Understanding the Melodic Interval Between B and Bbb in Satie's Vexations

Recently, while delving into Erik Satie's Vexations, I encountered a musical interval that intrigued me: the melodic interval between B and Bbb. This note sequence, while unusual, provides a fascinating study in enharmonic intervals and augmented unisons. Understanding this interval requires a bit of theory, so let's break it down.

The Melodic Interval in Context

Firstly, the notes B and Bbb are not part of the same scale, given the strict rules for the construction of scales. B is enharmonically the same as C, while Bbb is enharmonically the same as A. This means that from B to A, the interval is a minor third. This understanding is crucial for analyzing the interval from B to Bbb.

Enharmonic Equivalents and Augmented Unisons

In music theory, two notes with the same pitch but different names are called enharmonic equivalents. When dealing with intervals, the enharmonic relationship can affect how we classify the interval. For example, B to Bbb is an enharmonic interval that can be described as a triple-augmented unison.

Here's a breakdown of the interval: B to B (same note in the same octave): Perfect Unison B to Bb (same octave, descending): Augmented Unison B to Bbb (same octave, descending): Double-Augmented Unison B to Bbb (same octave, descending): Triple-Augmented Unison

The interval B to Bbb is a triple-augmented unison, and it's a significant interval in terms of theory and performance. However, if the direction is reversed (Bbb to B), it becomes a triple-diminished octave, which is a more rarely encountered interval.

Theoretical Background and Vexations

While theory tells us that a triple-augmented unison is a valid interval, it's important to note that this situation does not commonly occur in published music. In Erik Satie's Vexations, such notation is more of a conceptual joke. Satie loved the playfully surreal, so it aligns with his compositional style.

One could argue that this interval could also be called a triple-diminished prime, but the term minor third is more accurate. Satie's notation in Vexations with the abundance of wild accidentals is a form of musical humor, making the piece both challenging and entertaining.

Conclusion

The melodic interval between B and Bbb, as seen in Satie's Vexations, is a complex and interesting subject. It combines theoretical principles with a playful compositional approach. Understanding this interval not only enhances our musical knowledge but also provides insight into the innovative and sometimes whimsical nature of Erik Satie's work.

For those who are deeply interested in music theory and composition, this interval is a fascinating area to explore. It challenges traditional notation and encourages a deeper appreciation of the nuances within musical intervals.