“Machine Sound” and Microtonal Music

In the essay devoted to the invention of “machine” (or electromechanical) sound, one tries to rethink the familiar word combination “machine and artificial”. The latter one is not a word game. By the user-friendly separation of an octave into 12 uniform tone steps, the modern tonal system of the western hemisphere is therefore artificial by definition. In contrast to that, the vocal polyphony of the Renaissance is based on an increased usage of acoustically pure or natural intervals. Early attempts to extend instrumental compositions with the benefits of just intonation failed. An unexpected support for microtonal structures within instrumental music came from machines. Primarily by the dynamophone, one of the first electromechanical instruments, developed close to the beginning of the 20th century. Beside its primary task — the additive synthesis — its inventor Thaddeus Cahill aimed for a union of sound art and the laws of acoustics. Therefore, this instrument had the sheer amount of 36 keys per octave. From the point of view of representatives of the musical avant-garde, the control over pitch that came with the mastery of sound synthesis allowed the use of new tonal systems.

Isaac Newton's Microtonal Approach to Just Intonation

In 1665 Isaac Newton wrote a notebook in which he collected materials for a musical treatise which was never completed. He investigated ways of approximately representing just intonation scales by dividing the octave into many equally sized intervals. Strictly speaking, equal divisions of the octave are incompatible with just intonation, and just intonation intervals are audibly different from the intervals played on a modern equally tempered modern piano. By increasing the number of parts of an equal division, just intonation can be approximated arbitrarily well. Scales with more than 60 microtonal steps per octave, however, never gained wide acceptance in music theory or practice. Newton divided the octave into 612 equal parts so that he could represent the syntonic chromatic scale very accurately and he studied several equal divisions of the octave with fewer parts. His approximation problem is looked at in three ways: (1) A reconstruction of how he determined the many EDO-representations listed in the notebook is given. (2) Using computer programs Newton's tuning problem is solved "empirically" through calculating and evaluating the related approximations comprehensively. (3) The findings from the computer-assisted analysis are used to develop a more general geometric approach to the approximation problem.

Consistent Pitch Height Forms: A commentary on Daniel Muzzulini's contribution Isaac Newton's Microtonal Approach to Just Intonation

This text revisits selected aspects of Muzzulini's article and reformulates them on the basis of a three-dimensional interval space E and its dual E*. The pitch height of just intonation is conceived as an element h of the dual space. From octave-fifth-third coordinates it becomes transformed into chromatic coordinates. The dual chromatic basis is spanned by the duals a* of a minor second a and the duals b* and c* of two kinds of augmented primes b and c. Then for every natural number n a modified pitch height form hn is derived from h by augmenting its coordinates with the factor n, followed by rounding to nearest integers. Of particular interest are the octave-consitent forms hn mapping the octave to the value n. The three forms hn for n = 612, 118, 53 (yielding smallest deviations from the respective values of n h) form the Muzzulini basis of E*. The respective transformation matrix T* between the coordinate representations of linear forms in the Muzzulini basis and the dual chromatic basis is unimodular and a Pisot matrix with the dominant eigen-co-vector very close to h. Certain selections of the linear forms hn are displayed in Muzzuli coordinates as ball-like point clouds within a suitable cuboid containing the origin. As an open problem remains the estimation of the musical relevance of Newton's chromatic mode, and chromatic modes in general. As a possible direction of further investigation it is proposed to study the exo-mode of Newton's chromatic mode

ORCHESTRATION AND PITCH PRECISION IN THE ORCHESTRAL MUSIC OF MARC SABAT

This article examines the relationship between orchestration and microtonality in the music of Marc Sabat through a score-based analysis of two recent works, Asking Ocean (2016), for string quartet and large ensemble, and The Luminiferous Aether (2018), for large orchestra. Excerpts from these two compositions are discussed to highlight the challenges of composing for orchestral forces in a musical style that demands a high degree of microtonal pitch precision. Through retuning, alteration, and a sensitivity to the construction, techniques and performance practices of orchestral instruments, Sabat has developed a unique manner of orchestrating that is at once timbrally rich and uncompromising in pitch precision. After a brief introduction to the extended just intonation framework that Sabat employs, his concepts of ‘fixed microtonal pitches’ and ‘tuneable intervals’ are discussed and connected to orchestration in his scores. Drawing upon this analysis, connections are made between the microtonal system with orchestration and musical aesthetics broadly.

