On their latest CD, New Magnetic Wonder, The Apples in Stereo feature two songs composed in a new type of scale called a Non-Pythagorean scale. Apples frontman Robert Schneider’s dual fascinations with music and math led him to create the scale as a way to explore new musical avenues. But what’s so different about it?
WARNING: Music Theory and Mathematics Content
Music scales are basically defined by the intervals they contain. Standard scales are arrangements of whole steps and half steps. These steps are defined by the ratio of the frequencies of the pitches, measured in Hertz (Hz). An octave of a typical scale is made up of the notes that fall between the frequency of the first note and the next occurrence of that note, which is at precisely double the frequency. For example, a C Major scale can start on Middle C (264 Hz) and end on the next C (528 Hz). The eleven notes between are arranged at equal intervals between the two notes (at least they are when you use equal temperament…but that’s another story…). Using all of these notes gives us a chromatic scale. Most modern music is made using scales that leave out many of the notes. The result is the familiar series of tensions and resolution we are accustomed to. This system was first written down by Greek mathematician Pythagoras, so these can be considered Pythagorean Scales.
So, what’s so different about Robert Schneider’s Non-Pythagorean Scale? The ratio of the intervals’ frequencies is not equal. It’s based on the natural logarithm of the scale tone, leading to a non-linear distribution of intervals. The space between notes at the bottom of the scale is much larger than the space at the top of it. Most of the pitches defined this way do not correspond to notes found in traditional scales because their pitches end up being irrational numbers (numbers that that cannot be derived by n/m, where n and m are integers), and all of the pitches in the Pythagorean system are rational. This results in melodies and harmonies that are at once completely foreign and oddly satisfying.
“Non-Pythagorean Composition 1”
For more information on the Non-Pythagorean Scale check out the bonus materials on the New Magnetic Wonder CD.
ANOTHER UPDATE: They’ve redesigned their site and the explanation isn’t there anymore.