Pitch Names Research Articles

정악곡 세령산을 활용한 국악 창작 수업 개발 - 개러지 밴드를 통한 실음 학습을 중심으로 -

The purpose of this study is to develop a Korean traditional music creation class program using Jeongak. Yeongsanhoesang, a representative piece of Korean traditional music that has been completed through a long period of transmission, has a variety of creative techniques and is highly utilized in creative classes. In this study, Seryeongsan was selected from the Yeongsanhoesang as a sanction song for the 5th to 6th graders of elementary school, and a class was developed to learn basic notation systems such as Yulmyeong(pitch names) and Jeongganbo, and to create music through tonal group learning and melody construction learning. In addition, for realistic music learning, a digital medium called the GarageBand was used so that the results of creative learning could be realized into actual music. This study is meaningful in expanding the scope of Korean traditional music creation classes and enhancing the applicability of actual music-oriented Korean traditional music learning using digital media by suggesting educational application of creative classes for Jeongak pieces, which was mainly used as music for appreciation.

Uluslararası Müzik Sertifika Programı Teori Sınavı İçeriklerine Yönelik Öğretim Elemanı Görüşleri

Araştırmanın amacı, müzik öğretmenliği lisans programındaki müzik teorisi derslerine yönelik içeriğin, The Associated Board of the Royal Schools of Music (ABRSM)’in baraj niteliği taşıyan 5. seviye teori sınavını aşmak için yeterli olup olmadığına ilişkin öğretim elemanları görüşlerini ortaya koymaktır. Araştırma, yöntemi bakımından niteldir. Araştırmada, Batı müziği teori ve uygulaması dersini yürüten 6 öğretim elemanı ile ABRSM 5. seviye teori sınavı içeriklerine yönelik görüşmeler yapılmıştır. Görüşmeler, yapılandırılmış görüşme tekniği ile gerçekleştirilmiş; veriler içerik ana lizi ile çözümlenmiştir. Öğretim elemanlarının görüşleri doğrultusunda ders içeriğini oluşturan nota/sus işareti değerleri, aralıklar, enarmonik perde bilgisi ve ilgili tonaliteyi bulma konularının öncelikli konular olarak sıralandığı; bu konular yeterince anlaşılmadan transpoze, terimler ve işaretler, çalgı ve ses grupları konularına geçilmediği anlaşılmakla birlikte; öncelikli konular dışındaki sorularda öğretim elemanlarının farklı görüşlerde olduğu ortaya çıkmıştır.

Relationship between synthetic colors for ambiguous sounds and presented pitch names

Relationship between synthetic colors for ambiguous sounds and presented pitch names

Auditory T-Complex Reveals Reduced Neural Activities in the Right Auditory Cortex in Musicians With Absolute Pitch.

Absolute pitch (AP) is the ability to identify the pitch names of arbitrary musical tones without being given a reference pitch. The acquisition of AP typically requires early musical training, the critical time window for which is similar to that for the acquisition of a first language. This study investigated the left–right asymmetry of the auditory cortical functions responsible for AP by focusing on the T-complex of auditory evoked potentials (AEPs), which shows morphological changes during the critical period for language acquisition. AEPs evoked by a pure-tone stimulus were recorded in high-AP musicians, low-AP musicians, and non-musicians (n = 19 each). A balanced non-cephalic electrode (BNE) reference was used to examine the left–right asymmetry of the N1a and N1c components of the T-complex. As a result, a left-dominant N1c was observed only in the high-AP musician group, indicating “AP negativity,” which has previously been described as an electrophysiological marker of AP. Notably, this hemispheric asymmetry was due to a diminution of the right N1c rather than enhancement of the left N1c. A left-dominant N1a was found in both musician groups, irrespective of AP. N1c and N1a exhibited no left–right asymmetry in non-musicians. Hence, music training and the acquisition of AP are both accompanied by a left-dominant hemispheric specialization of auditory cortical functions, as indexed by N1a and N1c, respectively, but the N1c asymmetry in AP possessors was due to reduced neural activities in the right hemisphere. The use of a BNE is recommended for evaluating these radially oriented components of the T-complex.

Spatial-musical association of response codes without sound.

