a quint, from the fundamental (n-N = 19).
  • The fourth harmonic (k = 4) is twenty-four half-steps, or two octaves, from the fundamental (n-N = 24).
  • The fifth harmonic (k = 5) is twenty-wight half-steps, or two octaves and a third, from the fundamental (n-N = 28).

So indeed the formula produces the correct overtone series for any note. And for any note the same is true: The second overtone is exactly one octave higher, the third harmonic one octave and a quint higher, and so on. The corresponding major chord is always contained within the first five harmonics.

Top Relaxing Classical Music Pieces

Here’s a collection of my favorite relaxing classical music pieces. Enjoy!

1. Piano Concerto in C minor, Adagio – Sergei Rachmaninov (Russian, b1873)

2. The Lark Ascending – Ralph Vaughan Williams (English, b1872)

3. Clarinet Concerto in A Major, Adagio – Wolgang Amadeus Mozart (Austrian, b1756)

4. Symphony No.2 in E Minor, Adagio – Sergei Rachmaninov (Russian, b1873)

5. Symphony No. 9, Adagio – Ludwig van Beethoven (German, b1770)

6. String Quartett in C (Kaiserquartett), Adagio – Joseph Haydn (German, b1732)

7. Nimrod – Edward Elgar (English, b1857)

8. The Planets, Venus – Gustav Holst (English, b1874)

9. Romance for Violin and Orchestra No. 2 in F Major – Ludwig van Beethoven (German, b1770)

Intensity: How Much Power Will Burst Your Eardrums?

Under ideal circumstances, sound or light waves emitted from a point source propagate in a spherical fashion from the source. As the distance to the source grows, the energy of the waves is spread over a larger area and thus the perceived intensity decreases. We’ll take a look at the formula that allows us to compute the intensity at any distance from a source.

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First of all, what do we mean by intensity? The intensity I tells us how much energy we receive from the source per second and per square meter. Accordingly, it is measured in the unit J per s and m² or simply W/m². To calculate it properly we need the power of the source P (in W) and the distance r (in m) to it.

I = P / (4 · π · r²)

This is one of these formulas that can quickly get you hooked on physics. It’s simple and extremely useful. In a later section you will meet the denominator again. It is the expression for the surface area of a sphere with radius r.

Before we go to the examples, let’s take a look at a special intensity scale that is often used in acoustics. Instead of expressing the sound intensity in the common physical unit W/m², we convert it to its decibel value dB using this formula:

dB ≈ 120 + 4.34 · ln(I)

with ln being the natural logarithm. For example, a sound intensity of I = 0.00001 W/m² (busy traffic) translates into 70 dB. This conversion is done to avoid dealing with very small or large numbers. Here are some typical values to keep in mind:

0 dB → Threshold of Hearing
20 dB → Whispering
60 dB → Normal Conversation
80 dB → Vacuum Cleaner
110 dB → Front Row at Rock Concert
130 dB → Threshold of Pain
160 dB → Bursting Eardrums

No onto the examples.

———————-

We just bought a P = 300 W speaker and want to try it out at maximal power. To get the full dose, we sit at a distance of only r = 1 m. Is that a bad idea? To find out, let’s calculate the intensity at this distance and the matching decibel value.

I = 300 W / (4 · π · (1 m)²) ≈ 23.9 W/m²

dB ≈ 120 + 4.34 · ln(23.9) ≈ 134 dB

This is already past the threshold of pain, so yes, it is a bad idea. But on the bright side, there’s no danger of the eardrums bursting. So it shouldn’t be dangerous to your health as long as you’re not exposed to this intensity for a longer period of time.

As a side note: the speaker is of course no point source, so all these values are just estimates founded on the idea that as long as you’re not too close to a source, it can be regarded as a point source in good approximation. The more the source resembles a point source and the farther you’re from it, the better the estimates computed using the formula will be.

———————-

Let’s reverse the situation from the previous example. Again we assume a distance of r = 1 m from the speaker. At what power P would our eardrums burst? Have a guess before reading on.

As we can see from the table, this happens at 160 dB. To be able to use the intensity formula, we need to know the corresponding intensity in the common physical quantity W/m². We can find that out using this equation:

160 ≈ 120 + 4.34 · ln(I)

We’ll subtract 120 from both sides and divide by 4.34:

40 ≈ 4.34 · ln(I)   

9.22 ≈ ln(I)

The inverse of the natural logarithm ln is Euler’s number e. In other words: e to the power of ln(I) is just I. So in order to get rid of the natural logarithm in this equation, we’ll just use Euler’s number as the basis on both sides:

e^9.22 ≈ e^ln(I)

10,100 ≈ I

Thus, 160 dB correspond to I = 10,100 W/m². At this intensity eardrums will burst. Now we can answer the question of which amount of power P will do that, given that we are only r = 1 m from the sound source. We insert the values into the intensity formula and solve for P:

10,100 = P / (4 · π · 1²)

10,100 = 0.08 · P

P ≈ 126,000 W

So don’t worry about ever bursting your eardrums with a speaker or a set of speakers. Not even the powerful sound systems at rock concerts could accomplish this.

