Final answer:
Notes with the same chroma have fundamental frequencies that are integer multiples of one another. Different instruments have unique overtone structures, affecting the timbre of the note played. Understanding the harmonics and the relationship between fundamental frequencies and overtones is crucial in music and physics of sound.
Step-by-step explanation:
Notes with the same chroma have fundamental frequencies that are integer multiples of one another. This relationship is a fundamental concept in music and physics dealing with sound, known as harmonics. When the fundamental frequency is played, it can be accompanied by other frequencies called overtones, which are higher pitches related to the fundamental frequency. Fundamentals and overtones together create the full sound of a musical note.
For example, if you had two tubes with the same fundamental frequency, one open at both ends and the other closed at one end, the spectrum of overtones they produce would be different. This is because the open tube will have both even and odd multiples of the fundamental frequency, while the closed tube will only have odd multiples. These differences in overtone structure contribute to the unique timbre of instruments. Middle C played on a trumpet, which acts like a tube closed at one end, will sound different from Middle C on a piano due to their distinct overtone combinations.