Humans tasked with pressing a key on a computer keyboard in response to a pitch can respond more quickly to a high-pitched sound by pressing a key higher on the keyboard and to a low-pitched sound by pressing a lower key, compared with the opposite configuration. This so-called spatial-musical association of response codes (SMARC) has been considered to reflect the spatial coding of sound pitch rather than to be an artefact of the verbal labels denoting spatial positions for localising sounds. In this study, we completely excluded the latter possibility, that is, the directional effects of automatic sound localisation on the SMARC effect. We did this by examining whether the SMARC effect occurs without sound; that is, we investigated whether the effect would be elicited by written pitch names alone. We found that when musically trained participants judged pitch height labelled by visually presented word stimuli, the SMARC effect still occurred. This also happened among musically naïve participants when the height of the pitch was explicitly comparable with that of a referential pitch. We also found that musically trained participants exhibited the SMARC effect in response to pitch names even when the indicated pitch height was irrelevant to the task they were asked to perform. These results suggest that the SMARC effect can occur at the semantic level in the absence of sound, clearly excluding the directional effects of automatic sound localisation.

Increased activation in the left ventrolateral prefrontal cortex and temporal pole during tonality change in music

In human music, the tonality (key) may change to punctuate sectional structures and to produce emotional effects. A tonality change would sound “smoother” when it is supported by appropriate harmony. This functional magnetic resonance imaging study examined the neural substrates of the processing of tonality change. We used a 2 × 2 factorial design with factors tonality change (tonality changed versus tonality unchanged) and harmonization (harmonized versus unharmonized). Participants were asked to covertly sing the pitch names in the movable-do system along with the heard melody. Repetitions of this melody were associated with or without a tonality change, with equal probability in a pseudo-random order. Our result demonstrated that tonality changes elicited increased activation in the left ventrolateral prefrontal cortex and left temporal pole. When a tonality change occurred, the left ventrolateral prefrontal cortex might underpin the cognitive control for retrieving the pitch-naming rule of the new tonality, whereas the left temporal pole might integrate the melodic/harmonic context and emotional meanings of music. This study provides a new insight into the cognitive and emotional processing of music.

The magic square of Olocin Ozzaniugnas

In 2009 Herbert Seifert published a description of certain Vivaldi sources held in the Estensischen Musikalien collection at the Österreichische Nationalbibliothek. In passing he described an unusual manuscript pasted into a print of Vivaldi’s op.2 violin sonatas—a ‘magic square’, consisting of a repeated array of alphabet symbols, running both horizontally and vertically, with an obscure series of pitch names running in four columns alongside. Although Seifert could not explain this document, he did identify the scribe as Nicolo Sanguinazzi (who tended to sign his name backwards), a bass string player who also copied many of the other items in the collection. Although Sanguinazzi held the collection prior to its acquisition by the Obizzi family in the late 18th century, no connection between the families has yet been made. This article offers both an explanation of the magic square and a possible identification of Nicolo Sanguinazzi as the uncle of Angela Sala, wife to Fernando Obizzi and mother to Tommaso Obizzi, the founder of the collection. The ‘magic square’ is in fact a visual guide to aid in the transposition of harmonic patterns using the alphabet symbols of 17th-century guitar notation (alfabeto). Alfabeto represents an anomaly in relation to the rest of the collection. These symbols do not appear anywhere else within the Vivaldi print, and are in any case stylistically inappropriate for that repertory. And Sanguinazzi’s other contributions to the collection postdate 1710, when alfabeto symbols were no longer current—he himself seems to have lived at least until 1740, at which point the alfabeto system was over 150 years old. There are antecedents, going back to the 16th century, of charts combining the alfabeto system with other types of harmonic notation, and Sanguinazzi’s magic square can be interpreted in that tradition. It is unique, however, in the extent to which it attempts to merge the alfabeto system with major–minor harmonic tonality. This remarkable visual artefact argues for the influence of 17th-century harmonic practice, in the form of alfabeto symbols, well into the early 18th century, long past the currency of alfabeto as a performance practice.

The effect of harmonization on cortical magnetic responses evoked by music of rapidly changing tonalities

The act of shifting from one key to another is termed tonal modulation, which has been used to articulate emotion expressions and formal structures in Western music. The present study recorded cortical activity to examine how the auditory-evoked magnetic fields are affected by harmonizing music of rapidly changing tonalities. Participants were asked to covertly sing the pitch names of well-learned modulating melodies along with the harmonized or unharmonized melodies. In our musical stimuli, three flats were added to the key signature for every four beats. Such a rapid modulation is achieved by a chromatic inflection of the submediant tone between the third and fourth beats. Tonal modulations with such chromatic progressions are termed chromatic modulations. A major finding was that the amplitude of N1m (neuromagnetic response at approximately 110 ms after the onset of a stimulus) was significantly reduced by harmonization only when a modulation occurred. We also observed that harmonization enhanced the P2m (neuromagnetic response at approximately 200 ms after the onset of a stimulus) amplitude. The results provide evidence of the impacts of harmonization on attention efforts and pitch categorization.

