Understanding the Interval Between C and E: A Harmonic Analysis

The interval between the notes C and E is a fundamental concept in music theory and can be determined through a careful examination of the harmonic series. This analysis not only provides a precise understanding but also delves into the natural and mathematical underpinnings of this interval.

Interval Calculation

The interval between C and E can be determined by counting the number of half steps (semitones) between the two notes. Let's break it down:

C to D: 1 half step D to E: 1 half step

Adding these together, we have:

C to E 3 half steps

This interval is known as a minor third. A minor third consists of three half steps.

The Harmonic Series and Natural Phenomena

For a more in-depth understanding, we can look at the natural harmonic or overtone series. This series is a fundamental phenomenon of frequential correlations that is found everywhere from the subatomic fabric of the material universe to the largest possible cosmological scales. According to Fourier’s theorem, this series formally dominates 'creation.'

When examining the natural harmonic series observed in music, such as in overblown oblong open wind sources like natural trumpets or horns, we can identify the lowest instance where the notes C and E are present. In the case of natural trumpets, the lowest instance is found in harmonics 5 and 6 of a natural trumpet or horn pitched in the fundamental A.

The succession of pitches in a natural trumpet (or horn) can be represented as follows:

1: A 2: A 3: E 4: A 5: C 6: E

Here, we can observe the 'A major triad' conceived with pitches [A, C, E], enclosed by the perfect fifth [A, E]. The fifth is split into two just natural thirds:

a. The lower and wider one: [A, C] between harmonics 4 and 5 (frequency ratio 5/4, a just natural major third) b. The higher and narrower one: [C, E] between harmonics 5 and 6 (frequency ratio 6/5, a just natural minor third)

Conclusion

Through this analysis, we have not only determined the interval between C and E but also explored the natural harmony and mathematical underpinnings that govern this interval. Understanding these concepts provides a deeper appreciation for the fundamental principles of music and the natural world.