ADDAC System ADDAC207 User Manual page 31

ADDAC207 INTUITIVE QUANTIZER
Revision.05 April.2021
REMARKS ON TEMPERAMENTS
Temperaments are just a different way of tuning the intervals between notes.
Our common Equal Temperament scale defines that every interval is Equal which translates to 1v/octave
equals (1v/12notes) 0.08333333v between each note. This is refered to as the Interval Ratio.
The Equal Temperament that we are so used to is atributed to Johann Faulhaber circa 1630 and it survived all
these years because it is the easiest way to tune an instrument so that any scale can be played without the
need to calculate and retune everytime you change the scale Root.
This was strictly a functional decision and in disagreement with the nature and mathematics of music.
So everything comes down to Ratios.
Imagine that we're on A4 minor scale and we want to calculate the frequency of the 3rd from the Root or C5
Ex. I - Equal Temperament
In Equal Temperament to calculate any desired note frequency we simply multiply the Root frequency by 2
powered to the semitone divided by 12:
Root * 2^(3/12)
if our A4 is 440Hz then C is:
440* (2^(3/12))
440*1.1892
=
523.25Hz C5, which is also true for the frequency we tune C5 in a piano.
Although valid in our Equal Temperament system this is not true in other Temperaments.
Ex. II - Just Temperament
In Just Temperament every interval has its own ratio and none of them are equal.
These are the Ratios used for the Just Temperament:
16/15, 9/8, 6/5, 5/4, 4/3, 7/5, 3/2, 8/5, 5/3, 7/4, 15/8
If we try making the same calculation from the previous example we'll find that:
440* (6/5) = 528 C5
So C5 in Just Temperament does not have the same frequency as pure C5.
The implications of this example is that if you tune an instrument in Just Temperament it will only be valid
for the Root you tune it to. To play in any other scale the whole instrument needs to be tuned accordingly.
Which leads us to a particular function:
For any Temperament other than EQUAL the b/N/# + KEY / OCTAVE Switches will set the Root for the tuning
to comply with the procedure described above.
Although this will change the Tuning it will not change the keyboard layout and led indicators.
As an example if the User selects the Natural A Root selecting a C on the keyboard is actually selecting an A
note. So all Roots are relative to the same C keyboard layout.
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USER'S GUIDE