Tuning your synthesizer

If your synth has microtuning or scale tuning features, it can be tuned using a MIDI System Exclusive Message (SysEx). Most synthesizers are designed so that tuning the 12 notes of one octave will tune all the octaves. You will find the SysEx format in the manual. If not, you can use Pitch Bend for a single instrument, as described below.

In either case, you will need to convert your natural musical ratio to decimal and then to cents.

Synthesizers are tuned using a different measurement system called cents, where there are 100 cents between each of the 12 notes of the octave. However, as MIDI is a computer language, we now have to convert cents to hexadecimal, a numbering system based on 16 instead of 10. Then build the SysEx by starting with the header information, which may include options for you to tune only certain channels, and add the tuning data. Some SysEx's require a "checksum" which is a hex number that is complementary to the sum of certain data preceeding it. All SysEx messages begin with hex F0 and end with hex F7.

Here is an example: To create a well tempered perfect third (5/4 of the Root)

Most musicians agree that base pitch is A = 440 Hertz or cycles per second. So, a perfect third of A would be C#, 440 Hertz x 5/4 = 550 Hertz.

• Using the formula below, converting ratios to cents, 5/4 equals 386.3137 cents. This is 13.6863 cents lower than the closest equal tempered note of 400 cents.
• In this example, the tuning range of the synth is 0 to 127 cents. So equal temperament (ET) is in the middle at 64, 0 is 64 cents lower than ET and 127 is 63 cents higher than ET. If the tuning range is 0 to 100, then ET would be at 50.
• As we want to tune the third to 386 cents, we have to flatten the C# from 400 cents. Subtract 14 cents from the ET value of 64 and then convert remaining value of 50 into hex, which is hex 32 . As tuning data is sent from C to B, the data for the second note (C#) is hex 32.
• Determine the 12 hex values for the SysEx, calculate the checksum, if required, add the header info, begin every SysEx with a hex F0 and end it with hex F7.
• Enter the SysEx in a MIDI editor or sequencer and add it to a Standard MIDI File (SMF) as another MIDI event.
• Make sure your sequencer can send a SysEx during performance, as some well-known sequencers cannot do it.
• Tip: also create a SysEx to tune your synth back to ET.

MIDI System Exclusive Message (SysEx) is a MIDI command that can be sent to any MIDI synthesizer from a Standard MIDI File (.MID), MIDI editor or can be generated by software on a computer connected to the synth. The format of the tuning message is different for each manufacturer.

Pitch Bend is a MIDI command that applies to one of the 16 MIDI channels. Because it applies to every note in the channel, in order to create an instrument with flexible tuning for every note, Justonic Pitch Bend mode redirects each of the 12 semitones to a different channel to which it sends the tuning data, playing the instrument of your choice..

Converting ratios to cents: We know that there are 1,200 cents in the octave rising from 1 to 2. Each of the 12 notes can be identified by cents = the 12th root of (two to the power of n) where n equals any one of the notes from 1 to 12. So, using this next formula: Cents = (log(ratio to the power of 12)/log(2)), we find that 1.25 = 386.3137 cents. In a spreadsheet, the formula is: =(LN(1.25^12)/LN(2))*100.

Converting Hertz to cents: Express Hertz as a ratio of base pitch: 660 /440 = 1.5 and then convert ratio to cents as shown above.

Details for the Real Time and Non Real Time, 1 and 2 byte format, system exclusive messages are available at the MIDI Manufactuers Association.

Justonic Pitch Palette software, for Windows XP and Mac OS9 , calculates and sends the MIDI data necessary to keep your synthesizer tuned to pure harmony in every Root of every Key in any Scale. It also includes a collection of tools for any musician interested in experimenting with adding new tuning to their performance.