MofA Week 3: Music in theory, theory in practice

Announcements

• CSL sheets - must be signed and returned by September 26!
• See http://www.csl.ualberta.ca/ to sign up via their Portal, then print, sign, and return form to them directly.

Music Practicum and theory intro

• Ear training
  • maqam Rast: scale degrees, qafla
  • Durub: wahda, maqsum
  • Dulab Rast
  • Octave species of the Rast scale: Rast, Bayyati, Sikah
• Concepts in practice (refer to http://maqamworld.com)
  • Pitch, interval, tetrachord, scale, mode (bu`d, jins, sillim, maqam)
  • Scale as the sum of two or more ajnas ("tetrachords") - conjunct or disjunct; lower and upper - defining key tones (qarar, ghammaz)
  • Tetrachords: Rast, Bayyati, Sikah (lower) PLUS Rast, Nahawand (on G)(upper)
  • Maqam upper tetrachord variants: switch to Hijaz to get: Suznak, Shuri, Huzam. (Detect which maqam I'm playing).

Review

• Main phases of Arab - Islamicate history
• Bird's eye view of the history of "Arab music" in the "Arab world"
• Film: Dananeer (1940). Beautifully illustrates multiple phases of this history via different readings of this classic film, starring Umm Kulthum in the role of a qayna (take notes and write up in your SC paper)

1. as an (explicit) representation of 9th c Abbasid culture (the era of Harun al-Rashid and the Islamic Golden Age in Baghdad): REFERENCE
2. as an (implicit) representation of Egyptian perceptions of "Arab history" in 1940: SOURCE
3. as an (implicit) representation of Egyptian film music in 1940: SOURCE.

What sorts of Arab music culture did you find in the film? (consider: musical style, transmission, famous personalities, musical roles, social life, urban/rural divide, ethnicity...)

• What is music of the Arab world? Unity and diversity. Key:
  • Arab language. Singing is central, and so is poetry, hence language itself. (NB: For Greeks, "music" is the art presided over by the Muses, especially poetry sung to music)
  • Tonal and rhythmic theory. We'll turn to this today.

Theory and practice in Arab music

• consider the relation among
  • formal (music) theory (e.g. philosophical treatises)
  • informal discourse (about music) (e.g. work of Scott Marcus on intonation, modulation)
  • (musical) practice (composition, improvisation) (e.g. analysis of performances by Dr Jihad Racy)
• In relation to practice, theory can be
  • Prescriptive (and then often ideological, polemical): streamlined (Safi al-Din al-Urmawi)
  • Descriptive (ethnographic): accumulative (al-Farabi)
  • Autonomous and metaphysical (often venturing far beyond music per se, a metaphor for cosmic relationships: e.g. cosmological theory, music of the spheres, relation of modes to zodiac, seasons, bodily humors...we'll talk about this next week)
• Why read music theory?
  • Theory projects ideologies of musical aesthetics, helps to attain an emic understanding
  • Theory condenses broader cultural values
  • Theory reflects cultural politics (e.g. Abbasid inclusiveness)
  • Theory reflects broader historical and discursive trends and provides historical insights (e.g. influence of Greek philosophy, Western practice)
  • Theory may be useful to you as a musician!
• Arab music theory includes:
  • Focus on urban "art" music synthesis (a complex mix of Arabian, Persian, Byzantine, and other musics, a fusion catalyzed by Islamicate civilization), but not music of rural areas, local music, music of ethnic minorities, or religious music
  • High value of music (from Greeks) that "music" is a key subject for philosophy, part of the medieval "quadrivium" (arithmetic=number, geometry=number in space, music=number in time, astronomy=number in space/time) traceable to the Greeks (Pythagoras, Plato) via Roman Boethius (6th century) {contrasted with the lower trivium: study of rhetoric, grammar, logic}
  • Borrowings from Greek theory (from Euclid to Aristoxenus via Bayt al-Hikma), but adapted to new musical practices (word "musiqa" itself comes from Greek and designates at first music theory)
  • Scientific/descriptive theory
    • Acoustical and psychoacoustical theory of
      • pitch, interval, tetrachord, scale
      • rhythm and meter
    • Modal theory of maqam
    • Theory of melody, composition
    • Theory of musical instruments
  • Objective (cosmological) theory: music's connection to the cosmos
  • Subjective (microcosmological) theory: music's influence on the human being
    • Music therapy
    • Music, emotion (tarab), spirituality (sama`)
    • Music and ethos
  • Musical polemics vis a vis Islam
    • Malahi
    • Sama`

A crash course in acoustics and tonal theory

• Music is mathematics, number in time - part of the quadrivium
• Review of basic pitch, frequency, interval concepts

Medieval Arabic theory of music (science, metaphysics)

