Tsao PLUS OR MINUS by ScoresOnDemand

TSAO

Plus or Minus for two pianos and electronics

Full Score

Plus or Minus MING TSAO

for two pianos and electronics

(2017/18)

Plus or Minus (2017-18)

A realization of all 7 pages of Karlheinz Stockhausens’ “Plus Minus” (1963) in two layers (with each piano representing an independent layer).

For 2 pianos and electronics.

Each piano must be equipped with a sostenuto pedal. Each pianist must have: (a) 2 superball mallets (b)2 thick plectrums

Each piano has 4 strings detuned a quarter-tone:

gradually release pedal over the duration of the arrow

In areas where pedal markings are not specifically notated, pedal use is left up to the performers.

Sostenuto notes

white note, black note and full chromatic clusters Glissandi

full chromatic, white note and black note glissandi

P P Palm glissandi, softly rotate the palm of the hand across the keys in an upward or downward manner to effect a glissando. If neither a B or W is indicated, then the glissandi should be chromatic.

Tremolo

Superballmallet

always sixteenth rhythm in the indicated tempo Superballmallet x y x

Meter

The presence of irrational measures where the denominator is not a power of 2 indicates sudden shifts in tempi that are related to either triplet or quintuplet values in the original tempo.

When the denominator is either 5, 10, 20, then the tempo is multiplied by 5/4:{

If the denominator is 3, then the tempo is multiplied by 3/4:

When the denominator is either 6, 12, 24, then the tempo is multiplied by 3/2: {

When the octave line is indicated, it refers to all pitches on that stave that fall under or above it.

Repetitions

Note that the “first” repetition refers to the first time played (not the first time repeated)

Special actions inside piano

Superball mallet

Electronics

slowly scrape a thick plectrum along the indicated string. Produce a “clicking” sound with tone

œ slowly drag superball mallets along the indicated strings. Produce low glissandi tones

plectrum glissando across indicated string(s) inside the piano

The electronic part for each piano is notated on the lower 2 staves for each piano. Each piano uses 8 transducers placed inside the piano as follows: (All sounds produced by the transducers should sound organically integrated with the actually performed piano sounds)

Setup for pianos I and II:

Note: Transducers 2, 4, 5 are attached to the bridge Transducers 1, 3, 6, 7, 8 are attached to the wooden soundboard Transducers 7, 8 are not securely attached to the soundboard but loosely lie on the soundboard, thus producing a “rattling” sound when activated. The only sounds produced by the transducers are sampled pitches from the 88 piano keys, which is why these pitches are notated on 2 staves. Occasionally, the sampled sounds include the superball mallet action along the piano strings. In these cases, the electronic part is notated on a 1-line stave since exact pitch is indeterminate.

Every sound produced by the transducers have the following envelope:

where x and y are variable duration times in seconds and z is a variable dynamic level. (Note that each sound begins and ends in silence to produce the effect of resonances in relation to the performed sounds by the two pianists). As a general rule, it is important to have each event last longer than actually notated in the score so that an event does not completely disappear before a new event begins to appear – assuming that the events immediately succeed one another in time. In other words, successive events for each piano part in the electronics should overlap slightly.

All or some of the transducers may be activated.

There are three different movement shapes for transducers:

static

cycle

oscillation (or osc.)

Static: 1, 3, 5 the notated sound will be sent simultaneously to transducers 1, 3, 5

Cycle: 1–6 (fast) the notated sound will be sent first to transducer 1, then to transducer 2, ..., finally to transducer 6 and then back to transducer 1 again, the rate of movement ocurring at fast speed.

Cycle: 1, 3, 7, 5 (slow) the notated sound will be sent first to transducer 1, then transducer 3, then transducer 7, then to transducer 5 and finally back to transducer 1, the rate of movement ocurring at slow speed.

Osc.: 3, 4 <—> 1, 2, 6 (med.) the notated sound will oscillate between transducers 3, 4 and transducers 1, 2, 6 at medium speed of oscillation.

The three notated rates of movement are slow, medium (med.) and fast.

It is incumbent for the programmer to program variations of each speed so that an exact value of “medium speed” is not used more than 3 times in the piece. This would mean that medium speed will consist of many different values, all within the range of what we perceive “medium speed” to be. The same applies to “fast” and “slow” speeds. The general range for the three speeds is:

- fast x, where q = 80–95 BPM

- medium x, where q = 65–80 BPM

- slow x, where q = 50–65 BPM

Other movement shapes include tremolo and vibrato.

Static: 1, 5 (tremolo fast) indicates that the notated sound will be sent through transducers 1 and 5 with the added effect of tremolo at fast speed

Static: 1, 5 (vibrato +/- quarter-tone, slow) indicates that the notated sound – usually followed by wavy lines rather than straight lines – will be sent through transducers 1 and 5 with the added effect of a pitch vibrato of a quarter-tone (50¢) at slow speed.

Note that the movement shapes of tremolo and vibrato can be combined with each other as well as with the movement shapes of cycle and oscillation.

The detuning effect allows for glissandi to occur with the notated pitches in the electronic part. Instead of the pitches being followed by straight lines which indicate duration, they are followed by slanted lines up or down. The destination to which they are glissing is notated by pitches in parentheses at the end. The slanted lines indicate the rate of glissandi and the total duration. Occasionally, the glissando finishes in the middle of the sustained sound:

or a glissando begins in the middle of a sustained sound:

In both cases, x and y are variable durations in seconds.

The numbered events in the electronic part of the score must be triggered independently by a separate performer in a live concert situation. There are 368 events which must be triggered when they appear in the score.

“Plus or Minus”

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