Organum – discantus – contrapunctus in the Middle Ages

Reading guide
Christensen, ch. 15
“Organum – discantus – contrapunctus in the Middle Ages” by Sarah Fuller
Know who and where Fuller is.
Preparation:
?
p. 477
1 incipit = beginning, i.e. first words
What intervals are allowed between the two voices according to Quilibet affectans?
What two categories are these intervals assigned to?
Which intervals are allowed to move in parallel motion?
Which intervals are allowed at neginnings and endings?
2
How does the implied definition of “theory” compare to what we read in Bower and Cohen?
p. 478
0 How does the tone of Cum notum sit differ from that of Quilibet affectans?
1 When are these two treatises from? When does writing on counterpoint begin?
2 Does the medieval history of counterpoint theory form a continuous line of development?
p. 479
0 First we heard that if it doesn't have to do with composition or performance, it's not real
theory. Now we hear that instruction in composition and performance isn't intellectual.
Surely the truth is somewhere between these two extremes!
1 Of the four common kinds of rules, which does Quilibet affectans deal with?
p. 480
2 What centuries correspond to each of the three special words in the title of the chapter? (Look
here and at the subheadings through the rest of the chapter.)
3 Where are the first accounts of multi-voiced singing found?
What is a symphonia, and which intervals are recognized as symphoniae?
p. 481
1 Now we see why the enchiriadis treatises have a tone system that replicates intervallic patterns
at the fifth!
Refer back to the enchiriadis tone system on p. 324 as you follow the explanation of organum
at the fourth below.
p. 482
0 Which harmonic intervals other than symphoniae are used in the oblique motion associated
with organum at the fourth?
1 Has organum changed much by Guido's time?

p. 483
0 What four harmonic intervals are used in “flexible” organum according to Guido.
Note: it is common to rank the harmonic intervals. What is Guido's ordering?
p. 484
How closely do the theoriectical accounts seem to reflect practice?
Chapter 15 – p. 2
p. 485
Heading and 1 What other term is used to refer to two-part writing in the 1200s?
What is the significance of the new term?
What “retronym” is given to chant? (Ask me in class about retronyms.)
How are the eight modes treated in the discantus theories?
How is the word mode used in the discantus writings?
2 Who is the author of the key Parisian treatise on musica mensurabilis? What is its title?
th
Coussemaker was a 19 -century French musicologist who discovered, collected, and
transcribed many early manuscripts on music. He published a four-volume set of Latin
works entitled Scriptorum de musica.
p. 486
0 According to John of Garland, how are the two independent voices coordinated?
How many harmonic intervals does John put into his hierarchy? How are they ordered? Are
there any surprises there?
What numerical justification does John give for his hierarchy? What details show that he isn't
exclusively following an abstract mathematical theory in constructing his scheme?
p. 487
1 A little confusing: an earlier treatise is named, but I think the rest of the paragraph continues
to refer to John of Garland.
What two reasons are given for waiving certain rules based on the intervallic heirarchy?
John of Garland is characterized as part of an intellectual tradition of discantus writing. Why?
2 What characterizes the other tradition of discantus writing?
p. 488
1 A little confusing again. Note that Fuller now places “Discantus positio vulgaris” among the
treatises that show which intervals to write with few explanations. Notice that the title
indicates that this is the common way to do it, not the elite way.
Are accidentals mentioned in these treatises?
What kinds of general rules are mentioned occasionally?
p. 489
0 According to Fuller, why does the intervallic-succession tradition avoid general explanatory
rules? What do you think: Did this policy necessarily reflect good pedagogy?
1 According to Anonymous IV, what distinguishes discantors from plain singers?

Chapter 15 – p. 3
p. 490
1 Fuller says that variety of content among contrapunctus treatises, most of which exist in only
one copy, suggests an informal pedagogical motivation. Why do you think this would be
so? What other kind of treatise does Fuller mention here?
th
2 In the new, 14 -century terminology, what is the difference between contrapunctus and
discant?
p. 491
0 How do the new rhythmic ideas of rhe ars nova relate to contrapunctus teaching?
1 What intervals begin to counted among the consonances (suitable for note-against-note
counterpoint) in this new phase?
What interval formerly commonly counted as a symphonia is now not among the
consonances?
How do the theorists talk about unstable intervals?
What are the most common combinations of imperfect interval and resolution?
What staple pattern of organum is now prohibited in contrpunctus teaching?
p. 492
1 This topic may get overlooked in this book: The Berkeley manuscript, sometimes attributed to
Goscalcus, recognized various accidentals and added them to the accepted tone system by
means of Guidonian hexachords in different places. Any accidental makes a half step, and
MI-FA marks the half step in the hexachord. So F can occur if G becomes FA. E can
occur if D becomes MI.
2 Add these three names to your list of theorists. Go through the example carefully and note
how accidentals are used to make the imperfect interval as “close” to the perfect interval
as possible while still being consonant. (Refer back to the three common combinations of
intervals on p. 491.) In each case, what interval would be occur without the inflection?
What interval would result if a second accidental were added, making the imperfect
interval even closer to the perfect consonance ?
p. 493
0 Who characterizes ficta as coloring a note? What word do we use that comes from the Greek
for color?
1 What two treatises are mentioned as teaching how to create rhythmicized, elaborate
decorations of note-to-note contrapunctus?
p. 494
0 What combination does the “Parisian theorist” (Goscalcus, author of the Berkeley manuscript
of 1375) see as a basic error even in elaborated polyphony?
1 Dissonances begin to be discussed in the treatises on decoration. How much are they used?
2 etc. Here's a method for improvising a big, complex sound that requires only one singer versed
in contrapuntal technique. It's a kind of music that doesn't get into anthologies because it
never got written down. How is this technique like and unlike the doo-wop texture of 50

years ago or other improvised, popular vocal textures?
Chapter 15 – p. 4
p. 496
1 How does the Italian gradus system make beginning counterpoint easier?
2 How does the English “sights” system work, and how is it similar to the gradus system?
p. 497
1 What restrictions does the faburden system add to the sights system? What three-note
sonorities result? What contrapuntal rules does the faburden system follow that the sights
system may not?
p. 498
1 What fifteenth-century theorist transmits English faburden practice to Italy?
2 and p. 499 0 Fuller stretches the term “Middle Ages” and looks to the future here. How
does the Renaissance theorist Tinctoris differ from most contrapuntal theorists before him.
th
What earlier 15 -century theorist makes this distinction? (More on these two and Ugolino
in other chapters.)
p. 499
1 Hugo Riemann's book is considered the first attempt at a comprehensive history of music
theory. What criticism does Fuller have of the book?
Summary
What three stages of theory does Fuller outline?
What two treatises does she present as representative of the first stage? How do their focuses
differ?
What two treatises does she present from the second stage? How do their focuses differ?
What branches of contrapunctus theory does Fuller trace? Who respresents each?