Introduction to Colundi

Some users of our µTune eurorack quantizer and midi interface have asked if about the Colundi scale and how to use it with µTune.

Here is a quick tutorial how to set it up.

The Colundi Scale is somewhat different from traditional scales in that it consists of absolute pitches, rather than relative intervals.

There are different Colundi scales, in this tutorial we will use the list published here:
http://colundi.net/data.php

The scl. file we created using these frequencies can be found here:
Colundi scl file

Update: Here is the scl-file for the complete final list with 128 frequencies:
Colundi-full-everyOne.scl

At the end of this tutorial, we will show how to create such a scale file yourself.

Using a Colundi scale file with µTune

Using the Colundi scale file is pretty simple with µTune. This explanation might look complicated, but it is only very detailed.

1. Put the scl file on the SD card an load it in µTune
   (Alternatively you could use µTune’s scale editor and enter the scale manually)
2. We need to define a reference frequency used by µTune’s tuner:
   As a reference you could use the lowest note (10.8Hz), but probably more practical is to use a note in the audible range. Looking at the list of frequencies again, we notice that note number 30 is supposed to be 440Hz. Great.
   Go into TUN->Scale Mapping and define out reference note to be 29 (The base note is note 0) and the reference frequency to be 440Hz. (Note: You can use any other note and frequency as a reference)
3. µTune is now able to calculate all absolute frequencies of your scale.
4. Connect the output of your VCO to µTune’s GATE-in input. This can be used to measure the VCO’s frequency.
5. In µTune’s tuner, you can use different display modes. You could display the frequency in Hz and check the frequencies of the different notes. Better is to use ‘relative mode’ to display the difference between the expected and measured frequency from the VCO.
6. Adjust the Tune knob on your VCO until it is in tune. You might have to adjust The ‘Middle volt’ and ‘middle note’ settings to get the VCO in range. Please refer to the µTune user manual chapter ‘Scale Mapping’ for a detailed explanation.
7. You can now play your Colundi scale and have fun!
8. Optionally: You can now also use the ‘automatic tuning’ feature to make sure your VCO stays in tune automatically at all times

Creeating a Colundi scale file yourself

As you can see, the first frequency is 10.8Hz, followed by 33Hz, 33.8Hz, 55Hz,…

We now have to convert these frequencies into ratios based on the base frequency and calculate the difference in cents.
By the time of writing this, in Scala you can enter the frequencies directly, Scale workshop does currently not support this however. A simple Excel script can do the job for you as well.

Our base frequency f_base = 10.8Hz which we define to be 0 Cent.

The cent distance from our base frequency can be calculated as:

cent = 1200 × log₂ (f_n / f_base)

The cent value of out next frequency f₁ = 33Hz can therefore be calculated as:

cent₁ = 1200 x log₂ (33Hz / 10.8Hz) = 1933.72165 Cent

The next entry in our scale is:

cent₁ = 1200 x log₂ (33.8Hz / 10.8Hz) = 1975.19032 Cent

and so on.

When you are done you can use your list to create an .scl file. You can do so using Scala, Scale Workshop, µTune’s scale editor or a simple text editor. The .scl file format is very simple and described here.