Pentatonic Scale Research Articles

The Aesthetics of Dissociation: Radiohead's “How to Disappear Completely” and Jasper Johns's Device Paintings

The Aesthetics of Dissociation: Radiohead's “How to Disappear Completely” and Jasper Johns's <i>Device</i> Paintings

Changes in acoustical design from ancient shakuhachi to modern shakuhachi

The shakuhachi was originally introduced from China in the Tang dynasty around 750. Since this ancient shakuhachi has been preserved in the Shousouin of the Toudaiji temple, it is called the “Shousouin shakuhachi”. This shakuhachi, which has six tone holes to play a Chinese diatonic scale (e.g., A-B-Db-D-E-Gb-A, D-E-Gb-G-A-B-D), was adapted to play a Japanese pentatonic scale (D-E-G-A-B-D) by removing the second tone hole (Gb) around early 16th century. Moreover, the positions of five tone holes were modified to make effective use of the pitch bending (e.g., Eb) by drawing down player's jaw and half-covering the tone hole(s) around the 17th century, and a scale pattern D-F-G-A-C-D was established. Since this shakuhachi (made from the root end of bamboo) was played exclusively by a group of wondering priests (“Komusou”), it is called the “Komusou shakuhachi” and regarded as the origin of the modern shakuhachi. Changes in acoustical design from the Sousouin shakuhachi to the Komusou shakuhachi are considered based on the input admittance calculated from the inner geometry. The blowing conditions of the Shousouin shakuhachi are estimated from the investigation carried out during 1948 to 1952. Some problematic points in cross-fingerings of the Shousouin shakuhachi are also discussed.

Use of Traditional and Nontraditional Instruments with Traumatized Children in Bethlehem, West Bank

The purpose of this paper is to discuss the author's experiences and observations concerning Palestinian children's musical responses when playing traditional and nontraditional music instruments during music therapy sessions and reflect upon the implications for music therapists working in other cultures. The children involved were 20 first to fifth graders from two different schools in the Bethlehem within the West Bank of the OPT. They ranged in age from 7 to 1 2, with a mean age of 9.45 years. The focuses of the entire project involved evaluating the potential for using a seven-component music therapy protocol (Behrens, 2008) to develop the emotional coping skills of children traumatized by the ongoing conflict within Bethlehem (Thabet, Abdulla, Elhelou, & Vostanis, 2006; Thabet, Abed, & Vostanis, 2002, 2004), and to investigate the emotional support provided by families and social support systems within the community. Although Palestinians have traditionally tended to be fairly stoic in their expression of emotions (Baker & Shalhoub-Kevorkian, 1999; Pines & Zaidman, 2003), most people in Bethlehem stated that the on-going multitraumatic situation now warrants a change (Mapp, Behrens, & Socha, 2012). Many now believe talking about emotions is a way for the children to cope and develop resilience (Mapp et al., 2012). I left with only minimal plans for the music therapy sessions based on my limited email interactions with one health care professional at a facility in Bethlehem. As the setting and limited opportunity to prepare provided challenges in setting up the program, I therefore needed to explore and make all arrangements for the music therapy sessions once I arrived, including the purchase of some instruments.Use of Instruments as Reported by Other Music TherapistsUnfortunately, there is little written about what music therapists might consider when selecting music instruments for use in sessions involving clients from other cultures. At most, music therapists working with traumatized individuals from other countries or with clients from other cultures only listed or briefly discussed the instruments with which they worked. Orth and Verbingt (1998) reported working with refugee clients using instruments from their native countries as well as what they called universal instruments such as guitar and (p. 86). Chase (2003) referred to the piano and guitar as more Western-European instruments and suggested using rhythm and accompanying instruments from other countries such as cabasas, maracas, and guiros. These instruments, however, have become common in most music therapy sessions in the United States. In a later report of their work, Orth, Doorschodt, Verburgt, and Drozdek (2004) discussed that they also used drums, xylophones, and harps tuned to a pentatonic scale, rainmakers, ocean drums, small rhythm instruments, and rhythm eggs. Within the Sing and Crow programs in Australia, Williams and Abad (2008) used indigenous instruments that were supplied by the organizations with whom they worked. Pavlicevic (2002) wrote about using any instrument or sound surface that was available such as tables, glasses, or the floor, with the children in Africa. Lang and Mclnerney (2002) discussed using drums, piano, and xylophones with the children in Bosnia. Although Bergmann (2002) also reported the benefits of music therapy programs in Bosnia, her discussion did not involve a list of selected music instruments.Though this literature provides some context for music selection, it does not adequately contextual ize how instruments may be selected and used. This created somewhat of a dilemma - how does one go about selecting instruments when working with clients in a new cultural setting. As no clear guidelines were provided, I began by examining multicultural literature to see if suggestions or guidelines might emerge.Review of Multicultural ConceptsWhen working with clients from other cultures, there is a growing body of literature about various multicultural principles that could influence a therapist's choice of music instruments and interpretation of resulting musical responses. …

