MofA Week 3: Music in theory, theory in practice

From CCE wiki archived
Jump to: navigation, search


  • CSL sheets - must be signed and returned by September 26!
  • See to sign up via their Portal, then print, sign, and return form to them directly.
  • How to log into our youtube/gmail account...
  • You're all joining a band! Here are the tentative El Mastaba band assignments (spreadsheet). Each group will have a Zotero group where you'll list relevant bibliographic materials. Please check out Zotero and become familiar with how it works.
  • Take 3 minutes to introduce yourselves and exchange emails. See me if you have questions.
  • Let's review how to access videos on our YouTube account.
  • CSL with El Mastaba
  • El Mastaba in the Egyptian revolution (time permitting)

Music Practicum and theory intro

  • Ear training
    • maqam Rast: scale degrees, qafla
    • Durub: wahda, maqsum
    • Dulab Rast


  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...)

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) vs. Descriptive (ethnographic): accumulative (al-Farabi)
    • More practical vs. more philosophical
    • More musical vs. 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`

Thursday - intro

Ahlan wa Sahlan! - "Ahlan Biik!" ("Ahlan Biiki" for female, "Ahlan Biikum" for group)



  • Begin your annotated bibliographies immediately. You should have received Zotero group invitations; I will be browsing these groups to help out. Please sign your annotations by adding your name. Remember: an annotation comprises: (a) what's this book/article about? (b) what are its limitations? (critique: from "source" to "reference")
  • Try looking up your topic in various online encyclopedias, then check for bibliography there - including
  • Some databases to check (besides the library catalog):
  • Think about a paper topic. I'll ask you to hand in proposals in a few weeks.
  • Watch videos associated with your group, and begin to think about how you'll annotate and edit.
  • Start learning the Arab world countries and capitals for map quiz (Identify 22 countries of the Arab League, their capitals, and approximate populations. ) Practice website is available under Resources.

warm up:

  • maqam rast, dulab, with durub: wahda, maqsum
  • Darb: sama`i with Rast and modulation to Suznak, Nahawand, Nawa Athar
  • Octave species of the Rast scale: Rast, Bayyati, Sikah
  • Concepts in contemporary Egyptian/Levantine practice (refer to and MENAME theory resources
    • Rhythmic theory:
    • Tonal theory (see
      • Pitch, interval, tetrachord, scale, mode (naghama, bu`d, jins, sillim, maqam)
      • Pitch understood as related to vibratory speed, frequency
      • Interval understood as a ratio of frequencies, or string lengths
      • Tetrachord understood as a group of pitches, often 4 and sometimes 3 or 5, usually within the span of 4/3 or 3/2.
      • Scale as the sum of two or more ajnas ("tetrachords") - conjunct or disjunct; lower and upper - defining key tones (qarar, ghammaz)
      • Tetrachords: Rast, Hijaz, Nahawand, Nawa Athar
      • Rast becomes Suznak by replacing upper tetrachord with Hijaz
      • Rast becomes Nahawand or Nawa Athar by replacing lower tetrachord with Nahawand or Nawa Athar.
      • Try to determine which maqam I'm playing

Medieval Arabic theory of music (science, metaphysics)

  • Caliph Ma'mun (r. 813-33) and Bayt al-Hikma
  • Influence of Greek philosophical-scientific 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) [Epistle 5: On Music]
    • 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 as mnemonics, understood in conjunction with oral tradition - often details of the written tradition are incomplete and impossible to interpret unambiguously (see Wright on Ibn Munajjim)
    • Theory of earlier period is filtered by later ideologies
    • Many works and all sound is lost
  • Components of theory of sound in Arabic writings
    • Rhythmic theory of cycles or modes: iqa`, usul, or darb
    • Tonal theory (our focus today)
      • pitches, intervals
      • gamut: full pitch or interval set, a “tuning system”
      • ajnas (singular: jins): tetrachords
      • Scales: structured subsets, usually 7 tone, with additional structure added (tonic, dominant, starting, ending tones)
      • Melodic modes: melody-generators – scales with additional structure.

Basic acoustical concepts underlying Arab music theory

(use Audacity, tone generator, spreadsheet and associated audio examples to illustrate)

  • Time signal: music is number in time
  • Periodic signal: a signal repeating exactly, cycling - over all time (cps=cycles per second, or Hertz)
  • Locally periodic signal: a signal repeating exactly, for a while...
  • Period: shortest duration over which signal repeats (e.g. 0.0023 seconds)
  • Frequency: reciprocal of period, the number of periods per second (e.g. 1/0.0023 seconds = 440 Hertz)
  • Sound: pressure wave as time signal
  • Pitched sound: locally periodic signal
  • Constant pitched sound: fixed period or frequency (e.g. A4 = 440 Hertz)
  • 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 = 4/1; up two fifths = 9/4)
    • For intervals, reciprocals are equivalent but oppositely directed:
      • Ratio > 1 is ascending
      • Ratio between 0 and 1 is descending
      • ex: 3/2 = "up a fifth", 2/3 = "down a fifth"
    • String length ratio is the reciprocal of frequency ratio:
      • dividing a string in half raises the open string pitch by an interval 2/1 or an octave
      • dividing a string into 1/3 and 2/3 and plucking the longer segment raises the open string pitch by an interval of 3/2 or a fifth
  • DEMONSTRATION: with tone generator (from A 440 illustrate: ratios 2/1, 1/2, 3/2, 9/4, 9/8 = 880, 220, 660, 990, 495)
  • Octave equivalence and reducing intervals to a single octave
    • Two pitches that are an integral number of octaves apart (ratio: 2/1, 4/1, 8/1, 16/1...) sound "sort of" the same (same "chroma", different "height").
    • That is, multiplying or dividing the frequency by a power of two doesn't change the pitch "chroma"
    • A single octave can be represented by all ratios between 1 and 2 multiplied by the lower octave frequency (e.g. 440 Hertz to 880 Hertz)
    • All pitches can be mapped into this octave without changing chroma, as follows:
      • 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 and cents
    • 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
    • S = 12th root of 2
    • Cents (tempered semitone divided in 100 equal parts)
    • Each tempered semitone comprises 100 cents.
    • Thus there are 1200 cents to the octave.
    • All intervals can be measured in cents (or any other interval)
  • 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? How many cents?
      • Need to determine how many tempered semitones in the sequence: S x S x S x ... x S = R
      • Answer: Number of SEMITONES = log(R) base S. Number of CENTS = 100 * # semitones
      • E.g.: how many tempered semitones are in the frequency ratio 3:2? Take log(3/2)base (12th root of 2) = 7.02 semitones or 702 cents.

