SIMPLE HARMONIC MOTION

ART 1011 (c) (p) 1994 Larry Polansky BMI

Works by Larry Polansky for instruments in just intonation with Robert Black, Krystyna Bobrowski, Tom Erbe, Ron EricKson & Alyssa Hess Reit.

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TRACKS

* Another You - Alyssa Hess Reit, harp * Movement for Andrea Smith (My Funny Valentine for just string quartet) * Movement for Lou Harrison (for just bass quartet) - Robert Black, basses * Horn (for horn and computer) - Krystyna Bobrowski, french horn

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Another You (1978; slight revisions, 1981) is a set of variations on a jazz standard, although the tune itself (and the chord changes) appears in only a few of the variations. Each variation explores different formal, textural, or harmonic ideas, and the entire piece deals in a somewhat unusual way with extremes of register, dynamics, and time.

Slightly different diatonic tunings, all drawn from the harmonic series, are used for each octave of the harp. The harp is treated like a large folk harp in that no pedals are used, except in the last variation, where the C/C# pedal is used briefly as a kind of tuning pun on the minute difference between the seventeenth harmonic and the equal-tempered minor second.

The harp tuning from the highest octave to the lowest is:

1/1 17/16 5/4 11/8 3/2 1/1 9/8 5/4 11/8 3/2 13/8 15/8 1/1 17/16 5/4 11/8 3/2 13/8 15/8 1/1 9/8 5/4 11/8 3/2 13/8 15/8 1/1 9/8 5/4 11/8 3/2 13/8 7/4 1/1 9/8 5/4 11/8 3/2 27/16 7/4 1/1 9/8 - - 3/2 27/16 7/4 (C) (D) (E) (F) (G) (A) (B)

Harmonic and melodic possibilities are expanded through the use of higher harmonics (2, 3, 4, 5) on the "open" harp strings. For example, the ratios 33/32, 39/32, 45/32, 51/32, 55/32, 21/16 and many others are all possible. Through the use of the second, third and fourth harmonics, ratios can be moved to different octaves, greatly increasing the scalar and chordal possibilities of each octave of the harp. It is possible, for example, to have a chord in the same octave with two different "sixths" (27/16 and 13/8), "fourths" (21/16 and 11/8), or "thirds" (81/64 and 5/4), as well as many other combinations.

The harmonic fingerings and the unusual retuning make the work difficult to play. I am extremely grateful to Alyssa Hess Reit who premiered the work in New York City in 1980 and has performed it many times since. Alyssa also served as an editor for the work, helping to nurture it from early versions to its current form.

Another You was recorded at Scores Unlimited Studios, New York City, September 14, 1991. Bruce Coughlin, recording engineer; Larry Polansky, producer.

Movement for Andrea Smith (My Funny Valentine for just string quartet) was written in 1978 for a dance by Toronto choreographer Andrea Smith, and revised a few months later to its current form. It is scored for two violins and two violas. Like the earlier Movement for Lou Harrison, for which it is a kind of companion piece, Movement for Andrea Smith is written for retuned strings in just intonation, using only natural harmonics (here only up to the fifth harmonic). Unlike Movement for Lou Harrison, which uses a large scale harmonically-derived form, the two short sections of Movement for Andrea Smith are loosely based on related "found" musical sources: the jazz standard "My Funny Valentine" and the opening chord from Carl Ruggles' Angels. Both these musics seemed to me suggestive of and suggested by the tuning itself.

The tuning is as follows (in octave-reduced form):

String IV III II I Violins 1/1 3/2 6/5 Q Violas 5/4 1/1 6/5 9/8

1/1 is the usual G-string (III for viola, IV for violin). As in Movement for Lou Harrison, the most radical retuning is about a minor third (violas, string II). The possible pitches, using only up to the fifth harmonic on any string, are (ratios octave-reduced to between 1/1 and 2/1):

Violins: (open string -> 5th harmonic) IV: 1/1 1/1 3/2 1/1 5/4 III: 3/2 3/2 9/8 3/2 15/8 II: 6/5 6/5 9/5 6/5 3/2

Violas: IV: 5/4 5/4 15/8 5/4 25/16 III: 1/1 1/1 3/2 1/1 5/4 II: 6/5 6/5 9/5 6/5 3/2 I: 9/8 9/8 27/16 9/8 45/32

Movement for Andrea Smith was recorded by Tom Erbe at Mills College, Oakland, California, December 1992. Jim Alexander, assistant producer. The score was first published in Xenharmonikon 7/8, Spring 1979.

Movement for Lou Harrison (for just bass quartet) is one of my earliest works. It was first written as a duet for two violins in 1975-6, and later rewritten for four retuned string basses in 1976-77. The score was recopied and slightly revised in 1988. p> In Movement for Lou Harrison I was mainly interested in harmonic movement. All pitches are part of the harmonic series of a "phantom" 1/1, which is actually the III (A) string of the bass itself. That note is never sounded (the piece ends on the perfect fifth, or 3/2). Basses 1 and 3 are tuned in one way, 2 and 4 in another, shown below in octave-reduced form:

1 and 3: I = 7/4 (RGS), IV = 3/2 (RES) 2 and 4: I = 11/8 (REbS), II = 5/4 (RC#S)

Two strings of each bass are not played.

