Paul Erlich facts for kids

Paul Erlich, born in 1972, is a guitarist and music theorist. He lives near Boston, Massachusetts, in the United States. He studied physics at Yale University, earning a Bachelor of Science degree.

Erlich is well-known for his important work in developing the idea of regular temperaments. These are special ways to tune musical instruments. He was the first to describe something called pajara temperament and its unique scales. He developed these for a tuning system known as 22-ET, which divides an octave into 22 equal parts.

What is Harmonic Entropy?

Paul Erlich also created a concept called harmonic entropy. This idea helps us understand why some musical sounds feel "right" or "pleasant" (consonant) and others feel "tense" or "clashing" (dissonant).

Understanding Dissonance

Harmonic entropy measures how hard or easy it is for different musical notes to fit together into a single harmonic series. Think of a harmonic series as the natural set of notes that vibrate together when you play a single note.

For example, a musical chord like {4:5:6:7} sounds very smooth and pleasant. This is because its notes fit easily into a harmonic series. But a chord like sounds much more clashing. Even though the distances between the notes are similar, the second chord is much harder to fit into a simple harmonic series.

How Harmonic Entropy is Calculated

Calculating harmonic entropy involves a few steps. It uses mathematical ideas like the Farey sequence, which is a way to list fractions in order.

Here's a simplified way to think about it:

• Imagine a bell-shaped curve, like a hill.
• You look at how different musical intervals (the distance between two notes) relate to each other.
• Then, you calculate areas under this curve based on these relationships.
• These areas are turned into probabilities, meaning how likely it is that notes will fit together.
• Finally, you use these probabilities to figure out the "entropy," which tells you how much "uncertainty" or "disorder" there is in how the notes fit. More uncertainty means more dissonance.

This theory helps explain one part of why music sounds the way it does. However, it doesn't explain everything. For instance, it doesn't cover how loud or soft notes are, or how they fit into a larger musical piece.

Images for kids

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  Harmonic entropy for three-note chords. It shows how "pleasant" or "clashing" different chords sound.

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  This image shows how musical intervals are related using the Farey sequence.