Neuromagnetic brain activities associated with perceptual categorization and sound-content incongruency: a comparison between monosyllabic words and pitch names.

In human cultures, the perceptual categorization of musical pitches relies on pitch-naming systems. A sung pitch name concurrently holds the information of fundamental frequency and pitch name. These two aspects may be either congruent or incongruent with regard to pitch categorization. The present study aimed to compare the neuromagnetic responses to musical and verbal stimuli for congruency judgments, for example a congruent pair for the pitch C4 sung with the pitch name do in a C-major context (the pitch-semantic task) or for the meaning of a word to match the speaker’s identity (the voice-semantic task). Both the behavioral data and neuromagnetic data showed that congruency detection of the speaker’s identity and word meaning was slower than that of the pitch and pitch name. Congruency effects of musical stimuli revealed that pitch categorization and semantic processing of pitch information were associated with P2m and N400m, respectively. For verbal stimuli, P2m and N400m did not show any congruency effect. In both the pitch-semantic task and the voice-semantic task, we found that incongruent stimuli evoked stronger slow waves with the latency of 500–600 ms than congruent stimuli. These findings shed new light on the neural mechanisms underlying pitch-naming processes.

To understand staff notation aurally

Name: Suzanne Konings Main subject: Master of Music Theory Research coach: Lázsló Nemes Title of research: What's in a name? The relation between pitch notation, note names and sight singing in different forms of pitch notation and in different ways of approaching pitch notation Research questions: Are absolute note names necessary in sight singing, when reading pitch notation on the stave relatively? Mental process: one sees ‘do’ (a name that indicates a function) and thinks ‘F’ (indicating a pitch). Are relative note names necessary in sight singing, when reading pitch notation on the stave ‘absolute’? Mental process: one sees ‘F’ (a name that indicates a pitch) and thinks ‘do’ (indicating a function). Abstract: Sight singing is a part of almost every music theory curriculum in conservatoires. But one might ask oneself why lessons in sight singing are needed for students who can already read music notation? The answer usually is: to develop the aural imagination in relation to music notation. The way students have learned to read music notation in the first place did not develop this skill well enough then? Experiences in teaching made me think that we need functional note names (unique sound names) to be able to aurally understand pitch in staff notation, and that the absolute note names (unique pitch names) may be an instrumentally useful, but less effective step ‘in between’ in aural imagination. From existing literature and recorded tests with students performing special designed scores I hoped to learn more about connecting the inner hearing world to music notation in the most effective way. Biography Suzanne Konings studied music theory and musicology and has been the head of the music theory department in the Royal Conservatoire The Hague since 2004. From 2009 she has been specialising in teaching music according to the Kodály concept. Together with colleagues in and outside the conservatoire she is organising training programmes for teachers and musicians in elementary schools, music schools and higher music education. She teaches musicianship classes for students in the Royal Conservatoire and the National Youth Choir of the Netherlands.

Optimizing Chew and Chen's Pitch-Spelling Algorithm

Pitch-spelling algorithms attempt to compute the correct pitch names (e.g., C#4, Bb5) of the notes in a passage of tonal music, when given only the onset time, MIDI note number, and possibly the duration and voice of each note. This article reports on a study in which Chew and Chen’s (2003a, 2003b, 2005) pitch-spelling algorithm was re-implemented and then optimized by running it with a range of different parameter value combinations on a test corpus containing 195,972 notes and consisting of 216 movements from works by eight Baroque and Classical composers. The results of this evaluation cast doubt upon some of the claims made by Chew and Chen that were based on results obtained by running their algorithm on a much smaller test corpus containing only 4,462 notes and consisting of just two movements from sonatas by Beethoven and You-Di Huang’s Song of Ali-Shan. The results presented here suggest that Chew and Chen’s algorithm could be simplified in various ways without compromising its performance.

