Attunement

Music is often made using tuned sounds, but there are many, infinite different ways that we can tune sounds to one another, called attunement, temperament, or intonation.

While humans across the planet have made music using pentatonic and diatonic scales, considerable variations in tuning have also been a potent method for heightening musical expressiveness.

A goal of mine is to help bring the vast potential for diverse tuning methods into the 21st century and open new horizons through invention, innovation, and creative expression.

Here you will find my foray into poly- and micro- tonalities, including scientific and phenomenological analysis, philosophical questioning, and sonic experimentation, both ancient and contemporary.

Ancient Harmony

Ptolemy's Just Intonations

Based on the tuning systems of the ancient Pythagorean, Archytas of Tarentum, and the second century musicologist, Claudius Ptolemy of Alexandria. The last of the four pieces uses an inversion of Ptolemy's Soft Diatonic, made by ascending to form the order of the tetrachord, rather than descending.

Written and performed by: Jack Bagby (piano and virtual instruments) Jonathan Kay (soprano and tenor sax)

Ptolemy is famous for inventing the modern "Just Intonation" but this is actually a slight misconception. First of all, Pythagorean Tuning (tuning by fifths and fourths) is also a form of "just intonation". Ptolemy describes many forms of just intonation! The Renaissance composers just perfered the tense diatonic (and who can blame them, its an incredibly good tuning system!)

Ptolemy's tense diatonic is also the closest to 12 tone equal temperament, so most easily listened to without really even noting the difference. The rest of his tunings, and the ones he analyses from history (Pythagoreans, Philolaus, Archytas, Aristoxenus)

Here is a versions of Eric Satie Gymnopédie 1 in Pythagorean Tuning

Modern Temperaments

1/4 Comma Meantone and its variations...

One of the major innovations in European Renaissance music was the elaborate systems aimed at approximating just intervals, in this case, the major (5:4) and minor (6:5) thirds. SO, basically they are attempts to make Ptolemy's Intense Diatonic more versatile to key changes.

The most basic and systematically simple way of doing this in whats called Meantone temperament. Its constructed by tuning a circle of fifths like Pythagoras, but each time, slightly detuning from the just 3:2 ratio, by about ~5 cents.

All the other major temperament systems were complex variations on the same project of incorporating better tuned thirds and avoiding wolf intervals. Eventually the desire for modulation one out and we switched to 12 tone equal temperament. New Inventions are cropping up every week that help expand our tonal horizons!

Carlos Alpha

While equal temperament became the pervasive tuning method in the 19th century and continues to be to this day, just intonation has never entirely gone away nor have people stopped experimenting and inventing!

Wendy Carlos was a pioneer of electronic music and musicologist who invented several tuning systems.