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Here are definitions for some key world music theory terms: Maqam – Melodic modes that form the foundation of Arabic, Turkish, and Persian music. Raga – Melodic frameworks for improvisation and composition in Indian classical music. Tala – Rhythmic cycles and patterns that form the rhythmic foundation in Indian music.
- Pythagoras’ Experiments
- The Mathematics of Musical Scales
- By Finding Notes from Frequencies
- Logarithm in Music
- Going Further
- Final Thoughts
Okay, so before we continue, let’s go back to the past, to Ancient Greece. At that time, there was a man named Pythagoras who made very important discoveries for mathematics (and for music). This we have just shown about octaves, he discovered while “playing” with a taut string. Imagine a stretched rope, attached to its ends. When we play this stri...
Many peoples and cultures have created their own musical scales. An example was the Chinese people, who started from the experience of Pythagoras (using ropes). They played the C note on a stretched string and then divided that string into 3 parts, as we just showed. The result of this division was the G note. When observing that these notes had a ...
Everything we discussed will become clearer by looking at the notes on a piano: If we consider that the first C (leftmost) has an f frequency, the second C (one octave higher will have a 2f frequency). To get to the next C, we will have to take C 2f and multiply by 2 once again, reaching C 4f. By repeating the process, the last C of that piano will...
If you understand a bit of mathematics you noticed that, when doing the calculations of frequencies and roots, we work intrinsically with the logarithm to the base 2. For this reason, piano builders placed the shape of a logarithm chart on the body of the piano, to make a reference to this mathematical-musical discovery. Observe: Example logarithmi...
There are many other mathematical explanations for various questions in music, and to show them here it will be necessary to address more advanced subjects, such as the Fourier series. A Fourier series can be used to describe the behavior of a wave in physics. Basically, this series is formed by a main harmonic added to other secondary harmonics. T...
Our goal was to show you how music works mathematically and how logical relationships are understood by our brain. Obviously, we did everything here using approximations (rounded numbers), as a more accurate analysis would be tedious for most readers and would also require more rigorous mathematical and physical testing. It is not necessary to memo...
Principle 1: Higher pitch corresponds to higher frequency. Recall that the frequency f f of a sound wave describes how many vibrations there are per second. This is the most important quantity here, because the frequency remains constant as the sound wave travels from its source through the medium into our ears.
Musical form is the plan by which a short piece of music is extended. The term "plan" is also used in architecture, to which musical form is often compared. Like the architect, the composer must take into account the function for which the work is intended and the means available, practicing economy and making use of repetition and order. [10]
May 3, 2024 · Music Rhythm: The Pulse of Mathematics. At the heart of music lies rhythm, the arrangement of sounds and silences in time. Surprisingly, rhythm is deeply rooted in mathematical concepts such as fractions, ratios, and patterns. For instance, a simple time signature like 4/4 denotes four beats per measure, where each beat can be subdivided into ...
In this book, Leon Harkleroad explores the math-related aspects of music from its acoustical bases to compositional techniques to music criticism, touching on. overtones, scales, and tuning systems the musical dice games attributed to Mozart and Haydn the several-hundred-year-old style of bell-playing known as ring-ing the changes the twelve ...
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In general, music theory maps well to mathematical concepts. Notable sub-areas of music theory that work particularly well are: set theory, twelve-tone theory, scales, and tunings. Music did not come from math, but numeric notation and mathematic operations work well to describe music. In this article, I’ll look at some of the ways math and ...
