Hammer that Voice

 

We think of a person’s voice, and how it is impacted by how one breathes, how the vocal cords work, how the sound resonates in head’s cavities, and how the mouth and tongue work. It’s complicated!  And each voice is unique.

What about the voice of the piano? Yes, it has one, and it is unique. But is the tuning and the piano’s hammers that determine that voice.

A piano tuner adjusts the string’s tension so that the tone sociated with each key is evened out.

The piano’s tune is obviously impacted in how the player hits the keys—the strength and the speed—and how those keys physically connect with the piano hammers; each mechanical piece and its connections impact how the hammer moves. Moreover, as the hammers wear down, the voice can change.

Less obvious is the hammer’s felt coverings. The felt can vary significantly in terms of its surface area, its density, its hardness, and its quality.

AND, just as the head’s “cavities” impact a person’s voice, the piano’s own soundboard and cavity also impact how the sound resonates: producing a unique voice.

 Similarly to a person’s voice being described as lyric or dramatic, bright or deep, so to the voice of a piano can be described. A piano’s voice my be warm and mellow, which means the piano is well-balanced. A bright piano voice has a higher voice, which can seem lively and clear—or shrill. A dark piano voice is bass-heavy, and may be rich—or booming. A rich piano voice typically has enhanced treble and bass tones. Concert pianos often have a big, powerful voice, largely due to their size.

Now imagine matching a person’s voice and a piano’s voice. Yes, indeed, complicated and unique.

The Mathematical Harmony in Music

 

“Music is the mathematics of one who does not know that he is counting.” Gottfried Wilhelm Leibniz (1646-1716)

 Tomoko realizes the preciseness and patterns of music. Not surprisingly then, math helps in reading music. The simplest task such as counting the beats uses math. Each time signature codes the number of beats per measure, and the notes represent fractions of a measure and beat – such as whole notes, quarter notes, eighth notes and so on. In turn, reading these rhythmic notations can help one read and solve math equations. 

In fact, mathematics lies underneath much musical composition and reflects the very nature of music itself. Even the concept of octaves is mathematical. An octave is the distance between a given note with a set sound frequency (that is, the string’s vibration) with another note with double that frequency. A perfect fifth is 1.5 times the frequency of the octave’s base note. Ratios help make music harmonious.

Music compositions reflect patterns, just as math does: symmetry, repetition, transposition, inversion.  The process for perceiving and generating those patterns mirrors mathematical processes. Johann Sebastian Bach very consciously incorporated mathematical principles into his keyboard compositions. His work “Musical Offering” is comprised of ten canons, in which each canon is a mathematical transformation of the principal musical line. In fact, a mathematical breakthrough enabled Bach to write “The Well-Tempered Clavier.” Keyboard instruments used to be tuned using a just-toned scale, which made shifting to keys other than the tonic sounded “off.” The equal (even)-tempered scale, popularized by Bach, evened out the frequency ratios between all 12 notes of the chromic scale so that shifts of harmonies to other keys would sound the same.

Tomoko rightly asserts that reading and playing music require good discipline, improve listening and collaborative skills, and strengthens mental and muscle memory.  Those practices can also build math skills and recall of math details. A harmonious blend!