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What is the frequency resolution in Kyma? Can you produce custom scales and intervals that involve fractions or cents or do you round to the nearest cent?

The frequency resolution in Kyma is 0.0026 hz. At 4 c (middle C), that would be about 0.000172 cents. You can specify frequencies in hertz, in pitch (octave number followed by pitch class), or as a MIDI notenumber with an optional fractional part. For example to specify one cent above middle C, you would use 60.01.

Are there any alternate tunings built in?

There is a Tool for setting up new scales and testing them out using any sample or a synthesized waveform. Templates are available for:

Once you have defined a tuning, you can save it as a text file, so you can reuse it later.