Abaana Bange Na-Ka-Lwa for soprano saxophone in B flat, electric guitar and marimba

Abaana Bange Na-Ka-Lwa (My Children Na-Ka-Lwa) is programmatic in nature and reflects two major compositional influences of ethnic Ganda music and Western music. The instrumentation is Western, whereas the style is broadly Ganda because of the extensive use of the pentatonic scale, fixed harmony, polymeters and polyrhythms, metric shifts, the steady and strict metric pulse, and the simulated Ganda music tone colors. JOURNAL OF THE MUSICAL ARTS IN AFRICA VOLUME 8 2011, 113–114

The Musical Bow of the Bununs Tribe in Formosa and Suggestion as to the Origin of the Pentatonic Scale

The Musical Bow of the Bununs Tribe in Formosa and Suggestion as to the Origin of the Pentatonic Scale

Model Development of Isan Country Song Compositions for Economic, Social and Cultural Value-Added

Problem statement: Country Song was related to history, society, culture and economic. The objectives of this study were: (1) the historical background in composing the Isan Country Song, (2) the current situation and problem of composing style of Isan Country Song and (3) the development of composing pattern the Isan Country Song for elevating the economic value. Approach: The research area consisted of Isan Region including Chiaya Phume, Ubon Rachatani, Amnat Charoen and Sri-Sa-ket Provinces. The samples providing information included 170 persons. The instruments using for collecting data included: The Survey Form, Interview Form, Focus Group Discussion and Participatory Workshop. The data were classified into groups. Qualitative data were analyzed according to the specified objectives. The research findings were presented in descriptive analysis. Results: The research findings found that the historical background of Isan Country Song, reflected lifestyle, social situation, ideal, and Thai Culture with the rhyme developed from traditional Country Song blending with Big Brand Music Band mixing with the local singing words and rhythm. The current situation and problem after listening to the Country Song was more increasing popular since there were many song composers and chords. There were advertisements through the media as radio, television, mobile phone and internet network. Therefore, the buying and selling of song were easier and quicker. For the song composing, the text of a song didn’t focus on the rhyme and lacked of morality enhancement. The supplementary music sometimes lacked of beauty based on aesthetic principle. For the commercial problems, there were many violations of right. Consequently, the entrepreneur sometimes faced with the lost. For development, the god points of Isan Country Song were analyzed both of the text and rhyme. The composed song model was created by bringing Pentatonic scale mixing with message of Dorian Mode. The musical instrument using for playing consisted of Isan Country Song and Western Music. Conclusion/Recommendations: Isan Country Song was still necessary for opposing the entertainment like the villager representatives. Besides, it could be developed for beauty based on music principle. In some viewpoints, it could be used as commercial usefulness. Therefore, in order to maintain the identity of Country Song which needed to be studied for knowing the development of song work, it would be good. This research could be able to be a model for new style Country Song.

Woody Shaw, Above and Beyond: An Analysis of Woody Shaw’s Use of the Pentatonic Scale and Chromatic Substitution in the Improvised Solo’s of Moontrane

Woody Shaw, Above and Beyond: An Analysis of Woody Shaw’s Use of the Pentatonic Scale and Chromatic Substitution in the Improvised Solo’s of Moontrane