Effects of Tonic Drone Accompaniments on the Intonation of Collegiate Wind Instrumentalists

The purpose of this study was to examine the effects of tonic drone accompaniments on the intonation of collegiate wind instrumentalists. Participants ( N = 68) played an excerpt of the melody “Long, Long Ago” in three conditions: a mono drone (tonic note only), dyad drone (tonic plus fifth), and a control condition (no drone). Results indicated no significant effects on intonation performance due to drone condition. However, participants’ ratings of their own intonation accuracy differed significantly based on drone condition. The majority of the performances of the melody aligned more closely with equal temperament ( n = 159), and fewer aligned more closely with just intonation ( n = 45). Most participants believed the dyad drone (59.74%) resulted in their best intonation accuracy, followed by the mono drone (28.57%) and the control condition (11.68%). In response to open-ended questions, participants cited reasons why they preferred particular drone conditions, with the most common themes being “easier to hear and match,” “multiple reference pitches,” and “focused/directed listening.” Given that participants expressed preferences regarding drone use in the absence of performance differences, music educators may consider the role of comfort and familiarity with these instructional tools.

Ellen Arkbro and Marcus Pal; Claudia Molitor, Decay, hcmf//, 16 November 2019

Ellen Arkbro has been much fêted in experimental scenes (though not – or not yet – so much in the sort of new music scenes with which hcmf// remains associated) for her two records, For Organ and Brass (2017) and CHORDS (2019). Her performance with Marcus Pal in St Paul's Hall in Huddersfield follows a number of other shows in the UK, including at TUSK festival in Newcastle and at the Barbican in London. The pair are based in Stockholm, where they seem to be part of a burgeoning experimental organ scene. Their just intonation drone music comes with impeccable credentials: both studied with La Monte Young, and Pal also studied with Catherine Christer Hennix. The organ emitted a quiet diminished octave as the audience filed in, a dissonance resolved as soon as Arkbro sat down at the organ manual. What followed appeared to be a reworked and extended version of CHORDS for organ: the organ articulating perfect intervals and single tones, sounding something like a harmonic series and something like the I–IV–V of rock and blues, while Pal's computer-generated additive synthesis, speakers carefully directed upwards parallel to the organ's pipes, combine with the organ's familiar sound to create dense and jagged masses, chords transforming into timbres and back again.

Comprehensibility and Ben Johnston’s String Quartet No. 9

Ben Johnston’s just-intonation music is of startling aural variety and presents novel solutions to age-old tuning problems. In this paper, I describe the way that Johnston reoriented his compositional practice in the 1980s as evidenced in his musical procedures. Johnston became aware of the disconnect between Western art music composers and their audiences. He therefore set about composing more accessible music that listeners could easily comprehend. His String Quartet No. 9 gives an instructive example of the negotiation between just intonation and comprehensibility. By integrating unusual triadic sonorities with background tonal relationships, Johnston reveals an evolution of just-intonation pitch structures across the work. This paper provides an example of an analytical method for exploring Johnston’s works in a way that moves beyond simply describing the structure of his system and into more musically tangible questions of form and process.

The effect of piano accompaniment type and harmonic context on the tuning performance of college-level choral musicians

This study was designed to evaluate the effect of piano accompaniment style on the intonation performance of college-level choral musicians. It was hypothesized that using a piano accompaniment comprised solely of referential tones (RT), as opposed to having all voice parts doubled by the piano (PD), would encourage more desirable intonation performance. Participants (N = 34) sang a researcher-composed melody harmonized with traditional Western functional harmony under both accompaniment conditions. Accompaniment type was not found to have a significant effect on the tuning performance of target intervals, but harmonic context did significantly affect the singers' intonation. Most notably, intonation of major 3rds in the I and IV chords closely approximated just intonation, regardless of accompaniment type. In the context of the V chord, performances more closely approximated the high Pythagorean 3rd, which was attributed to a tendency to heighten the leading tone. When comparing intonation performance to the just intonation, equal temperament, and Pythagorean tuning systems, results indicated that performances did not conform perfectly to any one tuning system, supporting the conclusion that the singers' intonation performance was dependent on harmonic context.

Playing Music in Just Intonation: A Dynamically Adaptive Tuning Scheme

We investigate a dynamically adaptive tuning scheme for microtonal tuning of musical instruments, allowing the performer to play music in just intonation in any key. Unlike other methods, which are based on a procedural analysis of the chordal structure, our tuning scheme continually solves a system of linear equations, rather than relying on sequences of conditional if-then clauses. In complex situations, where not all intervals of a chord can be tuned according to the frequency ratios of just intonation, the method automatically yields a tempered compromise. We outline the implementation of the algorithm in an open-source software project that we have provided to demonstrate the feasibility of the tuning method.