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symbol marks changed chapters.

 

Microtonal adjustment

Principle


The most common tuning for occidental (Western) music uses the 12-step, equally tempered (12ET) tuning.
In this tuning, each octave is divided into 12 equally spaced (in logarithmic scale) intervals called semitones:

  1. C
  2. C sharp (or D flat)
  3. D
  4. D sharp (or E flat)
  5. E
  6. F
  7. F sharp (or G flat)
  8. G
  9. G sharp (or A flat)
  10. A
  11. A sharp (or B flat)
  12. 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 non-fretted 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
  • Double-click 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 microtonal-adjusted 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 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) 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, equally-spaced 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 (94-100) =  -6 cents.



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