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Musical Time Blog

Music 575 Fall 2009
John Rahn
The seminar is held Tuesdays from 1:30 to 3:30 in room 212 Music.

Readings and discussion about time in music, ranging from theory of meter in tonal music to time in avant-garde music. We will begin with the avant-garde!

For a sort of continuation in Winter 2010, more philosophical and less analytical in orientation, see


Week 1. Introductory discussion about interests of people in the seminar, and some general remarks on time.

About the relativistic effects -- here is an introductory ref for the Lorentz factor we were talking about today:
1  http://en.wikipedia.org/wiki/Length_contraction

Note here re observability, related to other remarks in class:
"In 1959 Roger Penrose and James Terrell published papers saying that the Length contraction cannot be observed[20][21]. Rather there would be a kind of rotation now called Penrose-Terrell rotation[22]."

For time dilation see also
2  http://www.daviddarling.info/encyclopedia/L/Lorentz_contraction.html

The Lorentz transformation equations for length and time are derived here (I have an issue with the step from 7a to 8 for t, however):
3  http://www.relativitycalculator.com/Lorentz_Transformation_Equations.shtml
A better and more comprehensive historical ref is given here and this is a good place to start, if you can drink ether:
4  http://en.wikipedia.org/wiki/Lorentz_ether_theory

It is a little frustrating that I can not easily find a ref that simply lays out the frames for all three relativistic Lorentz transformations, mass, length, and time. Moreover, the refs 1 2 and 3 above appear to contradict each other as to the exact formulations, and ref 4 does not give the formulations in readily comprehensible form. Such is the internet. If we were going to study this we would have to go to some more authoritative texts, such as:

A popularization from the horse’s mouth:

Relativity The Special and General Theory   Albert Einstein


The real thing, with the math and the physics:

The meaning of relativity
A Einstein, EP Adams – 19


I attach the PDF of this below in case this link breaks.

This is all quite amusing and at least as complex as music theory. Note that Poincare was  a major player in all this; Einstein stood on many tall shoulders and refined existing notions.

We also talked about quantum entanglement puzzles for the issue of simultaneity -- you can look this up yourself. I'll postpone the refs and discussion we started about orreries, predictability, reversible systems, and chaos theory.

I referred to Henri Bergson, "la duree", and Spinoza monads, and their influence on Deleuze (e.g. Deleuze Difference et Repetition.) See also Husserl, Heidegger, and of course, Hegel Phenomenology of Mind. Re Husserl, see Lewin's classic article in Music Perception 1/1.

Week 2.
1950s and 60s time...mostly Stockhausen. Readings and discussion of works below. This looks like a lot of reading so do it in the order listed on the site here.

We may have to find his classic paper, "Wie die Zeit Vergeht" or "...how time passes..." in the English version of Die Reihe 3, Musical Craftsmanship, on paper.  I have this journal. I can't find it online. (You can snoop around JSTOR and others for related material.) Copies hanging on my door. Die Reihe is in  our library under 780.5 REHA.

Also, listen to Mikrophonie, Carre, and the wind quintet, Zeitmasse

Zeitmasze, Work No. 5, Kontra-Punkte, Work No. 1, Refrain, Work No. 11, Schlagtrio, Work No. 1/3

Mantra and Stimmung here

score for Carre M1530.S84 C3 1971  no.1

refs for Mikrophonie

Week 3:

Stockhausen's rhythmic analysis of some Webern, "Structure and Experiential Time", Die Reihe 2 (Webern) 780.5 REHA. in music library periodicals

Ligeti, "Pierre Boulez", Die Riehe 4 (Young Composers), p 36ff. This is the famous critique of Structures for two pianos.

Week 4:
Orit presents -- for two hours! -- on analysis of Stockhausen's Gesang der Junglinge. Lots of good discussion.

Week 5:

and then some Americans:

MIlton Babbitt, "12 tone rhythm and the electronic medium," PNM 1/1 1962 (JSTOR); This is long and hard to read.

John Rahn, "On Pitch or Rhythm: Interpretations of Orderings of and in Pitch and Time" Perspectives of New Music, Vol. 13, No. 2 (Spring - Summer, 1975), pp. 182-20

Perspectives of New Music, Vol. 35, No. 2 (Summer, 1997), pp. 85-99

Babbitt, Philomel (for soprano and tape). This is a full flowering of the rhythmic ideas he sets forth in the article above.
Online audio at

and here are some links to synthesis software, all free:

1. The IRCAM link.
For Max/MSP synthesis:

2. Supercollider

3.  csound and my Lisp Kernel; the Kernel is available at

Csound is at

Nov 10th:
John presents on Sea of Souls.

Nov 17:
Jazz rhythm -- swing. Curtis presents the Morrison research.

Nov 24:
David Lewin, "Music Theory, Phenomenology, and Modes of Perception"
Music Perception Vol. 3 no. 4, Summer 1986

John Rahn, "The Swerve and the Flow" (attached to this page in PDF)
Dec 1: much stimulating discussion, and Amy talked about touches bloquees

Dec 8: discussion of final paper projects.

John Rahn,
Oct 7, 2009, 10:26 PM
John Rahn,
Nov 18, 2009, 2:31 PM