Sound is a vibration that travels through a medium such as a solid, liquid, or gas. Higher sound corresponds to higher frequency and lower sound corresponds to lower frequency. Frequency is often measured in hertz (Hz). One hertz means that an event is repeated once per second, or one cycle per second in the case of waves.


The note A, near the center of the piano and slightly to the right, is usually tuned to 440 Hz. Most music today is based on this A=440 Hz, although classical and other historical music may use different settings. A=440 is also registered as ISO 16.

ピアノの中央付近、少し右側にあるラ(A)の音は大抵440Hzに調律されます。クラシックや古典音楽では異なる設定が使われることもありますが、現代の音楽のほとんどはこのA=440Hzを基準にしています。A=440はISOにもISO 16として登録されています。

A note one octave higher doubles in frequency. If the frequency is tripled and lowered one octave, it is five degrees up or seven semitones up, i.e., E counting from A, or G counting from C. If you multiply the frequency by 5 and lower it by 2 octaves, it will be 3 degrees up or 4 semitones up, i.e., the note C# if you count from A and E if you count from C.


The way how overlapping pitches sound is related to the ratio of frequencies, and in general, the simpler the relationship is, the less muddy it sounds (which is not good or bad by itself).


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**Just Intonation


One of the tunings based on this simple whole number ratio is called just Intonation. As shown below, just Intonation is composed of notes with frequencies that can be expressed as simple fractional ratios from a certain reference note.