Mathematics in Music

“The mind counting without being conscious that it is counting.” That’s how the the philosopher Leibniz described listening to music.

Cognitive scientists have become very interested in the ways the brain grasps musical patterns. It turns out there are overlaps between musical and linguistic and mathematical ability, which have spawned all kinds of theories about how music arose in prehistory. 

Also maths has changed in recent times. It’s no longer just about numbers. It’s about groups and symmetries and chaos and complexity. Mathematicians are in search of patterns, and music is all about pattern-making. 

The Greek-French composer Iannis Xenakis conjured sounds out of Bernouilli’s equations, and Brownian motion.

All this was revealed in a brilliant lecture on music and symmetry, given by Marcus de Sautoy as part of the Swedish Radio Symphony Orchestra’s Interplay series. Symmetry is something music has at the very basic level of sound. 

"Look at the make-up of a single sound on a 3-d oscilloscope, and you find the more pure and beautiful the sound, the more symmetry it has. The purest sound of all is a sine wave, and that looks like a circle. And a circle has infinite axes of symmetry."

Why do we choose one rather than another? Because it captivates us, for a reason we can’t quite define. It may because in some way the progression bends the rules, or actually breaks them. Bach broke the rules quite often, but that doesn’t mean we lesser mortals can do it (as I was often reminded as a student, after handing in a ham-fisted chorale harmonisation). If we could define the thing that gives that special x factor to harmonic progressions, we could produce them to order, or get a computer to do it.

There’s a need to find a pattern with that extra something that is used also when composing music, because a perfect pattern on music is boring, which opens the door to a new world. 

Read the Full article at Telegraph

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Why do we Listen to Sad Music?

Read how the experiment demonstrated what could be the reason of this. 

Apparently, if we don't feel any real threat or danger that in a situation in life, we cannot get get affected by music, but it can change our mood in a good way.

Listen to what ever kind of music you want, using a portable Bluetooth speaker. Do not be afraid of music, because it will never make you go down, but all the other way, it will cheer you up.

Sad music can induce intense emotions, yet the type of sadness evoked by music also seems pleasing in its own way, “musical emotion” encompasses both, the felt emotion that the music induces in the listener and the perceived emotion that the listener judges the music to express. By observing how they related to each other, we hoped to gain a better understanding of sad music.

In an experiment, 44 people served as participants. We asked them to listen to one of three musical excerpts of approximately 30 seconds each. The excerpts were from Mikhail Glinka’s “La Séparation” (F minor), Felix Blumenfeld’s “Sur Mer” (G minor) and Enrique Granados’s “Allegro de Concierto” (C sharp major, though the excerpt was in G major, which we transposed to G minor).

A participant would listen to an excerpt and then answer a question about his felt emotions: “How did you feel when listening to this music?” Then he would listen to a “happy” version of the excerpt — i.e., transposed into the major key — and answer the same question. Next he would listen to the excerpt, again in both sad and happy versions, each time answering a question about other listeners that was designed to elicit perceived emotion: “How would normal people feel when listening to this music?”

Our participants answered each question by rating 62 emotion-related descriptive words and phrases — from happy to sad, from bouncy to solemn, from heroic to wistful — on a scale from 0 (not at all) to 4 (very much).

We found, as anticipated, that felt emotion did not correspond exactly to perceived emotion. Although the sad music was both perceived and felt as “tragic”, the listeners did not actually feel the tragic emotion as much as they perceived it. Likewise, when listening to sad music, the listeners felt more “romantic” emotion and “blithe” emotion than they perceived.

Something similar happened with the happy music: perceived blithe emotions were rated higher than their felt counterparts. In general, it appears that perceived emotions may be rated higher than felt emotions when it comes to emotional categories characteristically associated with a given key.

When listening to sad music, then, there is a tension, or slippage, between the two types of emotions. How are we to understand this gap?

One answer might be that in everyday life we typically experience emotions that have a direct connection to whatever object or situation gives rise to them. But when we listen to sad music (or watch a sad movie, or read a sad novel), we are inoculated from any real threat or danger that the music (or movie or novel) represents.

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