Thoughts on Analytical Method for Post-Tonal Music

by Richard Hermann, UNM, Albuquerque, NM

I. Context

1. Social use and expectations - the politics, economics, etc. of music as a business.

2. Relations with other contemporary works - employing similar media and social function

(inter-opus relations).

3. If it is a movement of a work, relations with other movements (intra-opus relations).

4. Relations with historical works - employing similar media and social function. Watch out for the misuse of the past: attempting to literally apply the concepts of past musical systems to the present, e.g. traditional tonality to serialism, etc. In other words, if the analytical techniques developed for older repertoires yields strange results, perhaps you are using the wrong technique (assuming you are using it correctly).

II. Aural Familiarity Through Developed Listening Skills

1. Listen for patterns and segmentation points, etc...

2. Recall that starting and ending points, extreme values in various musical dimensions, and places of change in the direction of a progression of events in some musical dimension are more likely to be remembered. (Gestalt Psych., Contour)

3. Remember to listen for proximity in dimensions in time and also other dimensions of subdimensions such as pitch, register, density, dynamics, etc. (Gestalt Psych.)

4. Remember that recorded performances may not be accurate, and that they are interpretations that may not be very insightful!

III. Segmentation into Parts (perhaps at several nested levels)

1. Through recognition of patterns: recurring strings of ordered events in one or more musical dimensions or subdimensions;

2. Through recognition of significant contrast: change in musical dimensions of:

a. pitch, with subdimensions of pc, pc ints, pitch, pitch ints, pitch-space, pc-space, set-classes, row-classes, frequency bandwidth and density, etc.

b. time, with subdivision of meter, durations, attack-points, release-points, rate of change in pitch, pc, dynamics, density patterns, etc.

c. timbre, with subdivisions of articulation, dynamics, harmonic series structure, formant area structure, etc.

d. contour, which can relate entities across musical dimensions, the master or abstract musical dimension.

e. density

f. spatial location of sound sources (i.e. on stage, in performance, in 3-dimensional space in recordings, etc.)

IV. Relating Patterns and Segmentations

1. Consider the whole

2. Note which musical dimensions display patterning (structural or primary dimensions), and which musical dimensions aurally 'highlight' patterns in the structural dimensions (secondary dimensions). N.B. In fruitfully considering each piece, the analyst may need to define the relationships of which are primary and secondary musical dimensions. Do not assume that any particular musical dimension is always primary and another always secondary from piece to piece, composer to composer, etc.

3. How does this piece play against expectation generated from the heading Context above; if it actually does!

4. Typical strategies for constructing pieces or understanding them

a. inclusion/exclusion,

b. unusual or unique events: what is their role in relation to typical or expected events?,

c. express/suppress patterns, then reverse roles,

d. foreshadowing an idea then give it a more complete and extensive realization later,

e. liquidation, take an idea then gradually strip it of its distinctive features,

f. relate patterns through operations such as transposition, inversion, augmentation, diminution, etc., creating or recognizing equivalences,

g. relate patterns through similarity relations or inclusion relations, variation technique,

h. transforming one distinct pattern gradually into a different distinct pattern,morphing,

i. symmetry vs. asymmetry,

j. ordered, partially ordered, unordered relations.

5. Consider that some patterns may exist that cut across segmentation boundaries. They can act as links between segments. Recall that segmentations at anything but the largest and most global level have disjunctions or contrast (significant difference) in some musical dimensions (thereby causing the segmentation at that level), but also contain conjunction in other musical dimensions (thereby causing that segment to locally merge with others to create segments at more global levels).

V. Verification

1. Can you specify exactly what another musician should do in order to reproduce significantly similar results to yours? If not, your results may be dismissed as subjective or arbitrary. If reproduced by many, then you have 'intersubjective agreement', a kind of validation.

2. Are the methods you specify internally consistent as a theory?

3. Can the results be heard with practice by reasonably experienced and knowledgeable listeners? Another way of thinking about this is: what parts of your results can be heard by interested people, and what parts can only be heard by 'theory gods' or 'comp critters' with practice? Both sets of results are legitimate.

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