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Principle
The most current tuning for occidental music uses
the 12 steps equally tempered (12ET) tuning.
It means each octave is divided into 12 equally
spaced (in logarithmic scale) intervals called semitones :
-
C
-
C sharp (or D flat)
-
D
-
D sharp (or E flat)
-
E
-
F
-
F sharp (or G flat)
-
G
-
G sharp (or A flat)
-
A
-
A sharp (or B flat)
-
B
But it is sometimes necessary to write a note that
does not match exactly a semitone. Violin players (as all those who deal
with a non-fretted string instrument, wind instruments or voice) are familiar
with quartertones, i.e. a subdivision of the semitone.
Melody/Harmony enables to write and play such notes.
Adjusting a note pitch
The "turkish comma" effect is designed to apply a standard pitch change
to the note so that it matches the scale commonly used in turkish music.
These note effects are located into "Mark tools 2" palette and look like
inverted or crossed flat symbol or altered sharp.
But these effects can be edited to match any microtonal adjustment
you can need :
-
Select any of these "turkish comma" effects.
-
Insert a note on score. Note is inserted along with this effect symbol
-
Select the lasso tool in "Editing tools" palette
-
Double-click the turkish comma effect symbol on score
-
Click "Edit effect" button
-
Move the slider to match the required microtonal adjustment (in 100th of
semitone).
From then, this note will be played using the pitch shift you selected
from its original 12ET value.
Playing a microtonal-adjusted
note
In digital output, each note is independent from
each other. Therefore, microtonal adjustment are completely free, and won't
interfere with other notes.
In Midi output however, this microtonal shift
is related to a Midi channel. It means all notes that are played at this
moment on the same channel will be shifted by this effect.
So, if you need to use Midi output, only apply
microtonal adjustment to "solo" staves (no chords) and be careful no other
staff uses the same Midi channel.
Adjusting the note appearance
Maybe you do not want this pitch-adjusted note
to be displayed using a turkish comma symbol.
Here is how you can change its appearance according
to your needs :
-
From the Note options window ("Effect" tab) you got
in the previous chapter, select "Play effect" and "invisible". The turkish
comma symbol won't be displayed anymore.
-
Select the "General" tab.
-
In this window, you can select either a note color
or head shape that will highlight this note on score.
Calculating a pitch shift (microtonal)
value
This part needs some mathematical background.
We saw each note pitch matches a given frequency
in Hertz (Hz).
Traditionally, the A4 (A, 4th octave) is 440
Hz.
A physical rule says the frequency for the same
note played one octave up will be doubled. For example, A5 will be 880
Hz.
Due to this, splitting one octave into 12 logarithmic
equally-space intervals means each note frequency is the one of the previous
semitone multiplied by 12th root of 2, i.e. about 1.059463094359
It means A sharp (or B flat) of octave 4 will
be 440 x 1.059463094359 = 466.16 Hz
In the same way, A flat (or G sharp) of octave
4 will be 440 / 1.059463094359 = 415.3 Hz
Thanks to this, we can calculate the whole frequencies
for each semitone in the fourth octave (and by extension, in every octave
because we just have to mutiply or divide these frequencies by 2 to get
the values for adjacent octaves) :
-
C 4 : 261.63 Hz
-
C 4 sharp (or D 4 flat) : 277.18 Hz
-
D 4 : 293.66 Hz
-
D 4 sharp (or E 4 flat) : 311.13 Hz
-
E 4 : 329.63 Hz
-
F 4 : 349.23 Hz
-
F 4 sharp (or G 4 flat) : 369.99 Hz
-
G 4 : 392 Hz
-
G 4 sharp (or A 4 flat) : 415.3 Hz
-
A 4 : 440 Hz
-
A 4 sharp (or B 4 flat) : 466.16 Hz
-
B 4 : 493.88 Hz
The value you set in the microtonal adjustment of
Melody/Harmony is a value in hundredth of semitone (cent). It means each semitone is logarithmically splitted into 100 parts.
Increasing note frequency by 1 cent means multiplying its frequency by the 1200th root of 2, i.e. 1.00057778950655
For example, if you insert an A4(440 Hz)
along with a microtonal adjustment of +50 cents (a quarter tone),
resulting frequency for this note will be 440 Hz multiplied by the 50th
power of the cents mutiplier, i.e. (using ^ as power symbol) : 440 x 1.00057778950655 ^ 50 = 452,89 Hz
IIn a reverse way, knowing a frequency F
in Hertz, it is possible to calculate all values for the note :
1200 x log(F/16/3515978312876)/log(2)= total number of cents from C0, called C
- Divide the result C by 1200. The integer part of this result is the octave number N for the note to play.
- Calculate C' by subtracting 1200 x N to C.
- Divide this value C' by 100. The integer part of this result is D, the semitone number within octave (0=C, 1= C#, 2=D, 3=D#, 4=E,...11=B)
- Subtract 100 x D to the value in C'. You get A, the microtonal adjustment value in cent.
For example, if we need to get a frequency F of 310 Hz :
C = 1200 x log(310/16.3515978312876)/log(2)
C = 5093.72
Octave (N) = integer part of C/1200 = 5093.72/1200 = 4
We subtract 4 x 1200 from 5093,72. It gives C' = 293,72
Semitone D = integer part of 293,72 / 100 = 2. The note to insert is a D(1=C#, 2=D, 3=D#)
We subtract 100 x 2 to 293,72. It remains 93,72, rounded to A = 94 cents
We will have to insert a D, 4th octave, with a microtonal adjustment of 94 cents
We can also obtain the same frequency by using a D#, 4t octave, with a microtonal adjustment of (94-100) = -6 cents.
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