Notes on Notation, Hexachords, and Polyphony (Transcript Notes)
Notation: From Neumes to Staffs
Early purpose of notation: primarily for preservation rather than perfect transport or absolute precision; notational systems varied across world regions and disciplines.
Neumes and their limitations: shapes were informal and didn’t provide as much specific information as later printed notation.
Shift to specificity: the introduction of staff lines made notation more precise; from single-line orientation to full staffs; over time, pitch names were attached and then evolved into the modern notation we use today.
Hexachord system: pitch organization before fixed pitches. The main hexachords discussed were:
The G hexachord: g, a, b, c, d, e. Where is the half step in this set? Between B\text{ to }C. Also, starting on C places the half step between E\text{ and }F.
The F hexachord: included an accidental, the B\flat, to avoid an undesirable tritone between B\text{ natural} and F.
Tritone avoidance: the tritone is typically described here as the interval between B\flat and F (in the unaltered set, this would be the B–F tritone when spelled as B natural vs F).
Solmization and half steps:
The helpful way to imagine pitch naming in the mode system is via the solfege sequence do, re, mi, fa, sol, la; the half step occurs between mi and fa (in the notation starting on C, that’s between E and F).
If you sing the sulfate syllables, a jump from mi to fa is a half step; otherwise, it’s a whole step.
Overlapping hexachords and mutation:
Overlapping hexachords allowed an extended range by mutating from one hexachord to another, effectively re-mapping the starting pitch to the next hexachord.
This created a practical way for leaders to indicate different pitches across the hand positions, enabling a wider pitch range to be used without reading an entirely new notation.
The singer could reproduce these pitches by following the leader’s hand gestures rather than reading a new staff for each range.
Practical example of hexachord usage:
G hexachord and its relation to pitch naming across hexachords. The same note (e.g., G) could be named differently depending on which hexachord it belonged to (e.g., “G in the G hexachord” vs. “G in the C hexachord”). Terms used in the lecture include variants like g\text{ oot}, g\text{ soul}, or g\text{ ray} (illustrating the idea of overlapping systems and naming conventions across hexachords).
Notation’s broader musical context:
Notation development occurred alongside the rise of polyphony in church music; this period saw competing demands for both precision and interpretive flexibility.
By this stage, notation shifted from a primarily mnemonic tool to a system that also supported more complex musical planning and teaching.
Polyphony: Emergence and Its Context
Polyphony birth and diffusion:
Polyphony appeared around the same period as notation development and spread from folk contexts into church music.
Polyphony often involved multiple voices with at least one drone (an anchor). The drone voice provides a sustained pitch while other voices move melodically.
Geographic and liturgical context:
Eastern Orthodox churches adopted polyphonic techniques earlier than Western churches.
In the Western church, polyphony began to flourish around the 9th century; organum became a core early form.
Organum and its stylistic branches:
Florid organum (also called organum purum) features a drone in the lower voice with the upper voice singing florid, melismatic lines that move above the drone.
Discant (or discantus) refers to a style where the upper voice moves more rhythmically against the lower voice; the bottom drone often remains more sustained.
Text and texture in polyphony:
In the early stages, polyphony was often sung in sections rather than continuously; the same chant might appear alongside polyphonic sections.
As polyphony grew, there was a discernible division between professional performers (who would sing more complex, polyphonic textures) and amateur performers (who would continue with the unison or simpler chant portions).
World music contrast:
Indian traditional music, with its ragas and drone-based textures, represents a monophonic-dominated tradition that differs from the Western move toward polyphonic complexity.
Practical implications for church services:
Early polyphony occasionally lengthened liturgical services due to the melismatic lines and expanded musical material.
The Catholic church’s demand for textual clarity influenced how and when polyphony could be used within services.
The Drone and Instrumental Realities
Instruments and drone culture:
Drones likely arose from or were reinforced by instruments that can sustain tones, such as bagpipes and similar drone-based instruments.
Anecdotes from field observations describe early practices where a drone instrument’s sound was considered too loud to perform indoors, necessitating outdoor performance contexts.
Hurdy-gurdy and bagpipes as examples:
The hurdy-gurdy and bagpipe families illustrate early drone-based musical thinking and how drones support polyphonic textures when combined with melody lines.
Orthodox vs Western usage:
The drone-based approach to texture was common across various traditions, with Orthodox churches showing early adoption in some regions.
Notation, Rhythm, and the Notre Dame School
Rhythm in early notation:
Rhythm was not initially encoded via note values; it was notated through ligatures (connections between notes) that implied grouping and timing.
The ligatures informed performers how to group notes, contributing to the perception of legato (the term legato ultimately derives from ligature-based bound notation).
The six basic rhythmic patterns:
Notre Dame-era notation codified six basic rhythmic patterns, roughly parallel to poetic meters (e.g., patterns akin to iambic or trochaic groupings).
These patterns are tied to how notes are grouped within ligatures, guiding performance practice.
Basic patterns and structure:
A pattern might begin with three notes grouped together and then two, producing a long-long-short and similar groupings that define the rhythm.
A second mode of rhythmic organization (the written modes) starts with two notes and ends with three.
The two modes and their naming:
Mode 1 (as described in the lecture): pattern starts with three notes and ends with two.
Mode 2 (the “written modes”): starts with two and ends with three.