Estimated reading time 4 minutes
Table of Contents
Why Micro Tune the Keyboard Using Supplemented Equal Temperament?
Does it ever bother you that the keyboard’s chords sound out of tune? Micro tuning the keyboard to Supplemented Equal Temperament yields chords that sound better than equal temperament – the standard piano tuning. In SET, the triads sound great:
Melody & Organ – Primary Triads:
This article uses technical musical terms. For definitions, see the Glossary at the end of the post.
Retuning the Keyboard Using Cents
Before we can micro tune the keyboard, we need to talk about cents. Tuning theory and ethnomusicology both use cents to better describe tunings.
On the piano, a semitone is the distance from one key to the very next key up or down. Cents break each semitone on the keyboard into 100 parts (1 cent = 1/100 of a semitone).
Mobile users: for best results reading the examples, tilt your screen 90o to the right.
The regular (equal tempered) piano tuning in cents:
The Type of Keyboard Needed to Retune the Keys
In order to micro tune keyboards using Supplemented Equal Temperament (SET), a microtonal capable keyboard is required. If you need to buy one, look for a keyboard that can retune globally and has a 1 cent tuning resolution.
Visit these websites to see some of your options:
For full versatility, consider getting a PC3K series keyboard. (I get nothing from Kurzweil for saying this.)
- I designed SET to work with the PC3K keyboards.
- Particularly, the Intonation Key Parameter helps with smoother and more flexible modulations.
- It allows you to change the keyboard’s tuning with a few button presses, making all 24 major and minor keys available.
Micro Tuning the Keyboard with Supplemented Equal Temperament
SET works best with triadic harmony. The graphic above shows the SET keyboard micro tuning in cents.
- Not all note combinations work in Supplemented Equal Temperament. By design, some chords work better than others.
- Seventh chords and extensions, such as ninth chords, are not fully in tune. However, seventh chords sound alright, and triads sound fantastic.
- Similarly, the keyboard’s black keys have either a sharp or a flat. In SET, the black keys tune to one accidental or the other, but not both.
- The micro tuned keyboard template above tunes up the key of C major, minus the D minor triad, as well as the relative minor key. It also tunes partial versions of G and D major.
- In Supplemented Equal Temperament, the tonal notes are equal tempered, while the modal notes are just tuned.
- In other words, in the key of C, the note C, D, F, and G tune like the piano. The notes E, A, and B are tuned to sound better than the piano, especially when used in the C, F, and G triads respectively.
This means that equal tempered instruments can always play at least some notes that will work with SET tuned instruments.
Retuning the Keyboard Using the Global Tuning Parameter
- Global tuning has the advantage of tuning all of the octaves at the same time for each of the letter name notes. Specifically, you can tune all of the C’s, D’s, E’s, etc., each with one parameter.
- Exactly how the global retuning works depends on what keyboard you own. On the micro tuned PC3K keyboard, the global tuning offsets from equal temperament.
- As an example, the PC3K intonation table is set up with a keyboard graphic interface. All of the E’s on the keyboard are 400 cents and all of the Ab’s are 800 cents.
- When entering -14 on the E key on the keyboard graphic, all of the E’s will be retuned to 386 cents: 400 – 14 = 386. Likewise, when entering +14 cents on the Ab key, all of the Ab’s will be retuned to 814 cents: 800 + 14 = 814.
- Similarly, the C#s are offset from equal temperament by -28 cents yielding C#s tuned at 72 cents. The note D is offset by 0 cents, so the D keys remain 200 cents.
Playing the Micro Tuned Keyboard
Once the keyboard is tuned up, try playing it. Listen for which note combinations work, and which do not.
- Try the C, F, and G major triads, and the A and E minor triads.
- Try brass, string, and vocal keyboard programs. They sound awesome with the major triads.
- If a chord does not work while sustained, try playing through it quickly or with repeated, short staccato stabs. This often makes it workable.
- For more on micro tuning keyboards using Supplemented Equal Temperament, read the Intonation post.
The next post examines harmony. Later posts deal with modulation, retuning the guitar to work with the SET keyboard tuning, and using the SET keyboard for ear training.
© 2020 Geoffrey Keith
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Glossary
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