Draft:Sing free/The physics of music

Physics of music, or musical acoustics is an effort to understand music from a scientific point of view. Here the goal is to understand musical consonance and dissonance using basic concepts.

Terminology
The words used to describe something often depend on who is speaking, and things can get tricky when musicians and scientists are involved. The pitch of a musical note is measured by it's frequency, or the number of cycles that occur each second. While musicians often refer to a notes pitch by a number (e.g., "440A"), scientists and engineers prefer to attach units to everything (e.g., "440 Hertz" or simply: 440Hz). One "Hertz" is defined as one cycle per second. The term musical interval can refer to the difference between two pitches. Encyclopædia Britannica distinguishes between the melodic interval (two consecutive notes played consecutively), and the harmonic interval  (two pitches played simultaneously). While one is allowed to refer interval as a chord, calling it an "harmonic interval" precisely states that we are talking about two pitches sounded at the same time. An excellent alternative to "harmonic interval" would be to call it a  dyad.

An important distinction between different intervals is consonance versus dissonance, which might be expressed as a distinction between smoothness and roughness. By no means is dissonance "bad". In his Ninth Symphony, Beethoven famously interrupts an extremely dissonant passage by a singer who announces Ode to Joy with these words:
 * Oh friends, not these sounds!
 * Let us instead strike up more pleasing
 * and more joyful ones!

These terms are not always absolute: While some might argue that the tritone is consonant, all would agree that it is more dissonant than the established consonant intervals.

Stackexchange ranking

 * stackexchange ranked them as follows: 3:2 (P5); 4:3 (P4); 5:3 (M6); 5:4 (M3); 6:5 (m3); 8:5 (m6);

1:1 (unison); 2:1 (octave); 3:2 (P5); 4:3 (P4); 5:3 (M6); 5:4 (M3); 6:5 (m3); 8:5 (m6); 9:5 (m7); 9:8 (M2); 15:8 (M7); 16:15 (m2); 45:32 (A4)


 * Note that 5*45-7*32=1= 5*10-7*7
 * The exact ranking of consonance among the intervals is not fully agreed on.

List
List of pitch intervals --- Interval_(music) --- Pythagorean_tuning --- Music_and_mathematics -- Musical_temperament

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Sing_free/List_of_musical_intervals_(ear_training)

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intervals


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