———————-

This was an excerpt from the ebook “Great Formulas Explained – Physics, Mathematics, Economics”, released yesterday and available here: http://www.amazon.com/dp/B00G807Y00.

Tips for writing orchestral pieces – Part IV: Other

  • Soli

If you’re writing a piece for piano, it is common to include a somewhat virtous solo passage. For example, use the main theme and expand on that. Such soli are also possible for any other instrument capable of playing more than one note at a time: harp, guitar, strings (to some extend).

  • Convergence and Divergence

If the high notes go higher and the low notes go lower (bandwidth increases), it is called divergence. In this case make sure to fill the arising spaces between bass and melody with more texture. Convergence is the opposite situation: the high notes go lower and the low notes go higher (bandwidth decreases). In this case texture has to be eliminated between bass and melody as the distance between them shrinks. Use divergence and convergence when appropriate.

  • Short dissonance

The shorter the duration of a note, the more dissonant it can be without producing an insatisfactory sound. Such short dissonances can make a piece much more vivid. Do not hesitate to use them.

  • Performance techniques

Many instruments offer performance techniques like staccato, legato and pizzicato. Again, using those will make a piece more vivid. A slow, romantic string passage should be played legato, while in fast passages it is a good idea to use staccato notes.

  • Panning

Panning the instruments in your mix will make the sound more three dimensional. One idea is to pan the instruments according to where they are located in an orchestra from the perspective of a listener:

Image

far left → first violins, piano
left → second violins, french horns
somewhat left → flutes, timpani
slightly left → clarinets
center → trumpets, trombones
slightly right → basoons
somewhat right →  oboes
right → violas, tuba
far right → cellos, doublebasses

Tips for writing orchestral pieces – Part III: Texture

  • Chords

One note usually won’t do as a texture. Your texture should consist of several different notes, namely the chord notes and related notes. Unlike in the bass, full chords are permitted and desired.

  • Instruments

Violins, Violas and Cellos go nicely together when making a texture since they all have a similar timbre. As for woodwinds, make sure to use more of one kind rather than combining all. That is, instead of a combination of one clarinet, oboe and flute, rather use three clarinets or two clarinets and one other woodwind. It will give a much nicer blend. Mixing strings and woodwinds is possible and usually sounds well. French Horns are also very much capable of producing a nice texture.

  • Dynamics

As mentioned, the focus should be on the melody. Still, there should be some dynamics in the texture. It is not just “laying out” the chords. Couple the progression and transitions in the texture with the bass line and the melody. And make sure such transitions are audible, for example by doubling with another instrument or increasing volume of the texture for the time the transitions takes place.

Tips for writing orchestral pieces – Part II: Melody

  • Audibility

If there is a melody, it should stand out. You can either do that by using one instrument in forte or louder, or combine several instruments to play the melody. For example, practically any combination of strings and woodwind will do.

  • Repetition

Most pieces have at least one theme, which gets repeated every now and then. It allows the listener to get familiar with your piece quickly. Be sure to include some variations though with every repetition, unlike in pop music, you should not do exact repetitions in orchestral pieces. Vary the melody, vary the texture, vary the tempo, … it’s a must.

  • Idle-Time

Having one melody after the other or repeating the same theme over and over can sound confusing and/or boring. Allow some “idle-time” between the themes.

Tips for writing orchestral pieces – Part I: Bass

  • Instruments

The orchestra has several instruments which can used to form the bass:

Cello: This should be your standard bass instrument.

Double Bass: This instrument supports the cello. It usually plays the same note as the cello but one octave lower. I would recommend to stick to this principle at most times. Other than the cello, it can not play fast passages well. Keep that in mind.

Basoon: This is the standard bass instrument for the woodwinds. It goes very well unisono with the cello.

French Horn: The French Horn has a wide range and can also be used to form the bass. As for timbre, it can be seen as a bridge between the woodwinds and brass.

Tuba: This is the standard bass instrument for the brass.

Trombone: If a powerful and/or threatening bass is desired, this instrument will do the trick.

  • Balance

As you can see, there are a lot of possible instruments for forming the bass in an orchestral piece. But be sure not too use too many bass instruments at the same time, as it can sound very dull and boomy quickly (especially if you add reverb to it). Find a balance between the high and low notes. The more high notes there are, the more bass you can use.

  • Chords

Chords and close harmonies in the bass are a “no go”. Playing a full chord with cellos ore any other combination of bass instruments can sound dull and boomy quickly (especially with reverb). Use single notes to form the bass, that is, the bass instruments in unisono, plus/minus a full octave.

  • Bass line

Having the bass always play the keynote of a chord is possible. It often sounds better though, if you construct a series of neighboring notes for your bass as the chords change. For example, if you go through the chords Am – Em – Dm – Am in that order, the bass A – E – D – A will always work. But here you could also use the neighboring notes A – G – F – E as all of these notes are in the corresponding chords. You can create nice effects with such ascending or descending bass lines.