Tuning Systems

Open Well-Tempered Clavier

Kimiko Ishizaka and the Open Goldberg team have less than 3 days remaining in their Kickstarter campaign to record and release Bach’s Well-Tempered Clavier into the public domain.

If you haven’t been following the project, the team is focused on converting the Well-Tempered Clavier and over 50,000 other scores into Braille for musicians of different ability.  This is an important and ground-breaking project that will help musicians all over the globe.  Make sure to check out the campaign over the next few days to learn more about this unique project.

Tuning Systems

We have been getting some inquiries as to what :”Well-Tempered” actually means – below, you can find some information on various tuning systems and their history.

Just Intonation
Before there was a standardized tuning system, players used Just Intonation to tune relative to other musicians and their instruments.

Just Intonation is based off of the harmonic series and naturally sounds pleasing to our ears. Intervals (the distance between notes) are measured using ratios.  An excellent example is when two voices harmonize, the frequencies of the pitches being sung are adapted in real-time to create a pleasing and pure interval relationship. Since interval ratios in Just Intonation are not uniform, this type of tuning system does not meet the demands of modulating music. With fixed-pitch instruments, such as keyboard instruments, pitches cannot be adjusted practically during a performance. Therefore, in order to modulate, freely tempered systems came into place.

Well Temperament
The “Well Tempered” tuning system is referred to by J.S. Bach in his title for “The Well-Tempered Clavier” (Das Wohltemperierte Klavier).

Bach’s method of tuning a keyboard was a huge step towards today’s tuning system. Tempered tuning makes small adjustments to the intervals between notes in such a way that it is possible to harmonize music without sounding overly dissonant in certain keys or when modulating.

Bach’s “Well-Tempered Clavier” was written to show off the musical possibilities of this revolutionary tuning technique – where the keyboard was in tune across all keys.

Equal Temperament
Fast forwarding to Western music today, most instruments are tuned using Equal Temperament. The earliest specific mathematical reference to equal temperament came in 1577 from Francisco Salinas, but wasn’t standardized until the Early Romantic era.

Equal Temperament relies on math to determine frequencies of pitches.  An octave is thus divided into a series of evenly spaced half steps calculated to share the same interval ratio. Therefor in Equal Temperament, each interval is slightly out of tune and the octave remains the only “pure” interval.  This means that a chord played on a piano or guitar will not be as pleasing as the same chord using Just Intonation, but it will be consistent and free to modulate.

It is important to note that many cultures and some Western composers (such as Lou Harrison) use “Just” tuning systems because of its unique tonal qualities.

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