Pythagorean scales - summary

  • Greeks sought just intonations: frequency (string) ratios always whole numbers (ideally small ones!). Only in modern times were tempered intonations introduced, subdividing the octave into equal pieces.
  • Your ear hears octaves as a kind of unison (different pitch "height", but same "chroma") - an octave doesn't present "new" pitch content, from a certain standpoint.
  • Basic ratios: 1/1 (unison), 2/1 (octave)...and the all-important 3/2 (generating "new" pitches).
  • What's important to recognize is that a sequence generated by 3/2 never repeats, even when wrapped back into a single octave. There's a clash between the "new" of 3/2 and the "same" of 2/1.
  • Greeks used "monochord" to illustrate intervals (whereas Arabs would use the `ud, the tambur, and other instruments). Try this Monochord simulator
  • Observe graph on spreadsheet and listen to accompanying examples: construction of the diatonic scale.
  • Note:
    • ^ Tone (@^2)
    • v Limma (@^5)
    • ^ Comma (@^12)
  • Then go through the following theory (time permitting).


  • Consider a series of fifths (3/2) always reduced to a single octave (by moving pitches up and down an integral number of octaves when necessary)
    • let a fifth be represented as @, ascending fifth @^1, descending fifth @v1
    • start at @0
    • ascending series: @^1, @^2, @^3, @^4...
    • descending series: @v1, @v2, @v3, @v4...
  • Then:
    • @^2 = ^whole tone = (3/2)*(3/2)*(1/2) = 9/8 (about 204 cents)
    • @v1 = ^fourth = (2/3) * 2 = 4/3
    • @v5 = ^limma = (2/3)^5 * 2^3 = 256/243 = L (about 90 cents)
    • @^12 = ^Pythagorean comma = (3/2)^12 / (2^7) = 3^12/2^19 = 531441 / 524288 = ^C (about 24 cents)
  • 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 @^5 corresponds to the small intervals -- 7th to tonic interval, and 3rd to 4th -- in the diatonic 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)
      • Divide a whole tone F-G as follows: From F ^@5 gets us to the note for which F is leading tone, which we can call Gb. Two more ^@2 moves us up a whole tone, which is also @^5 from G, i.e. G's leading tone, F#. These two leading tones are separated by @12 hence by a comma. So the interval F-G is divided: F (L) Gb (C) F# (L) G.
      • Thus: 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

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) (debate as to whether these are theoretical or real frets)
    • 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: scale and mode

  • Theorization of Old Arabian school (Hijazi, practical but with retroactive Greek and prescriptive influence): e.g. Ibn al-Munajjim's version of Ibrahim al-Mawsili's practice, in early Abbasid period, supposedly linked to the earlier Ibn Misjah's 8 "finger modes"
  • Theory of the Philosophers: e.g. Ibn Sina, and al-Farabi's Kitab al-Musiqi al-Kabir (Greek influence, with multicultural ethnographic approach), mid-Abbasid period
  • The Systematists: e.g. Safi al-Din al-Urmawi's Kitab al-Adwar (prescriptive systematizer), late Abbasids
  • Modern theorists from the 19th c onwards (e.g. Michel Mashaqa and move towards equal temperament; Westernization/systematization for transposability)

Refer to spreadsheet and associated audio examples

Touma's interpretation of scales and maqam

  • Critical reading: attempts to differentiate the "pure Arabian" from Turkish or Persian, on the one hand, and Western music, on the other.
    • Pure Arabian scales vs. mixture with Greeks
    • Temperament as "western"
    • Space/time distinction: Arabian as "spatial" vs European as "temporal".
  • Maqam vs. taqsim
  • There are many mistakes and inaccuracies in these sections, perhaps partly due to faulty translations.

Contemporary concept of maqam in Egypt and Levant

Review from Tuesday:

Tonal system (maqam): based on 24 tone gamut out of which are extracted 7 tone scales, adding pitch function (structure). Mode (maqam) is scale with additional melodic information.

  • maqam:
    • 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 (hertz)
    • intervals (ratios, cents)
    • Just vs equal tempered vs. "musical" (practical) intonation
    • e.g. Pythagorean theory/Arab theory vs. 24 tone vs. musical intuition
  • scale: structured set, double octave
    • decomposition: genres (ajnas)
    • pitch functions
      • tonic (qarar)
      • dominant (ghammaz)
      • subdominant
      • points of repose (marakiz)
      • leading tone
      • final tone
  • mode: network defined on the set
    • tonal ornaments
    • context-sensitive intonation, allotones
    • melodic patterning, material
    • scalar direction
    • progression of melodic development

Informal discourse about music

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

For next time: select one maqam from 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.