The ps13 pitch spelling algorithm

In the ps13 pitch spelling algorithm, the pitch name of a note is assumed to depend on the local key and voice-leading. In the first stage of ps13, the pitch name implied for a note by a tonic is assumed to be the one that lies closest to that tonic on the line of fifths. The strength with which a pitch name is implied for a note is assumed to be proportional to the sum of the frequencies of occurrence, within a context around the note, of the tonics that imply that pitch name. In the second stage of ps13, certain neighbour-note and passing-note errors in the output of the first stage are corrected. An implementation of ps13, called PS13, spelt correctly 99.31% of the notes in a 195972 note test corpus, . A post-processing phase was added to PS13 in which the pitch names computed by PS13 are transposed by a diminished second if this brings them closer on the line of fifths to the pitch names of the notes in their vicinity. This version of the algorithm spelt 99.43% of the notes in correctly. When the second stage was removed altogether from PS13, 99.44% of the notes in were spelt correctly. The ps13-based algorithms achieved higher note accuracies than the algorithms of Temperley, Longuet-Higgins, Cambouropoulos and Chew and Chen on both and a “noisy” version of containing temporal deviations similar to those that occur in MIDI files derived from human performances.

Real-Time Pitch Spelling Using the Spiral Array

This article describes and presents a real-time bootstrapping algorithm for pitch spelling based on the Spiral Array Model (Chew 2000). Pitch spelling is the process of assigning appropriate pitch names that are consistent with the key context of numeric representations of pitch, such as MIDI or pitch class numbers. The Spiral Array Model is a spatial model for representing pitch relations in the tonal system. It has been shown to be an effective tool for tracking evolving key contexts (Chew 2001, 2002). Our pitch-spelling method derives primarily from a twopart process consisting of the determining of context-defining windows and pitch-name assignment using the Spiral Array. The method assigns the appropriate pitch names without having to first ascertain the key. The Spiral Array Model clusters together closely related pitches and summarizes note content by spatial points in the interior of the structure. These interior points, called centers of effect (CEs), approximate and track the key context for the purpose of pitch spelling. The appropriate letter name is assigned to each pitch through a nearestneighbor search in the Spiral Array space. The algorithms use windows of varying sizes for determining local and long-term tonal contexts using the Spiral Array Model.

Aural Archetypes and Cyclic Perspectives in the Work of John Coltrane and Ancient Chinese Music Theory

shaman is, then, a cosmically instructed man. His initiation is appropriate to the outer forms of his existence, yet bears an archetypal stamp. --Stephen Larsen (1988, 81) following work, by relating musical constructs with cross-cultural concepts, proposes essential parallels between John Coltrane's enigmatic diagram of 1960 (see Lateef 1981, inside cover; Schott 2000, 355-356) and several ancient cyclic music theories of China. Consequently, with a reconsideration of commonly accepted analytical approaches to Coltrane's later musical periods, a perspective offers a more artistically relevant view toward his developing musical conceptions of the 1960s as well as a more integrated understanding of modal practices in general. Historically, the inclusivity of jazz tradition has inspired many musicians to introduce a variety of world influences into a predominantly African-American musical heritage. Beyond general concepts of pentatonicism, though, specific Chinese references to historical jazz practices have thus far remained untapped. Scholarly significance in this area must move both analytical and performance worlds forward, primarily because of the manifold potential in applying ancient Chinese theories toward the analysis of a twentieth-century musical culture like jazz. Indeed, from two seemingly far-removed worlds, tangible relationships are generated for Chinese traditional and American jazz music scholars alike in ways such as the following. * Ancient esoteric Chinese concepts applied practically by the jazz performer will affect cognitive interaction both socially with the listener and personally with the historical tradition at hand. * Theoretical insights, when compatible between two or more removed cultural-historical contexts, raise important potential for creating larger, more unifying musical theories--not necessarily of any particular practice in itself but rather for more cultural practices in general--in all, furthering our understanding of human commonalities through music. * Considering the possibility that similar resources could give rise to the conception of similar approaches between modulatory traditions, then from and beyond the singular jazz model presented here, speculation could be returned toward how ancient Chinese and other musical practices may relate to the surviving theoretical documents of their time. This comparative work hones theoretical aligning of those tonal processes that together reveal more than common pentatonic perceptions have thus far allowed. For example, in regard to a recently discovered Chinese bell-set from the fifth century B.C., Liang (1985, 74-75) points out that: The evidence for a modulation practice is especially compelling when one considers, for example, the purpose of having almost identical tuning modes, pitch names and registers in sub-sets G.5 and G.6, but with different temperaments.... Regrettably, the ancient tonal and modulation practice has long been a lost art ever since the end of the Zhou period (1075-256 B.C.).... [I]nstrumental artifacts suggest that the theoretical formula and recorded theoretical systems manifest a belated doctrine, whereas the actual music practices of the Zhou period may have been much more advanced than what was theoretically documented. By realigning our jazz perception of John Coltrane's modal periods of the 1960s with ancient Chinese musical theoretical constructs, whether actually practiced or not, a door opens onto a cross-cultural view compatible with more than one practice alone. And once again, as speculative (which in itself seems a redundant phrase, for all theory must, on some level, carry an inherent sense of the speculative), such cross-cultural study accepts the importance of comparing historically removed concepts, traditions, and individual practices for the sake of initiating new theories, thus inviting the potential of transcultural considerations to emerge from the models discussed. …

