ORCΛ Esosampler Companion
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Tuning

Folderkit uses the /x /y and /z addresses for special messages that will change the behavior of the transpose arguments. After one of those message is triggered all the successive transpose values will be affected, so you usually trigger the tuning messages rarely (maybe once for each orca file).

This chapter include a bit of math about frequency ratios, but for more informations about intonation and tuning i strongly advice the third chapter of Musimathics.

If you are not interested in microtunings, just read "Split", "Base Note" and "Default Tuning" for things that are still relevant if you are using standard western tempered tuning.

Split

The first argument of the all the tuning message will set the "split point" value for the Transpose. If you don't have to use any special microtuning, you use the /x message. After the tuning message, all the transpose values after the split point will traspose the pitch lower, giving you the possibility to tune a sample down.

This sample will be played an octave lower:

*=x2o.....
..........
.D........
.*=a4s1.o.
..........

Base Note

The second argument of all the tuning messages will set the base note for all the oscillators and effects, the note that is played when just the octave is used with no transpose.

orca 0 1 2 3 4 5 6 7 8 9 a b c
note C C# D D# E F F# G G# A B# B C

The tuning frequency for those note can be changed in settings.conf.

If there is a waveform in the w/q subfolder, it will be played as a F, fourth octave:

*=x2.5.......
.............
.D...........
.*=a7wq4..18.
.............

Default Tuning

This message will reset the tuning to the default tempered tuning with no transpose and a base note of C:

    *=x2..

More Info on Tuning

When you use the transpose value, what you are actually doing is generating another frequency for the note or sample, relative to the base note or to the normal sample playback speed. By using tuning messages you define the ratios of those multiplications, defining new sets of pitches to be used in various ways.

By default folderkit uses the standard western 12-degree tempered tuning. If tr is the transpose value (0-35), and freq the generated frequency, and base the base frequency, then :

    freq = base * 2^(tr/12)

( ^ is the simbol for "elevated to so " 2^4 means two elevated to the fourth ).

So the base frequency is multiplied to 2^(tr/12) to get the frequency of our played note or sample playback.

Tempered Tunings with Different Degrees

By using the third /x argument you can change the divisor in the previous expression, so we will call this argument den as denominator, so

    f = base * 2^(tr/den)

So you can get a tempered scale with any number of degrees. For example:

    *=x3..n

will generate a 23 degree tempered scale.

Pure Tunings

The /y will work as the /x message, but the resulting frequencies will be generated with ratios between integer numbers, so

    freq = base * (ind+den)/den 

With ind incrementing from 0 to den-1. After a number den of degrees is generated the same ratios will be used for the next octave, and so on and so on. The first two arguments for /y are still split point and base note. So for example

    *=y3.5a

will create a scale with frequency ratios with 10 as denominator and 10, 11, 12, 13 ... 19 as numerator, and base note F.

Pure Tuning with Degree Indices

If you use more than 3 arguments for the /y message, then all the arguments for the fourth onwards will be the offset of the numerator from the denominator. Writing as off the offset you are choosing, the formula for the ratio of each degree is:

    freq = base * (off+den)/den 

For example:

    *=y9..a.12579

will generate a scale of 6 degrees, with ratios 10/10, 11/10, 12/10, 15/10, 17/10 and 19/10 (the . after a is sent by orca-c as 0, and it's useful to separate the denominator from the degree and to rapresent the unison ratio).

Tempered Tuning with Degree Indices

An /x message with more than 3 degrees can be used in the same way of /y for generating diatonic temperated scales. Writing as off the offset you are choosing, the formula for the ratio of each degree is:

    freq = base * 2^(off/den)

For example

    *=x8.4c.357a

is a E minor pentatonic scale.

Pure Tuning with Ratio Couples

The /z message let you define ratios as /y, but with indipendent control for offset and denominator for each degree of the scale. The first two messages are still split point and base note, then you have to give a couple of numbers for each degree of the scale (usually you leave the first blank for the unison, any empty denominator will default to 12 do avoid division by 0). The formula is still:

    freq = base * (off+den)/den 

but you are choosing off and den for each degree.

For example:

    *=zeo...2a4a12168a

will generate a 6 degrees scale with the ratios 12/12 (unison), 12/10, 14/10, 3/2 (perfect fifth), 7/6, 18/10. The split point is set to orca value o.

next chapter : hints and tricks