Pitch Drift Research Articles

Boys Choirs in the Pandemic: Effects of Distance and Other Factors on Spectral and Temporal Accuracy

During the Covid-19 pandemic, choral singing has been either completely prohibited or regulated with safety measures due to increased transmission risks. However, the impact of larger inter-singer spacings on the performance and educational process in boys’ choirs is unclear. This study analyzed recordings of six groups of five singers each from two boys’ choirs aged 7–16 who sang Beethoven’s Ode to Joy while standing on an arc with a 4 m radius and an inter-subject spacing of 0.5–3 m. The effects of singers’ masks, distance, group age, and relative position on the timing of articulation and fundamental frequency were investigated, along with the amount, rate, and sign of pitch drift and loudness.The ANOCOVA results showed that onsets were robust to the tested factors, while errors in fundamental frequency tended to decrease with increasing age/experience. Loudness was affected by distance, mask, and relative position, with increasing loudness as spacing decreased. Understanding influencing factors can inform recommendations for choral singing and education.

Intonation trajectories within tones in unaccompanied soprano, alto, tenor, bass quartet singing.

Unlike fixed-pitch instruments, the voice requires careful regulation during each note in order to maintain a steady pitch. Previous studies have investigated aspects of singing performance such as intonation accuracy and pitch drift, treating pitch as fixed within notes, while the pitch trajectory within notes has hardly been investigated. The aim of this paper is to study pitch variation within vocal notes and ascertain what factors influence the various parts of a note. The authors recorded five soprano, alto, tenor, bass quartets singing two pieces of music in three different listening conditions, according to whether the singers can hear the other participants or not. After analysing all of the individual notes and extracting pitch over time, the authors observed the following regularities: (1) There are transient parts of approximately 120 ms duration at both the beginning and end of a note, where the pitch varies rapidly; (2) the shapes of transient parts differ significantly according to the adjacent pitch, although all singers tend to have a descending transient at the end of a note; (3) the trajectory shapes of female singers differ from those of male singers at the beginnings of notes; (4) between vocal parts, there is a tendency to expand harmonic intervals (by about 8 cents between adjacent voices); (5) the listening condition had no significant effect on within-note pitch trajectories.

Four-part choral synthesis system for investigating intonation in a cappella choral singing

Accurate tuning is an important aspect of singing in harmony in the context of a choir or vocal ensemble. Tuning and ‘pitch drift’ are concerning factors in performance for even the most accomplished professional choirs when singing a cappella (unaccompanied). In less experienced choirs tuning often lacks precision, typically because individual singers have not developed appropriate listening skills. In order to investigate accuracy of tuning in ensemble singing situations, a chorally appropriate reference is required against which frequency measurements can be made. Since most basic choral singing involves chords in four parts, a four-part reference template is used in which the fundamental frequencies of the notes in each chord can be accurately set. This template can now be used in experiments where three of the reference parts are tuned in any musical temperament (tuning system), in this case equal and just temperaments, and played over headphones to a singer to allow her/his tuning strategy to be investigated. This paper describes a practical implementation of a four-part choral synthesis system in Pure Data (Pd) and its use in an investigation of tuning of notes by individual singers using an exercise originally written to explore pitch drift in a cappella choral singing.

Roughness Minimization Through Automatic Intonation Adjustments

We have created a reintonation system that minimizes measured roughness of parallel sonorities as they are produced. Intonation adjustments are performed by finding, within a user-defined vicinity, a combination of fundamental frequencies that yields minimal roughness. The vicinity imposition limits pitch drift and eases real-time computation. Prior knowledge of the tones played and timbres used is not used for execution of the algorithm. We test a proof of concept prototype by adjusting equal temperament intervals rendered with a harmonic spectrum towards pure intervals in real-time. This prototype exemplifies musical and auditory characteristics of roughness minimization by adaptive techniques. We discuss the results obtained, limitations, possible improvements, and future work.

Intonation Drift in A Capella Soprano, Alto, Tenor, Bass Quartet Singing With Key Modulation

When a soprano, alto, tenor, bass (SATB) quartet sings unaccompanied, or a capella, the members of the group will tend to make use of non-equal-tempered intonation to govern their tuning. If the music they are performing visits different keys and they do maintain non-equal-tempered tuning, then the pitch center will have to shift from its starting point, which is a necessary consequence of the physics behind the use of a non-equal-tempered tuning system. The implication of this shift for tuning in a capella singing is that it is not possible both to maintain accurate non-equal-tempered tuning and to stay in pitch throughout music that modulates in key. To test this notion, a set of four-part exercises were written by the author that visit several different key chords in sequential progression. In each case, the starting and finishing chords were either identical or exactly an octave apart. Mean fundamental frequency values for each note were measured using four electrolaryngographs (one per singer), and the f0 data were normalized and plotted with respect to equal-tempered tuning to enable any overall tuning shift to be observed. The results indicate that singers do (1) tend to non-equal-tempered tuning and (b) do consequentially shift their intonation with modulation. These data indicate that pitch drift is potentially a necessary part of staying in-tune. Further work is required to identify items in the choral repertoire for which this effect is likely and then to inform the choral conducting and singing communities appropriately.

Pitch drift as a result of just intonation

The most easily recognized difficulty with just tuning is the large and confusing array of pitches that must be made available on a keyboard instrument in order to allow modulation to several keys. A given note name may have more than one pitch associated with it, sometimes several, depending on the context in which it is used. Using computer-generated instruments that provide a limitless supply of unique pitches, just intervals can be used exclusively and explored thoroughly. When applied to Giovani Gabrieli’s Sonata Pian’ E Forte, the strict use of just tuning forces the pitch center to drift lower as the music progresses. When pitches are held across certain chord changes, lower versions of previous pitches must be used in order to maintain just tuning. Though most nonkeyboard acoustic instruments, the brasses in this case, can vary the tuning of each pitch somewhat, most cannot match the degree of drift that occurs in the Gabrieli (‘‘A’’ begins the piece at 440 Hz and ends it at ∼398 Hz!). For players of these instruments a compromise between physical tuning limitations and the ideal of just intonation must be made. Players use just intervals wherever possible, until the pitch drift forces a decision as to where the ‘‘rub’’ will be. The pitch-drift phenomenon will be demonstrated.

Automation in General Aviation: Two Studies of Pilot Responses to Autopilot Malfunctions

Study 1 examined 4 automation-related malfunctions (runaway pitch trim up, roll servo failure, roll sensor failure, pitch drift up) and subsequent pilot responses. Study 2 examined 4 additional malfunctions, 2 more immediately obvious (runaway pitch trim down, runaway roll servo) and 2 more subtle (failed attitude indicator, pitch sensor drift down) than those in Study 1, and the effect of an auditory warning. Data collection was performed in the Civil Aeromedical Institute's Advanced General Aviation Research Simulator, configured as a Piper Malibu. Results suggest that maladaptive responses to some of these failures may, in a significant percentage of cases, lead to significant altitude loss, overstress of the airframe, disorientation of the pilot, or destruction of the aircraft. Percentages of successful recoveries, detection and correction times, and related indexes of performance are discussed in the context of malfunction type, flight profile, and auditory alerts.