The Paradoxes of Octave Identities

My study highlights an interesting phenomenon: that of the octave paradoxes. As is known, it is a commonplace in musical thinking that musical sounds an octave apart have the same pitch quality. That is indicated by the periodic repetition of pitch names by octaves. There are, however, scholarly endeavours pointing out that the awareness of the octaves as having two sounds of similar quality was the product of a historical process and there existed cultures in which the fact of octave identities was not evident, in which the octave had no distinguished role in structuring the musical relations. It is a common experience of music teachers that musically untrained people sometimes mistake the fifth or fourth for the octave. All this suggests that the recognition of octave identities is an acquired ability, without disproving that the phenomenon of the identity of octaves is based on psychoacoustic foundations. There have been animal experiments to prove that when eliciting a conditioned reflex implanted as a response to a definite pitch, the octave were sometimes confused, that is, pitches an octave apart mediate identical information to the experimental animals.' The question is: whether the similarity of the stimuli, or the pecularities of auditory sensations account for the mistaken octaves.2

A psychological experiment on quantitative judgment for transposition of melodies

Novice musicians have difficulty in judging the interval between a melody and its transpose quantitatively. It is expected that the more one accumulates musical experiences, the more he or she can improve their ability of quantitative judgment for the interval between a melody and its transpose. It is supposed that this ability depends on abilities of absolute pitch. Psychological experiments were conducted to investigate relations among these abilities. Single tones, pairs of single tones, and pairs of melodies and their transposes generated by a synthesizer were used for the experiments. Subjects (students majoring in music) were asked to give pitch names of single tones presented in isolation, to judge intervals between two single tones presented sequentially, and to estimate the interval between a melody and its transpose presented on a continuous rhythm pattern. From the experiments, it can be seen that there are various types of difficulties in judging musical intervals between two single tones and those between melodies and their transposes. Further, weak correlation has been found between the ability to judge intervals between two single tones, and the ability to judge intervals between a melody and its transpose.

Absolute pitch.

Absolute pitch (AP) is the ability to identify a tone's pitch or to produce a tone at a particular pitch without the use of an external reference pitch. AP exists in varying degrees among people generally described as AP possessors. AP possessors vary not only in the accuracy with which they can identify pitches but also in their ability to produce pitches absolutely and in their ability to identify tones of various timbers and in various pitch registers. AP possessors' memory for pitches is mediated by verbal pitch names; they do not have superior memory for pitches per se. Although the etiology of AP is not yet completely understood, evidence points toward the early-learning theory. This theory states that AP can be learned by anyone during a limited period early in development, up to about age 6, after which a general developmental shift from perceiving individual features to perceiving relations among features makes AP difficult or impossible to acquire.

Absolute-Pitch Judgments of Black and White-Key Pitches

Absolute-pitch possessors have been reported to identify black-key pitches less quickly and accurately than they identify white-key pitches. However, it is possible in these experiments that the greater speed of identifying white-compared with black-key pitches was due to a motor response bias because the motor requirements for indicating a black-key pitch were more difficult than those for indicating a white-key pitch. The greater accuracy in identifying white-compared with black-key pitches may have been due to a choice response bias favoring white-key pitch responses. We compared absolute- pitch judgments of black-and white-key pitches in a task free of motor response biases. Subjects compared the pitch of an auditory tone with a visually presented pitch name and responded Same or Different. The absolute- pitch possessors responded significantly more slowly to black- key auditory pitches, and to black- key visual pitch names, than to white-key pitches and pitch names. These differences may have been due to perceptual and retrieval processes associated with the frequencies with which black-and white-key pitches and pitch names occur in music literature. Another possible explanation is that absolute-pitch possessors may learn absolute pitch for only white-key pitches in development and may interpolate blackkey pitches from neighboring white-key pitches. Experiments to test these alternative accounts are proposed.

