Steve Reich's Phasing
スティーブ・ライヒのフェイジング

The term phasing, pioneered by composer Steve Reich, is not a common term even among music people, and may be a technique known only to a few people interested in contemporary music. In the 21st century, with the development of electronic technology, phaser, an effect pedal that generates a modulation effect by shifting phase, which is common on guitars and electric pianos, may be more familiar to you.

In this page, through the analysis of the technique and harmony of Reich's 1967 work Piano Phase, I will introduce the actual application of phasing and moiré to compositional techniques, and furthermore, I will reproduce the phasing technique using Max/MSP and consider the possibility of algorithmic composition on the PC and the originality that lies beyond that.

Steve Reich is an American composer of contemporary music. Reich's music makes extensive use of phases and repetitions, and has long made use of tape sampling and other techniques. Reich received a Bachelor of Arts degree in Philosophy from Cornell University in 1957, and also attended the Juilliard School of Music in New York from 1958 to 1961.
From 1961 to 1963, he studied composition at Mills College with Luciano Berio and Darius Milhaud. He also studied drumming at the University of Ghana's Institute of African Studies in 1970 and Balinese gamelan in Seattle from 1973 to 1974, actively studying the folk music of various regions.

Phasing in music is a technique in which two performers play a single repetitive phrase in slightly different tempo and listen to the changes in sound pattern caused by the interference.

However, it is difficult to imagine what kind of sound it is because the image is too abstract. If we step away from music and think about the phenomenon of moiré in the visual sense, it will be easier to get an idea of what it is. Moire is a phenomenon in which two objects of the same shape are superimposed at slightly different angles, or phases, to produce a certain degree of unpredictable pattern or rhythm. The same can be achieved with sound.

This can be considered a kind of polyrhythm. For example, composer Philip Glass pursues minimalism from a polyrhythmic perspective. Unlike conventional functional harmony, in which the harmony changes in discrete steps, phasing produces an effect in which the sound changes continuously and gently, as if morphing, and before you know it, a musical development takes place.

Prior to his instrumental works, Reich also utilized this phasing in tape works with electronics, such as Come Out and It's Gonna Rain. Its inspiration comes from medieval music, such as canon.

Piano Phase was written by Steve Reich in 1967 for two pianos and was the first piece in which Reich applied the phase technique to a live performance.
After Piano Phase, Violin Phase (1967), Phase Patterns (1970), and Drumming (1971) were written for live performance using similar techniques. In recent years, performers like Rob Kovacs and Paul David Kean have been playing two pianos by themselves.

In the case of a piece for two players, at first the two players play the same phrase in unison, but since they play at slightly different tempos, their beats and verses gradually shift, and at the beginning (when the notes are delayed by 32nd notes), the performance sounds as if it is following a note pattern with an echo-like effect.

Next, when the note delay reaches a certain level (sixteenth note), the pulses of the two players again overlap in time and unison playing reappears.
However, because one player repeats the phrase from a position one note behind the other in the note pattern, a different dyad (harmony consisting of two pitch classes) emerges from the first, forming a vertical harmony with a different pitch than the first perfect unison.
The harmony gradually changes with each rhythmic shift, and when the repetition is delayed by a cycle, it returns to the same perfect unison as at the beginning, and can be developed into a kind of final form.

Minimalist composers such as Steve Reich, Philip Glass, and Arvo Pärt often use diatonic pitch collection tone system in a non-classical, non-functional harmonic manner, as did Stravinsky and Debussy. While using diatonic scale, there are no major or minor keys, no cadences, and no central tones. They saw in it the possibility of expression for the next era, overcoming tonal music and atonal music.
Reich's piano phase also has [B, C#, D, E,. F#](11,1,2,4,6), and the piece is constructed from a pitch class set of five pentachordal elements, with consonant and dissonant intricately interwoven within the two-voice counterpoint-like sound development.

Analysis of the pentachord's note pattern shows that the sets can be classified into two groups: (1,6) dyad and (2,4,11) trichord. The right hand is responsible for (1,6) pitch class sets and the left hand for (2,4,11) pitch class sets, and a note from each set is selected and played in sequence by the right and left hands, alternately.

