Principle


The most common tuning for occidental (Western) music uses
the 12step, equally tempered (12ET) tuning.
In this tuning, 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 exactly match a semitone. Violin players (as well as all those
who deal
with a nonfretted string instrument, wind instruments or voice) are
familiar
with quartertones, i.e. a subdivision of the semitone.
Melody/Harmony lets you 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 in the "Mark tools 2" palette and look
like
an inverted or crossed flat symbol or an altered sharp.
But these effects can be edited to match any microtonal adjustment
you might need:

Select any of these "Turkish comma" effects

Insert a note on score. The note is inserted along with this effect
symbol

Select the lasso tool in the "Editing tools" palette

Doubleclick the Turkish comma effect symbol on the score

Click the "Edit effect" button

Move the slider to match the required microtonal adjustment (in 100ths
of
semitone)
This note will now be played using the pitch shift you selected
from its original 12ET value.
Playing a microtonaladjusted
note


In digital output, each note is independent from every
other. Therefore, microtonal adjustments are completely free, and won't
interfere with other notes.
In Midi output, however, this microtonal shift
is related to a Midi channel. That means that all notes played at that
moment on the same channel will be affected by this shift.
So, if you need to use Midi output, only apply
microtonal adjustment to "solo" staves (no chords) and be careful that
no other
staff uses the same Midi channel.
Adjusting the note appearance


Maybe you do not want this pitchadjusted 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) we saw
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 a head shape that will highlight this note on your score.
Calculating a pitch shift (microtonal)
value


This section requires some mathematical background.
We saw that each note pitch matches a given frequency
in Hertz (Hz).
Traditionally, the A4 (A, 4th octave) is 440
Hz.
A physical law says that 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,
equallyspaced intervals means that each note frequency is equal to the
frequency of the previous
(lower) semitone multiplied by the 12th root of 2, i.e. about
1.059463094359.
This means that 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 all the frequencies
for each semitone in the fourth octave (and by extension, in every
octave,
because we just have to multiply 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 hundredths of semitone (cent). It means
each semitone is logarithmically splitted into 100 parts.
Increasing the 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) with a microtonal adjustment
of +50 cents (a quarter tone),
the resulting frequency for this note will be 440 Hz multiplied by the
50th
power of the cents multiplier, i.e. (using ^ as power symbol): 440 x
1.00057778950655 ^ 50 = 452.89 Hz.
By reversing the math above, knowing a frequency Z
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. We will call this number Y.
 Divide the result Y by 1200. The integer part of this result is the
octave number N for the note to play.
 Calculate Y' by subtracting 1200 x N from Y.

Divide this value Y' by 100. The integer part of this result is S, the
semitone number within the octave (0=C, 1=C#, 2=D, 3=D#, 4=E,...11=B)
 Subtract 100 x S from Y'. You get M, the microtonal adjustment value
in cents.
For example, if we need a frequency Z of 310 Hz:
Y = 1200 x log(310/16.3515978312876)/log(2)
Y = 5093.72
Octave (N) = integer part of Y/1200 = 5093.72/1200 = 4
We subtract 4 x 1200 from 5093.72, which gives Y' = 293.72
Semitone S = 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 from 293.72. The result is 93.72, rounded to
M = 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#, 4th octave, with a
microtonal adjustment of (94100) = 6 cents.
