MofA Week 3: Music in theory, theory in practice

Announcements

• Article presentations
• Film: Dananeer (1940) = (watch this on your own)
  • Three ways of reading 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)
2. as an (implicit) representation of Egyptian perceptions of "Arab history" in 1940
3. as an (implicit) representation of Egyptian film music in 1940

Review

• Ear training:
  • Rast: scale degrees
  • Octave species: Rast, Bayyati, Sikah. Detect which maqam I'm playing.
  • Durub

• Bird's eye view of the history of "Arab music" in the Arab world

• Empirical investigations
  • Your empirical investigations and analyses
  • Comparative ethnomusicology: Berlin Phonogramm Archiv

• A contemporary typology of Music in the Arab world

Theory and practice in 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)
  • Descriptive (ethnographic)
  • Autonomous (often venturing far beyond music per se, e.g. cosmological theory)
• Reading music theory...
  • Theory projects ideology of musical aesthetics
  • Theory reflects broader historical and discursive trends (e.g. influence of Greek philosophy)
  • Theory condenses cultural values
  • Theory reflects cultural politics (e.g. Abbasid inclusiveness)
• Arab music theory includes:
  • Focus on urban "art" music (itself a complex mix of Arabian, Persian, Byzantine, and other musics, a fusion catalyzed by Islamicate civilization)
  • Idea (from Greeks) that "music" is a key subject for philosophy (quadrivium: arithmetic, geometry, astronomy, music)
  • Borrowings from Greek theory, 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`

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 as part of quadrivium (music, arithmetic, geometry, astronomy)
  • Importance of music in any philosophical oeuvre
• 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 (we'll talk about this today)
  • Metaphysical (we'll talk about this later in the course)
• 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 music theory, the circle of fifths, naming notes and intervals (see spreadsheet, hear Audacity files)
  • The octave (2/1)
  • The fifth (3/2)
    • as generator of an infinite series (3^n/2^n)...
    • ...but reduced to a single octave (3^n/2^m)
  • The fourth (4/3) = down a fifth (2/3) raised an octave
  • The tone (9/8) = up two fifths
  • The limma (256/243 = 2^8/3^5) = up five fifths
  • The comma (Pythagorean comma)(3^12:2^19) = up 12 fifths
• Pythagorean, Just, and Tempered scales (see spreadsheet, hear Audacity files)

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: bam - mathlath - mathna - zir - hadd
  • 4 frets: sababa - wusta - binsir - khinsir
  • 5 notes per string (but some are variable)
  • Each string provides 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, with retroactive Greek and prescriptive influence): e.g. Ibn al-Munajjim
• Theory of the philosophers: e.g. al-Farabi (Greek influence, ethnographic approach)
• The Systematists: e.g. Safi al-Din al-Urmawi (prescriptive systematizer)
• Modern theorists from the 19th c onwards

Refer to spreadsheet and associated audio examples

Informal discourse about music

• Intonation (Marcus article)
• 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.