Music math notes answers
Some of them are also on the scale of C others are very close, but not exactly equal and some fall in the middle of the notes in the scale of C. Take for instance the fifth of C (it's the G), and build a new major scale, now starting from G instead of C. If you take any note in the C major scale, you can treat that note as the start of another scale. Now, if you get the C note and use the "perfect" fractions, you'll get the "true" C major scale. The white keys in the piano correspond to the major scale, starting from the C note. Both scales (major and minor) have $7$ notes. The major and minor scales of Western music can be approximately derived from this scheme. So, in theory, you can start from an arbitrary frequency (or note) and build a scale of "harmonic" notes using these ratios (I'm using quotes because the term harmonic has a very specific meaning in music, and I'm talking in broad and imprecise terms). Some combinations sound better while others produce what we call "dissonance". When you combine several sine waves, you hear several different notes that are the result of the interference between the original waves. That's also the reason why some combinations sound better, as it can be explained by physics. They noticed that if you double or halve the string length, you get the same note (the concept of an octave) other fractions, such as $2/3$, $3/4$, also produced "harmonic" combinations. The Greeks had a lot of interest in mathemathics, and it seemed "right" for them to search for "perfect" combinations-perfect meaning that they should be expressed in terms of fractions of small integer numbers. They noticed (by hearing) that stringed instruments could produce different notes by adjusting the length of the string, and that some combinations sounded better. Our scale has a very long history that can be traced to the ancient Greeks and Pythagoras in particular. It depends on the mathematics of the instruments as much as on cultural factors. The first answer is great, so I'll try to approach the question from another angle.įirst, there are several different scales, and different cultures use different ones.
![music math notes answers music math notes answers](https://i.pinimg.com/736x/e2/d3/28/e2d328436f02f0942294b3559661ed8d.jpg)
There was a lot I didn't know, and I'm only in the introduction!
Music math notes answers full#
Otherwise, you get dissonance as you hear both types of overtones simultaneously and their frequencies will be similar, but not similar enough.Įdit: You should probably check out David Benson's "Music: A Mathematical Offering", the book Rahul Narain recommended in the comments for the full story. In equal temperament, a half-step is the same as a frequency ratio of $\sqrt$ is a ratio of small integers, then many (but not all) of the overtones will match in frequency with each other the result sounds a more complex note with certain overtones. I'll assume we're talking about equal temperament here. Everything depends on what tuning you use.
![music math notes answers music math notes answers](https://ecdn.teacherspayteachers.com/thumbitem/Music-Notes-and-Basic-Math-Learning-Durations-and-Subdivisions-of-Music-Notes-5054832-1575203731/original-5054832-1.jpg)
The first thing you have to understand is that notes are not uniquely defined.