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Resonant Spaces Notes Andrew McPherson Resonant Spaces for cello and live electronics Performance Notes Overview This piece involves three components: the cello, live electronic processing, and "sequenced" sounds which are predetermined but which render in real time to stay synchronized to the per- former. Each component is notated on a separate staff (or pair of staves) in the score. The cellist needs a bridge contact pickup on his or her instrument. It can be either integrated into the bridge or adhesively attached. A microphone will not work as a substitute, because the live sound plays back over speakers very near to the cello and feedback will inevitably result. The live sound simulates the sound of a resonating string (and, near the end of the piece, ringing bells). This virtual string is driven using audio from the cello. Depending on the fundamental frequency of the string and the note played by the cello, different pitches are produced and played back by speakers placed near the cellist. The sequenced sounds are predetermined, but are synchronized to the cellist by means of a series of cue points in the score. At each cue point, the computer pauses and waits for the press of a footswitch to advance. In some cases, several measures go by without any cue points, and it is up to the cellist to stay synchronized to the sequenced sound. An in-ear monitor with a click track is available in these instances to aid in synchronization. The electronics are designed to be controlled in real-time by the cellist, so no other technician is required in performance. A control box with a footswitch, numeric display, and multi-color LED indicator provides control and visual feedback for the performer. The harmonic series of the string and the cello note lines up at the pitch G4, so this pitch will be produced by the live electronics. # Harmonics of # # "# %# ! # # # # ## # $ string resonator # $ # # "# " # &# $# "# %# Cello spectrum ! &# # &# # # $ &# $ # &# " ! &" &# " % & means 1/6 tone lower than the normal accidental, as in the 7th partial are deviations of 1/4 tone (1/4 sharp, 1/4 flat, and 3/4 flat, respectively), as in the 11th partial. # $ $& ! $ ' ! $ ( ( ) ' ' ' Table of pitches produced by different cello notes with the resonating string set to a fundamental of C2. ! Some cello notes produce more than one possible pitch from the resonator, depending on slight variations of intonation. # *# *# *## *# # *# %# # Resonator ! # # # # ! # # # $ # # " # # $ # # # # # # Cello &# %# &# %# # ! # &# %# # *# # # &# %# &# %# # *# ! # *# #&# %# # *# ! $ ' Live Sound and Non-standard Intonation ! ( ) )' )' )' )' )' )' ' The sounds produced by the virtual resonating string are all part of the harmonic series of the string's fundamental pitch. In other words, if the string were tuned to C2 (the open C of the ! cello), it could produce the following pitches: 1. 2. 3. 4. 5. 6. 7. 8. 9. The10. harmonic11. 12. 13. series14. of15. the16. string and the cello # note lines up at# the# pitch%# G4,# etc.so this pitch will ! # # be# produced## # $by the" live electronics. # $ # "# # -14c# -31c -14c -49c -40c -31c # %# # " Harmonics of # # # # # $# " string resonator ! # # # # # $ # # " " The intonation of the harmonic series differs from the conventional even-tempered scale.# &# $While# "# %# most of the above notesCello differ spectrum by only a! few cents (100&# cents = 1 semitone),# &# some# # of$ the more &# $ # &# " "out-of-tune" pitches are labeled above. For the&" most substantially&# detuned notes, different sym- bols are used: ! " % & means 1/6 tone lower than the normal accidental, as in the 7th partial are deviations of 1/4 tone (1/4 sharp, 1/4 flat, and 3/4 flat, respectively), as in the 11th partial. # $ $& ! $ The live sound is not programmed into the computer:' it must be generated by the actions of the cellist. The computer sets only the fundamental pitch of the resonating string; it is up to the per- former to select which harmonic sounds. The sounding note arises from the interaction of the ! $ string( fundamental( )and the note played' in the cello. ' ' In the simplestTable case, of pitches the cellist produced plays by difa noteferent in cello the notesharmonic with the series resonating of the string string. set to That a fundamental pitch will of C2. ! be reinforcedSome and cello ring notes strongly produce in themore live than sound. one possible In the pitch more from complex the resonator case,, depending the cellist on plays slight avariations of intonation. note not in the harmonic series. However, since the cello is a timbrally rich source, any note will have its own set of harmonics.*# Wherever*# the harmonic*## series of* the# cello overlaps*# the% #harmonic# # ! # seriesResonator of the! string, that pitch# will be produced.