• Caliph Ma'mun (r. 813-33) and Bayt al-Hikma
• Influence of Greek philosophical treatises on Arab music theory
  • Word "musiqi" ("musiqa") enters Arabic from Greek, comes to imply theory
  • Pythagorean tuning
  • Double octave system
  • Tetrachords
  • General notion of systematic exposition
  • Music theory as a principal philosophical pursuit, part of quadrivium (music, arithmetic, geometry, astronomy)
  • Importance of music in any philosophical oeuvre
  • Music theory as also applied and mnemonic
• Key figures: philosophers
  • al-Kindi (d. 870)
  • al-Farabi (d. 950)
  • Ikhwan al-Safa (late 10th c)
  • Ibn Sina (d. 1037)
  • Safi al-Din al-Urmawi (d. 1294)
• Two kinds of theory:
  • Sonic, mathematical, and aesthetic (we'll talk about this today)
  • Metaphysical and spiritual (we'll talk about this next week)
• Difficulties in interpreting medieval theory
  • Relation of theory and practice? Theory may be prescriptive, descriptive, or independent.
  • Theory of earlier period is filtered by later ideologies
  • Many works and all sound is lost
• Components of theory of sound in Arabic writings
  • Tonal theory (our focus today)
    • gamut: full pitch or interval set, a “tuning system”
    • Scales: structured subsets, usually 7 tone, with additional structure added (tetrachords, tonic)
    • Melodic modes: melody-generators – scales with additional structure.
  • Rhythmic theory

Basic acoustical concepts underlying Arab music theory

• review from Tuesday
• Time signal
• Periodic signal: a signal repeating exactly, over all time (cps or Hertz)
• Locally periodic signal: a signal repeating exactly, for a while...
• Period: shortest duration over which signal repeats
• Frequency: reciprocal of period
• Sound: pressure wave as time signal
• Pitched sound: locally periodic signal
• Constant pitched sound: fixed period or frequency (e.g. A4 = 440 cps)
• Musical interval: fixed frequency ratio (e.g. octave = 2/1, fifth = 3/2, major 2nd = 9/8)
  • To stack intervals, multiply ratios (e.g. up two octaves = 4; up two fifths = 9/4)
  • For intervals, reciprocals are equivalent but opposite
    • Ratio > 1 is ascending
    • Ratio between 0 and 1 is descending
    • ex: 3/2 = "up a fifth", 2/3 = "down a fifth"
• Octave equivalence and reducing intervals to a single octave
  • Octave stretches from ratio 1 to 2 (e.g. 440 cps to 880 cps)
  • if the ratio is >2, then divide it by 2, and repeat until it's between 1 and 2
  • if the ratio is <1, then multiply it by 2, and repeat until it's between 1 and 2
  • ex: "up two fifths" = 9/4, but 9/4 > 2, so reduce it to 9/8
  • ex: "down a fifth" = 2/3, but 2/3 < 1, so reduce it to 4/3
• Equal divisions of the octave
  • Tempered semitones (octave divided in 12 equal parts, S, such that S x S x S x S x S x S x S x S x S x S x S x S = S^12= 2
  • Cents (tempered semitone divided in 100 equal parts)
• Measuring frequency ratios in intervallic units (log scales)
  • Given a frequency ratio R, how many octaves does it contain?
    • Need to determine how many 2s in the sequence: 2x2x2x...x2 = R
    • Answer: log(R) base 2
    • E.g.: how many octaves are in the frequency ratio 32?
  • Given a frequency ratio R, how many tempered semitones does it contain?
    • Need to determine how many tempered semitones in the sequence: S x S x S x ... x S = R
    • Answer: log(R) base S
    • E.g.: how many tempered semitones are in the frequency ratio 3:2?

