Maqams and Cents

Eastern Music Tone Production

• Equal Temperament vs Just Intonation
• Western scales vs Eastern maqamat
• Notating Microtones
• Learning to Hear and Play Microtones

Equal Temperament vs Just Intonation

Arabic music theory divides an octave into 24 quarter-tones. Edward Hines claims that these are equally spaced. If this is true in theory, it is not universally true in practice. "Many maqamat include notes that can be approximated with quarter tones (depicted using the half-flat sign or the half-sharp sign), although they rarely are precise quarters falling exactly halfway between two semitones... For this reason, when writing Arabic music using the Western notation system, there is an understanding that the exact tuning of each note might vary with each maqam and must be learned by ear... Another peculiarity of maqamat is that the same note is not always played with the same exact pitch. The pitch may vary slightly, depending on the melodic flow and what other notes are played before and after that note. The idea behind this effect is to round sharp corners in the melody by drawing the furthest notes nearer. This effect is sometimes called the law of attraction or gravity, and is common in other musical traditions (e.g. in Byzantine music)."— Maqamworld

Turkish music theory goes a step beyond Arabic, to what might be called eighth-tones, and no one makes any claim to evenly-spaced intervals.

"The development of equal temperament enabled the West to explore and exploit the vertical side of composition, harmony, along with the horizontal side, melody."— Edward Hines

"We're raised, as modern players, on equal temperament. . . But, as Geminiani demonstrates, when you play pure intervals, you realize that F-sharp is actually lower than G-flat. A-flat is higher than G-sharp. I talk about this in my book. You can really figure it out pretty easily by using pure intervals. . . We have to use pure intervals on the violin. However, to do so, we must play on strings tuned in narrow fifths, we have to. So people are confused because, using expressive intonation, you're taught to push sharps up and pull flats down — this is what I call horizontal intonation. But when playing in a string quartet or orchestra, this kind of intonation doesn't work. One has to use pure intervals, or vertical intonation, in order to be in tune with other players. Every interval's out of tune on the piano except the octave: as string players we don't have to play that way."— Stanley Richie

Western scales vs Eastern maqamat

1. Western: a series equally tempered whole-tones and half-tones.
2. Arabic: a series of whole-tones and half-tones with pitches augmented or diminished by one quarter-tone (2 Pythagorean commas).
3. Turkish: a series of whole-tones and half-tones with pitches augmented or diminished by one-eighth of a whole-tone (1 Pythagorean comma) or by one quarter-tone (2 Pythagorean commas).

Microtonal melodies are out of tune to the Western ear exposed only to equal temperament. But to the trained ear, they are a gateway to a variety of colors and sensations.

"The most remarkable peculiarity in the Arab system of music is the division of tones into thirds. Hence I have heard Egyptian musicians urge against the European systems of music that they are deficient in the number of sounds. These small and delicate gradations of sound give a peculiar softness to the performances of the Arab musicians, which are generally of a plaintive character: but they are difficult to discriminate with exactness, and are therefore seldom observed in the vocal and instrumental music of those persons who have not made a regular study of the art... The natives of Egypt are generally enraptured with the performances of their vocal and instrumental musicians: they applaud with frequent exclamations of Allah! and God approve thee! and God preserve the voice! and similar expressions."— Edward Lane

"Yet one point may be earnestly impressed upon the reader and musician at the outset. There is no definate scale that can be traced to any immutable physical law... We are so prone to imagine that our scale (major and minor) is the sum of all music... The Hindoo scale divides into third-tones and quarter-tones in a manner that defies notation by our system or performance upon our keyed instruments."— Louis Elson

"The fundamental points of divergence between Eastern and Western music are the employment of quarter tones, the displacement of F and B (which are respectively a quarter tone above and below the Western notes), the entire neglect of harmony and counterpoint, and the use of most complicated rhythms... Arab music differs in some particulars from the Western scale. Arab notes fall exactly on G, A, C, D and F: but the notes Iraq and Sigah fall a quarter-tone below B and E respectively. In other words, the Arab scale divides the intervals between A and C, and D and F, exactly in half, whereas the west divides them into two-thirds and a third."— Edward Hines

"The computation of the exact sizes of the microtones and the notation of makam are rather complicated, and several alternatives were presented at the Cairo Congress on Arab Music in 1932. Some of the scale systems discussed at this meeting were obtained through mathematical computation and some were established experimentally... The differences between theorists and musicians, as well as modern research on the tonal structure of vocal and instrumental music indicate that none of these systems provides an accurate description of actual musical practice. They are merely convenient tools for prescriptive and didactic purposes. Conservatories, musicians and theorists in different countries use different scale systems which leads to the differences in the notations of accidentals and makam names." —TurkishMusic.org.

