Tuning in Turkish Music
In equal temperament, all of the half steps are exactly the same distance apart, enabling us to create music that sounds the same in any major and minor key from any pitch on the piano. Turkish classical music, by contrast, is microtonal. This is because it uses intervals that are even smaller than a semitone, or the distance between two keys on the piano (or frets on the guitar).
Both Western music and Turkish music base their understanding of pitch on the findings of the Ancient Greek philosopher, Pythagoras. As legend has it, one day, Pythagoras was walking and heard blacksmiths hammering at metal. He noticed that when two hammers were struck simultaneously that some of them produced harmonious sounds while others produced dissonant sounds. Upon further examination, he realized that a hammer that was twice as small as another when struck produced a musical pitch that was exactly the same but one octave higher. This meant that musical pitches were generated from mathematical principles, in this case the ratio 2:1 produces an octave.
If dividing the size of a hammer by 2 produces an octave, what happens when we divide it by 3? Another harmonious interval is produced: the perfect fifth. Since fifths produce pitches that are different, and not simply octave reproductions of the same pitch class, Pythagoras was able to generate an entire gamut of musical tones out of perfect fifths. After 12 fifths, in theory we should arrive back to a level that matches with an octave reproduction of the first pitch. In reality, that pitch is actually a little higher by a microtonal interval called a comma.
Turkish musicians focus on the Pythagorean comma as the microtonal interval between semitones, creating more distinct pitches and intervals than exist in 12-tone, equal-tempered Western music. Using this comma enables Turkish musicians to adjust their tuning in order to maintain a harmonious relationship between different intervals depending on the musical context.
Based on this fact, theorists of Turkish, Arab, Greek and Persian music developed a series of tetrachords (four-note scales) measured typically by dividing the length of the strings of an oud. One such tetrachord is known as Çargah. This is a segment of the Pythagorean major scale, derived from pitches generated from purely-tuned perfect fifths.
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Example 1. Çargah tetrachord (Pythagorean tuning)
The first and third notes, however, are out of tune. If I lower the third by one comma, the third now forms a pure harmony with the first note at a ratio of 4/5. The flat sign used in the notation is indicative of one comma flat. This is known as the Rast tetrachord. In Western music, tuning according to the pure third is called just intonation.
Example 2. Rast tetrachord (Just Intonation)
Between Çargah and Rast there are two types of whole step: one slightly bigger (the Pythagorean, or Çargah tetrachord) and one slightly smaller (the just, or Rast tetrachord). In Western music, these are known as major and minor whole steps. In Turkish they are Tanini (T) and Büyük Mücennep (K). At the same time, if there are major/minor whole steps, there are major/minor half steps. In Turkish these are Bakiye (B) and Küçük Mücennep (S).
Example 3. Types of Whole and Half Step
Using the Rast pentachord’s backward B-flat but beginning from A, we have the UÅŸÅŸak tetrachord. This tetrachord in theory features the minor whole step, or Küçük Mücennep, and even uses the same accidental: the backward flat symbol. However, in practice, musicians will play this scale degree not one comma flat, but rather 2-3 commas flat. This concept, termed tonal gravity by Ross Daly, helps to pull the melodic force towards the pitch A, the tonic of this scale.
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Example 4. UÅŸÅŸak tetrachord
The next tetrachord is Kurdi. This scale is characterized by a B that is 5 commas flat. It is notated using the Western flat symbol and is analogous to the Phrygian mode. Its tuning is also Pythagorean and the flat note creates two major whole steps. However, the third above this note is out of tune.
Example 5. Kürdi tetrachord
To adjust for this, we have the Hicaz tetrachord, which raises the B-flat by one comma, to 4 commas flat. This now makes a pure third with the D. To go with that, we have a new symbol, the flat with a slash. The hicaz tetrachord also contains a C-sharp, which is 4 commas sharp. This forms a pure major third with the root of the scale, A.
Example 6. Hicaz tetrachord
Example 7. Intervals in UÅŸÅŸak, Kürdi, and Hicaz tetrachords