Only natural harmonics are used, up to the eleventh harmonic on each string, so that the following pitches are possible as resultants of the harmonic series on these retuned strings (ratios are octave-reduced to between 1/1 and 2/1):

Bass 1 (and 3), string I: 7/4 7/4 21/16 7/4 35/32 21/16 49/32 7/4 63/32 35/32 77/64

Bass 1 (and 3), string III: 3/2 3/2 9/8 3/2 15/8 9/8 21/16 3/2 27/16 15/8 33/32

Bass 2 (and 4), string I: 11/8 11/8 33/32 11/8 55/32 33/32 77/64 11/8 99/64 55/32 121/64

Bass 2 (and 4), string II: 5/4 5/4 15/8 5/4 25/16 15/8 35/32 5/4 45/32 25/16 55/32

The form of the piece is derived from the tuning. It is a chorale that starts with pitches based on higher primes (121/64, 77/64, etc.) and gradually modulates to the lower primes, ending on 3/2.

The idea of using natural harmonics on just tuned strings to create a complex intonational fabric was first suggested to me by the fifth movement of James Tenney's Quintext, published by Soundings Press.

Movement for Lou Harrison (for just bass quartet) was recorded by Eric Richardson at Dartmouth College, July 12, 1992. Larry Polansky, producer. The score was published in Xenharmonikon XI, 1989.

Horn (for Krystyna Bobrowski) is a version of the harmonic idea I first used in Psaltery (one of several such "orchestrations" I've done over the past fifteen years): a continual modulation between three harmonic series. (Psaltery itself appears on my previous Artifact CD, The Theory of Impossible Melody, Art 1004.)

The form is purely harmonic, and is concerned with continuity and transformation. These ideas have often been central to my work. Fifty-one pitches are used consisting of the first seventeen harmonics of three fundamentals, related to each other as ratios of 1:5:3, or a just major triad. The harmonics from the higher series (5 and 3) are actually higher harmonics of the first. The piece is in five sections, each with a different fundamental. After building up the initial series on 1 in the first section, pitches from the next series (5, or the major third) begin to replace their closest neighbors in pitch from the series on 1 until the series on 5 is complete. This process happens two more times (sections 3 and 4), moving to the perfect fifth (on 3), and then back to the fundamental. In the fifth section, the series on the fundamental gradually drops out.

Harmonics enter in the order of their "prime complexity": 17, 13, 11, 14, 7, 15, 10, 5, 9, 12, 6, 3, 16, 8, 4, 2, 1. More distantly-related harmonics of a new series enter first, crossfading with close pitches from the current series so that initially only a "mistuning" is heard. Closer harmonics of the new series gradually begin to imply the new fundamental, through difference tones and our own harmonic perception. The initial buildup of the first series is the reverse of this order and in the end, the pitches of the final series drop out in this order. In Horn, the computer uses a harmonic replacement algorithm to calculate in real-time which pitch from the "old" series will leave, and which pitch from the "new" series will replace it. The sonic material for the computer part consists of sixteen voices of quasi-sinusoids, each with slight spectral variations. The amplitude, duration, spatial location, and envelope for each note is chosen in real-time by the software. These choices are based upon the harmonic form of the piece. For example, lower pitches tend to be longer. Over the course of each measure, entering pitches are emphasized in both the horn and the computer part, while leaving pitches are faded out.

The horn part is largely improvisational. The score consists of eighty-five "measures," seventeen each for the introductions of series on 1:5:3:1, and seventeen measures for the final 1 series to decay. In each measure of sections 2-4 the performer plays freely from a set of eighteen pitches, consisting of seventeen pitches of a kind of transitional harmonic series plus an entering note from the new series that replaces a pre-existing one from the old series. In sections 1 and 5 , where the series on 1 is built up and taken away respectively, there are seventeen or fewer pitches in each measure.

Horn was recorded by Tom Erbe at California Institute for the Arts, January 16, 1994. Richard Zvonar, co-producer. A final copy of the score was made in 1991-2 and published in Xenharmonikon 14, 1993.

Technical history and notes: Horn was composed in 1989, and first performed by Krystyna Bobrowski at the Mills College Center for Contemporary Music in March, 1989. It was originally written in HMSL on a Commodore Amiga driving two low-cost tunable MIDI synthesizers. The software was completely lost through disk error one week before the premiere, and had to be rewritten from scratch. The piece was then migrated to the Macintosh version of HMSL by myself and Darren Gibbs in order to use Phil Burk's real-time HMSL/56k DSP library.

Recordings of this version were hindered and finally canceled by various technical failures and airline misplacement of Chris's french horn. At Tom Erbe's suggestion, I modified the HMSL software so that instead of sending out the real-time data to MIDI or the 56k processor, it generated a Csound score to facilitate recording of multiple takes (since in previous versions, the computer part would always differ slightly). Finally, this Csound-generated tape was used for a planned two-day recording session at Cal Arts. The second day (January 17, 1994) coincided with the Los Angeles earthquake, and as such, the planned final takes from that session do not exist (similarly, the concert hall itself). This recording is edited from the recordings made the day before the earthquake.

All pieces digitally remastered, edited and assembled for CD by Tom Erbe with Larry Polansky between January 1992 and July 1994 at Dartmouth College, the Mills College Center for Contemporary Music, and California Institute for the Arts. HMSL (Hierarchical Music Specification Language) is written by Phil Burk, Larry Polansky, and David Rosenboom, and produced and distributed by

Frog Peak Music , Box 1052 Lebanon, NH 03766.

All the scores for the pieces on this CD are available from Frog Peak Music.

LARRY POLANSKY is a composer, performer, theorist, and teacher working at Dartmouth College. For ten years he was a staff member of the Mills College Center for Contemporary Music. He is one of the three co-authors of HMSL, and is the founder and director of Frog Peak Music (A Composers' Collective). Home Page Larry.Polansky@Dartmouth.edu