Estimated reading time 3 minutes
Table of Contents
How to Tune Supplemented Equal Temperament
Are you frustrated that your synth chords sound out of tune? Read more to learn how to better tune your chords in Supplemented Equal Temperament tuning.
I designed Supplemented Equal Temperament (SET) to play chords that sound better in tune than the regular piano tuning: equal temperament.
The following diagram shows how to tune SET to scales centered around C major. The sound track above the diagram shows how primary and secondary triads sound in SET.
Melody & Organ – Major and Minor Chords:
Mobile users: for best results reading the examples, tilt your screen 90o to the right.
How Chords in Supplemented Equal Temperament Work
Most of the triads in the key of C major are useable. The D minor triad, however, does not work, and the B diminished triad remains incomplete. In the chart above, the notes, represented by the letters, have cent values attached.
For a detailed definition of cents (1 cent = 1/100 of a semitone) see the post: How to Micro Tune the Keyboard to Make the Chords Sound Awesome. The article also contains a more complete discussion of how to tune SET.
The keyboard contains partial versions of the keys of G and D major. It also contains C natural, harmonic, and melodic minor. Supplemented Equal Temperament compares well with meantone temperament, which Mozart used to tune his keyboards.
The chart below shows how the chords in Supplemented Equal Temperament works with the additional triads for G and D major, and C minor.
For additional keys, however, you need to retune the keyboard again. If you own a PC3K keyboard, use the intonation key parameter to quickly change the key. It takes just a button press or two to change the keynote the intonation map centers around.
Even if you do not use the PC3K’s intonation note parameter, the keyboard template still gives some modulation flexibility.
PC3K Keyboards and How Chords in Supplemented Equal Temperament Work
The PC3K manual states, “Intonation Key (Int. Key): This sets the tonic, or base note from which the currently selected intonation map calculates its intervals. If you select G as the intonation key, for example, and the intonation map you select tunes the minor 2nd down by 50 cents, the G# will be a quartertone flat relative to equal intonation. If you change the intonation key to D, the D# will be a quarter tone flat. If you use nonstandard intonations, you’ll want to set Int. Key to the key you’re playing in. If the Intonation Key parameter is set to Equal, changing the Int. Key has no effect” (Kurzweil).
The intervallic tuning relationships of the keyboard template in the first section stays the same when using the Intonation Key parameter. Yet, the tonic of the intonation map can be easily changed.
This powerful tool enables the PC3K owner to shift keys, progressing around the circle of fifths. It gives easy access to all 24 major and minor keys.
If a second person operates the keyboard’s touchpad, it gives you the capability to change the Intonation Key during live performance. This person functions as a sort of temperament conductor. Consequently, Int. Key makes it feasible for Supplemented Equal Temperament to exceed the modulation limitations of the meantone tuning that Mozart used.
This shows that the chords in Supplemented Equal Temperament work well when used with the PC3K keyboard.
Concluding Thoughts to How Chords in Supplemented Equal Temperament Work
The chords in Supplemented Equal Temperament work best when they are triads. When used with violin, brass, or vocal keyboard programs, the tuning makes the tone color really vibrant.
It also makes the synth programs sound more like the real instruments. However, beware keyboard sounds that use low frequency oscillators for vibrato, because they ruin the effect.
For more on retuning synths using SET, see the Intonation post.
© 2020 Geoffrey Keith
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