Western music scales are a collection of musical intervals in a set order, otherwise known as the intervallic structure of the scale. Major scales intervals, for instance, are ordered: whole, whole, half, whole, whole, whole, half with the common visual being the collection of white keys on the piano between C and C.

Arabic maqamat (singular, maqam) and Turkish makamlar (singular, makam) are often thought of by Western musicians as the equivalent of the Western concept of scales. However, Arabic music has over 50 maqamat, which means there are over 50 versions of intervallic structures that are used in Arabic music. Same with Turkish music: Turkish music has over 50 makamlar, and Persian music has just over 10. The sheer number seems overwhelming if you think of maqamat as loosely equivalent to Western scales. However, maqamat are actually built from smaller components and these smaller structures contain the controlling intervallic structures. Arabic music buids on ajna (singular, jins) of 3,4 and 5 notes each; Turkish music on tetrachords and pentachords of 4 and 5 notes each. [Note: trichord, tetrachord and pentachord are occasionally used instead of 'jins' when discussing Arabic music.]

There are a dozen (or so) commonly used ajna in Arabic music; ditto for Turkish music. Thinking in terms of combinations of these smaller components makes the task of learning the maqams less overwhelming.

In addition to making maqammat/ makamlar easier to memorize, the smaller components are associated with principles of modulation, moving from one maqam/ makam to another, which enhances ease of performance and improvisation.

Notating Microtones

"Classical Arab music is monophonic, and is based on melodic modes called maqam (plural, maqamat). These melodic modes often utilize microtonality: intervals that are smaller than the half-step and whole-step used in traditional Western art music. Unlike Western art music which uses twelve intervals to divide the octave, modern Arabic music theory divides the octave into twenty-four equivalent intervals (quarter-tones are used to achieve this scale). When Western notation is used to notate these quarter tones, a flat symbol with a slash through it is usually used for half-flats, and a sharp with only one vertical line is used for half-sharps. Some Arabic musicians use the 24 note scale as a point of reference, and assert some notes deviate even further from this scale by the slight interval of "a comma" (kuma). They use terminology such as the note should be played "a little high" or "a little low" to express how the note should be slightly lowered or raised from the note's standard position."— RK Deverich

Quarter-Tone Notation suggested by MicroTonalTrumpet.com

Eighth-Tone Notation as suggested by MicroTonalTrumpet.com.

Arrowheads are being added to some contemporary notation systems to indicate the direction the pitch should be pushed to.

Learning to Hear and Play Microtones

Karim Nagi and Sami Shumay, on the other hand, recommend listening to and singing along with recordings before picking up the instrument. Get the tones you want fixed in your mind and then aim for them with your instrument.

Eighth tone are the building blocks.

• The fundamental eighth-tone is approximately 24-25 cents and is also known as a Pythagorean comma.
• To achieve an eighth-tone adjustment, the performer slightly raises or lowers the original pitch until the effect of moving away is first recognized.
• An eighth-tone adjustment can be described as a rounding off or pushing up of an intonation, or playing just under or over the pitch.

Quarter-tones:

• The quarter-tone exists midway (48-50 cents or 2 Pythagorean commas) between any two half-tones, with neither half-tone predominating. To locate the quarter-tone, move away from the original pitch to the point where traits of both the original pitch and its neighboring half-tone are recognized and heard. It has a distinct quality which simultaneously is characteristic of both surrounding half-tones, yet is neither half-tone. Quarter-tones are sometimes referred to as neutral tones and are the basis of Arabic maqamat.
• Over time, the performer will develop sensitivity for how the eighth-tone and quarter-tone change pitch. Electronic tuners calibrated in cents are an ideal means of accurately measuring and identifying eighth and quarter-tones.
• If elements of the neighboring half-tone become apparent, the pitch has been altered by a quarter-tone (two eighth-tones).

• Tempered half-tones measured at 100 cents and whole-tones at 200 cents are equivalent to their respective Turkish tones of 90 and 204 cents.

Navid: Difference between quartertones in Persian, Turkish and Arabic Music:

• Persian overtones are flatter;
• Arabic are mid-way;
• Turkish are sharper.