A Musicological Interpretation of the Twelve Lus in China's Traditional Tone System

ery early in their recorded history the Chinese developed a tone system which divides the interval of the octave into twelve semitones by twelve consecutive steps of perfect fifths. The same system, with minor deviations, is known in Western music theory where it is called Pythagorean because tradition ascribes its mathematical construction to the Greek philosopher. In one of his studies the author was able to prove by physical evidence that this achievement was known in China several centuries before Pythagoras, probably in the ninth century B.C. or even earlier.3 The twelve semitones (Lus) received pitch names which are mentioned for the first time in the Kuo YUI, a work usually dated towards the end of the Chou Dynasty (3rd century B.C.). However, the Kuo Yi is believed to contain a good deal of much earlier material from ancient written sources4 and, as we shall see presently, the origin of the pitch names must be assigned to about 900 B.C. or earlier.

The Art of Tonal Thinking

T HE TOPIC of this paper has interested the writer intermittently for many years, and his interest in it has been responsible for more than twenty years of research and inventive effort to find means for facilitating accurate tonal thinking and the fluent expression of musical thought. This problem is as old as the phenomenon we call music. The ancient Greeks, including such intellectual giants as Aristotle (384-322 B.C.), Aristoxenus of Tarentum (4th Century B.C.), and Pythagoras (582487 B.C.), who invented the Monochord with frets to indicate pitch, sought solutions to this perplexing problem. Aristoxenus developed the Greek modes-Lydian, Dorian, Phrygian, Hypophrygian, Aeolian, etc. The tones of the modes were named after the seven strings of the lyre, from the highest, Hypate, to the middle or fourth string, Mesa, to the lowest or seventh string, Nete. To these basic names were added the prefix Para, meaning next to. Imagine trying to sing a foursyllable word like Paranete to a melodic succession in sixteenth-note rhythm, as in our song Dixie. Guido d'Arezzo (born c.990 A.D.), a choirmaster of the eleventh century, invented the music staff. Guido had the same difficulty then that we have today in training singers to think, read, and write in terms of tonal relations. Accordingly, he had his pupils practice singing while playing the tones on Pythagoras' Monochordused as a tonal space-frame. Guido, finding the polysyllabic Greek names of Aristoxenus unsingable, invented monosyllabic singing names, ut re mi fa so la, derived from the initial words of the lines of the Hymn to St. John. Here, as we all know, was the source of the British Tonic-Sol-Fa system, developed and promoted by John Curwen. This, in turn, was the source of the American Movable Do system. Carl Eitz, a German scientist and colleague of Wilhelm von Humbolt and of Hermann von Helmholz, developed an absolute system of arbitrary names which he called Tone-words. These consisted of monosyllabic phonetics for each of the tones and their chromatic inflections of sharps and flats, double sharps and double flats-some thirty-five different tonal phonetics with an initial consonant and the euphonious vowels a, e, i, o, u. The Eitz system has had wide use in Germany. It seems doubtful, however, that it could ever be adopted in our country because, unfortunately, the Eitz names have no connotation with our staff-notational system, with our pitch names, nor with the German pitch names. In France, the number system is used. It is known as the Galin-Paris-Cheve System-a method of teaching part-singing and part-reading with number 1 for do, 2 for re, 3 for mi, etc., and a zero for silence. The numerals are used only as graphic symbols, while the singing names are the sol-fa syllables with do the fixed pitch. Hence: the Fixed Do system. Even though the system was advocated by the French philosopher Jean Jacques Rousseau and the composer Hector Berlioz, it is difficult to see how it can help singers to think and sing precise intervals when the phonogram do-mi-so may represent a major triad, a minor, an augmented, or a diminished triad! The number system does not seem practical. Perhaps it is impractical because its authors were not practicing music teachers; Pierre Galin was a doctor, Aime Paris, a lawyer, and Emile Cheve another doctor.