The note pattern produced by this set (11,1,2,4,6), which combines both right and left hands, is a pitch collection that omits the 7 and 9 of the diatonic set (1,2,4,6,7,9,11), which is a characteristic of tonal music. From this melody, the tonal center cannot be determined as either E or B, nor can it be determined whether the mode is E-Dorian or B-Aeolian. Piano Phase preserves the beauty of the music's structure through an order different from the concepts of tonality and modality, namely the gradation of sound through phasing, which may be regarded as a kind of pandaiatonic. The piano phase, in which the two voices share the same pitch class set, does not deform its own members, but the pitches produced by the combination change incessantly, and the music changes expressions of tension and relaxation.

Looking at the vertical pitch relationship between the unison of the right and left hands at the beginning of the Piano Phase, it is obvious that they are playing the same phrase, so the set is monad.

Next, let's look at the pitch relationship in the musical notation of example [2] when the rhythmic phase between the second player and the first player, whose speed is played in a slightly faster loop, is off by a sixteenth note.

Analysis of the vertical intervals shows that, starting from the first beat, the intervals are 2nd, 4th, 2nd, 6th, 2nd, 6th, 2nd, 4th, 6th, 2nd, 6th and considering that the 4th was dissonant until the Renaissance, it is almost a dissonant interval except for the 6th. The time period of this two-voice combination can be regarded as a section where a kind of dominant, unstable and tense sound is produced.

Now let's look at an example of [3] with more sixteenth-note rhythmic lag on one of the voices.

The first six note patterns for the first half of the 6/8 time signature and the second six note patterns for the second half of the 6/8 time signature are exactly the same phrase repeated. In other words, we can say that a state in which the loop cycle of the rhythm pattern is halved has suddenly appeared. The vertical pitch interval relationship is a repetition of 5th, 5th, 3rd, 5th, 7th, and 5th, with most of the intervals being consonant intervals.
This could be interpreted as a class in which a kind of tonic-like stable sound is produced.

Even a melodic sequence of notes that does not even include transpositions or changes of members, by stacking two of them and shifting their phases, various sounds are generated, and these transitions are shown to be music by being done gently and somehow.

The fact that dissonant and consonant sounds appear at times, creating the tension and relaxation that are essential to music, can be attributed to the carefully calculated sound patterns created by the composer, Reich.
This work may be viewed from the angle that it is formed by a melodic sequence of 12 notes as data and an algorithm of superimposing them in rotation to form two voices, but unless the sequence of notes is carefully chosen, the music will not result in a dramatic development. In some parts, the music is monophonic but polyphonic, and in other parts, it is homophonic, rhythmic, and requires skill in determining the sequence of notes to manipulate the sound. Minimalism is not a simplification of music, etc., but rather a condensation of many things into a minimum of sound. And the most efficient way to prototype to determine the tone row would be to generate the sounds by prototyping them into a program like Max/MSP.

When considering music that uses Max/MSP to perform phasing, the setting of the difference in tempo between the two voices is of the utmost importance. The tempo of the first piano is set to 143 and connected to the second inlet of the [tempo] object. The tempo of the other piano is set to 142.6425. This is done by connecting the [numbers] object to the [* ] object connected to the [numbers] object to automatically calculate the numbers.

If necessary, change the number 0.9975 in this section. It will change the pace at which the set of dissonant and congruent classes shift.
Unlike human performance, where the tempo is adjusted while listening to the sound, phasing can be done quite faithfully to theory. It is difficult to create this kind of music on a DAW, but it can be achieved with fairly simple patches using a program like Max/MSP.

The [tempo] object generates numbers from 0 to 11 in the specified tempo rhythm. This is received by the [coll] object and converted to midi note numbers. The number converted here is the midi note number of the Piano Phase melody.
This is described in a file called pianophasemelody.txt, which must be placed in the same directory as the maxpat or in a directory with a file path. This is all that is needed to complete the phasing program.
Despite its minimal algorithmic structure, it is capable of producing such a large number of acoustic variations.

It is also possible to rewrite and save pianophasemelody.txt to generate phase music consisting of 12 notes of your choice. Please try to run this program with a melody different from the piano phase.

What do you think about creativity through a program that performs phasing using Max/MSP?
In the case of this kind of music generation, is it really composer's job to invent an algorithm, or is it composer's job to refine the output of an existing algorithm by feeding it with some data?
Just as there are two directions in the world of primary creators, who explore rough but uncharted territory, and secondary creators, who diligently refine established expressions, there may be two major vectors in composition.
There is no answer here. Please think for yourself..