Pythagorean scales - summary

• Consider a series of fifths (3/2) always reduced to a single octave:
  • let a fifth be represented as @, ascending fifth @^1, descending fifth @v1
  • ascending series: @^1, @^2, @^3, @^4...
  • descending series: @v1, @v2, @v3, @v4...
• Then:
  • @^2 = ^whole tone = (3/2)*(3/2)*(1/2) = 9/8
  • @v1 = ^fourth = (2/3) * 2 = 4/3
  • @v5 = ^limma = (2/3)^5 * 2^3 = 256/243 = L
  • @^12 = ^Pythagorean comma = (3/2)^12 / (2^7) = 3^12/2^19 = 531441 / 524288 = ^C
• See spreadsheet circle graph
• Creating a whole tone out of limmas and commas
  • What is @^7? @^7 = up seven fifths = up twelve fifths, down 5 fifths = @^12 - @^5 = comma + limma = ^CL
  • @^2 = @^7 - @^5 = CLL = whole tone = ^LLC
• The Pythagorean diatonic (heptatonic scale)
  • Fundamental plus 6 ascending fifths creates a scale: @^0, @^1, @^2, @^3, @^4, @^5, @^6
  • Taken in frequency order: @^0, @^2, @^4, @^6, @^1, @^3, @^5
  • Now start with @^1: @^1, @^3, @^5, @^0, @^2, @^4, @^6, repeating to @^1
  • In fifths: up 2, up 2, down 5, up two, up two, up two, down five, etc.
  • ..."up 2" = whole tone, or LLC
  • ..."down 5" = limma, L
  • Scale becomes: LLC LLC L LLC LLC LLC L
  • Note this scale contains two small intervals (limmas): @^5 to @^0, and @^6 to @^1. But they're non-adjacent (separated by whole tones).
  • Aside: Why seven tones?
    • If we added an eighth - @^7 - it'd fall between @^0 and @^2 - we'd have @^0, @^7, @^2, @^4, @^6, @^1, @^3, @^5
    • and thus three small intervals in a row:
      • @5 to @0 = limma (5 fifths)
      • @0 to @7 = limma + comma (7 fifths)
      • @7 to @2 = limma (5 fifths)
  • Aside: Naming
    • Since we use just 7 tones, we can name them with 7 letters (from @1): C D E F G A B
    • Note that @0 is F, and @6 is B.
    • If we shift everything up by a fifth, then we drop F=@0 and add @7, which is higher than F by LC, between F and G. So we can call it F#. Shift everything up another fifth and the note C drops out, replaced by C# (you can now see how key signatures are formed). The interval between a letter name and the same letter name shifted up or down by adding or subtracting a single flat or sharp is equivalent to a movement of 7 fifths; it's LC.
    • The limma interval corresponds to the 7th to tonic interval -- and the 3rd to 4th -- in the major scale; it's embedded in the scale, so its two tones - differing by a limma - must have successive letter names, e.g. E to F (@5 to @0, F# to G (@7 to @2)
    • Three intervals in the chromatic series: F - Gb - F# - G = L C L (F to Gb and F# to G are leading tone relations, while Gb to F# corresponds to 12 fifths - a Pythagorean comma. So ^C corresponds to respelling the note using the next lower letter.
• Compare: Pythagorean, Just, and Tempered scales (see spreadsheet, hear Audacity files)

Refer to spreadsheet and associated audio examples

concepts for tonal system theory (e.g. maqam, rag)

• components of tonal system: structured set with melodic pathways or material
  • collection (set) of pitches or intervals
  • tonal functions defined on the set: tonic, dominant, etc. on those pitches or intervals
  • mode - melodic tendencies, network pathways, materials ("licks") based on the set
• pitch or interval set
  • pitch scale degrees (cps)
  • intervals (ratios, cents)
  • Just vs equal tempered intonation
  • Pythagorean theory
• scale: structured set
  • decomposition: genres (ajnas)
  • pitch functions
    • tonic (qarar)
    • dominant (ghammaz)
    • subdominant
    • points of repose (marakiz)
    • leading tone
• mode: network defined on the set
  • tonal ornaments
  • context-sensitive intonation, allotones
  • melodic patterning, material
  • scalar direction
  • progression of melodic development

Tonal theory in medieval period in Arabic-speaking regions

• Theory is closely linked to instruments, particularly chordophones (ud and tanbur), providing flexible visual representation (monochord was Greek theoretical instrument)
• Most often the `ud serves as reference
  • 5 strings (low to high): bam - mathlath - mathna - zir - hadd (mix of Arabic and Persian terms)
  • 4 frets: sababa - wusta - binsir - khinsir (names of the fingers: index, middle, ring, pinky)
  • 5 notes per string (but some are variable)
  • Each string provides a tetrachord (jins)
  • Jins species (anwa`)
    • First degree fixed (mutlaq)
    • Fourth degree fixed (binsir) - major 3rd
    • fifth degree fixed (khinsir) - perfect 4th
    • Second and third degrees are variable (sababa and wusta)
  • Jins combine to form scales, basis for modes

Theoretical approaches

• Theorization of Old Arabian school (Hijazi, practical but with retroactive Greek and prescriptive influence): e.g. Ibn al-Munajjim
• Theory of the philosophers: e.g. al-Farabi (Greek influence, with multicultural ethnographic approach)
• The Systematists: e.g. Safi al-Din al-Urmawi (prescriptive systematizer)
• Modern theorists from the 19th c onwards (e.g. Michel Mashaqa and equal temperament)

Refer to spreadsheet and associated audio examples

Informal discourse about music

• Intonation
  • (Marcus article)
  • Sami Abu Shumays on microtones
• Modulation (Marcus article)

Musical practice

• of Dr Ali Jihad Racy, analyzed in Taqsim Nahawand (Nettl and Riddle article)
• video of Dr `Atif `Abd al-Hamid (Cairo)
• examples at www.maqamworld.com

For next time: select one maqam from www.maqamworld.com. Study the maqam's structure as presented there, and listen to all the examples. Using these examples as models, develop your own composition or improvisation in the same maqam.