# # For# example, suppose# the string# is tuned to# C2, $ # # " # # $ # and the cellist plays# Eb2: # # # # Cello # &# %# &# %# # ! The harmonic series of the string and the cello # *# # &# %# # *# note lines up at the #pitch*# G4,# & so# this%# &pitch# % #will # be *produced# #&# by%# the live electronics. # # # %# # Harmonics! of ! # # # ## # $ " string resonator # # # $ # # " " # &# $# "# %# Cello spectrum ! &# # &# # # $ &# $ # &# " ! $ &" &# ' ! ( ) )!' )' )' )' )' )' ' " % & means 1/6 tone lower than the normal accidental, as in the 7th partial are deviations of 1/4 tone (1/4 sharp, 1/4 flat, and 3/4 flat, respectively), as in the 11th partial. # $ $& ! ' ! $ 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. # etc. # # # $# "# %# ! # # # # # !# $ ( ( ) ' ' # $ #' # " " -14c -31c -14c -49c -40c -31c Table of pitches produced by different cello notes with the resonating string set to a fundamental of C2. ! Some cello notes produce more than one possible pitch from the resonator, depending on slight variations of intonation. # *# *# *## *# # *# %# # Resonator ! # # # # ! # # # $ # # " # # $ # # # # # # Cello &# %# &# %# # ! # &# %# # *# # # &# %# &# %# # *# ! # *# #&# %# # *# ! $ ' ! ( ) )' )' )' )' )' )' ' ! 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. # etc. # # # $# "# %# ! # # # # # # # $ # # " " -14c -31c -14c -49c -40c -31c The harmonic series of the string and the cello note lines up at the pitch G4, so this pitch will be produced by the live electronics. # %# # Harmonics of # # # # # $# " string resonator ! # # # # # $ # # " " # &# $# "# %# Cello spectrum ! &# # &# # # $ &# $ # &# " ! &" &# " % & means 1/6 tone lower than the normal accidental, as in the 7th partial are deviations of 1/4 tone (1/4 sharp, 1/4 flat, and 3/4 flat, respectively), as in the 11th partial. # $ $& ! $ ' Here is a reference table of the expected results of playing different notes against a string funda- ! $ mental( of (C2. Of course,) with a different' fundamental 'pitch, the whole table' transposes. Table of pitches produced by different cello notes with the resonating string set to a fundamental of C2. ! Some cello notes produce more than one possible pitch from the resonator, depending on slight variations of intonation. # *# *# *## *# # *# %# # Resonator ! # # # # ! # # # $ # # " # # $ # # # # # # # Cello ! # *# # &# %# &# %# &# %# &# %# # *# # &# %# # *# #&# %# # *# # The cellist! does not need to concern him- or herself with the precise mechanics of this process, because the pitches notated in the live sound staff already correspond to the notes given in the cello part. In other words, by playing what is written in the cello part, the notated live sound should be the inevitable result. However, the process' is highly sensitive to intonation, so a few! $ cents of pitch variation may be the difference between a very clear tone and a sort of vague re- verberation sound. Since the intonation required deviates from standard even-temperament, ! some( practice) is) required' to) get' all pitches)' to speak)' clearly. (In)' general, )the' higher the' harmonic, the more sensitive to intonation it is.) ! Sequenced Sound and Cue Points 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. The sequenced sounds are notated on the bottom staff of each system. They are rendered by theetc. # # # $# "# %# # computer regardless of what the cellist !plays. # # # # # # # $ # # " " -14c -31c -14c -49c -40c -31c Each cue point is a place that the rendering will pause. When the computer reaches this point, the indicator on the control box will turn green, meaning that it is ready to advance to the next cue point. Tapping the footswitch will advance the rendering. Cue points are notated in the score as large numbers in square boxes. A small arrow indicates the precise rhythmic location that the footswitch tap should take place. After each footswitch tap, the number shown on the control box display should correspond to the number of that cue. The display is not required for performance, but provides the security of knowing that the computer is in the right place. The cues can only be advanced when the green light is on, and there is no way to move back- wards. If the computer falls behind during performance, the performer should tap as soon as the green light comes on to advance it. If it gets ahead, it will wait at the next cue point for the per- former to catch up. In practice, these things rarely present a problem. Certain sections of the score are marked "Follow pulse." These are places where considerable activity takes place in the sequenced sounds, but no cue points are available. In these sections, the cellist must follow the computer by careful listening, by using an in-ear monitor (as described in the setup guide), or by watching
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