Letters

BOOKS Atlantic Yards is the largest project Frank Gehry, now seventy-eight, has ever undertaken. And if it proves to be his last large project, it will be a fitting capstone to a career utterly blind to the public function of architecture. For how better to assert your dedication to personal expression over context than to have your distinct visual style serve as the emblem for the death of two Brooklyn neighborhoods? Jacobs's legacy, on the other hand, is assured. Her influence continues to be present both where she is heeded and where she is ignored. I even know of one Manhattan bar where you can order a "Jane Jacobs" (Prosecco, elderflower liqueur, orange bitters, Hendrick's gin). I know of no establishment where you can order a "Frank Gehry." Certainly not in Brooklyn. • CHARLES TAYLOR is a columnist for the Newark Star-Ledger and a contributor to the New York Times, the New York Observer, the Nation, and other publications. SINUMINED The Rest Is Noise Editors: Barry Gewen's review of Alex Ross's The Rest Is Noise (Winter 2008) contains a factual error that illustrates the flaw in his argument. He describes the Beatles song "Norwegian Wood" as having a "pentatonic melody"—a melody restricted to five notes—which he says gives it a "skeletal quality." But the song's uncanniness comes from its use of an eccentric scale called the mixolydian. The mixolydian scale is exactly like the major scale— the do-re-mi scale from The Sound of Music—except that the seventh note—ti—is lowered by a half-step. After its E mixolydian opening, "Norwegian Wood" modulates abruptly into the key of E minor, adding yet an eighth note to its melodic palette. Gewen emphasizes the pentatonic scale because he equates tonality with simplicity. But as the surprising sophistication of "Norwegian Wood" demonstrates, that's a dangerous mistake to make. And while Gewen is right that African music frequently uses the pentatonic scale, it just as frequently has a rhythmic complexity that's daunting to even the best-trained Western musicians. The twentieth-century's classical music was not all one atonal shriek. Its best composers and its best songwriters were largely mining the same vein. Alex Ross knows this, which is why he devotes whole chapters of his book to tonal composers like Sibelius, Copland, and Britten. Portraying Ross as a champion of atonality is as gross a distortion as portraying the Beatles as naïve rubes. Lennon and McCartney, like Shostakovich and Britten, were tonal composers constantly testing themselves against the limits of their inherited forms. LARRY HARDESTY Somerville, Mass. Barry Gewen Replies Larry Hardesty is correct about "Norwegian Wood," and I apologize for the error. But I believe my general argument still holds. Hardesty's analysis either parallels or is derived from Wilfrid Mellers's analysis of "Norwegian Wood" in his 1973 book, The Music of the Beatles: Twilight of the Gods. Mellers too noted that the song is in the mixolydian mode (hardly an "eccentric scale"). But he also offered many examples of Beatles songs that are Pentatonic either in whole or in part—"She Loves You," "I Saw Her Standing There," "I Wanna Be Your Man," "I'm Happy to Dance with You," "Things We Said Today," "Help," "Michelle," "When I'm Sixty-Four," "A Day in the Life," and . . . but why go on? As Mellers observes, "the nature of the tunes (both of folk soloists and of rock groups) is conditioned by their origins. . .. The melodies tend to be pentatonic, or at most modally heptatonic." As for Hardesty's other points, I wasn't aware that I portrayed Ross as a "champion of atonality" but of modern music that grows out of the crisis of the European classical tradition. (If anything, I find Ross too eclectic.) And when Hardesty says I equate tonality with simplicity , I confess I don't recognize either myself or my argument . The B-minor Mass simple? Don Giovanni? My point, rather, was that tonality, both diatonic and pentatonic, grounds us in a universal humanity in a way that music written from within the modern classical tradition does not. CORRECTION: On page 73...

Time marching spectral analysis of a swept sine melody model

A melody is a progression of musical notes in a scale. Since the notes have identified frequencies, a melody rendering involves a quick sweep of frequencies between any two neighboring notes, and a dwell at the notes. A melody rendering is modeled as a dwell at the notes and a sinusoidal sweep in between. A time marching spectral analysis shows that the dwell time and the rate of sweep between notes have significant influence on the melody. Any two notes form the not-so-high harmonics of a periodic process which may or may not necessarily contain the fundamental and some of the lower harmonics. If a three-note combination of a first, a fifth, and an octave higher notes are taken, as the drone in Indian classical music, they have ratios of 1:3/2:2. The combination is a periodic process with half of the first note frequency as the fundamental which is missing, while the second, third, and fourth harmonics are present. A melodic rendering of seven notes or less may be construed as a periodic process with some of the harmonics varying or dancing with time. Results on a melody in pentatonic scale is presented and discussed.

Composers of Classical Music of Jewish Descent (review)

Reviewed by: Composers of Classical Music of Jewish Descent Stephen Luttmann Composers of Classical Music of Jewish Descent. By Lewis Stevens . London; Portland, OR: Vallentine Mitchell, 2003. [ xxiii, 384 p. ISBN 0-85303-486-6. $62.95.] Illustrations, index. Few would question the propriety of a work of this nature; fewer still would question its potential usefulness. A reference work largely devoted to biographical sketches of "composers of classical music of Jewish descent" has to address three fairly prickly issues at the outset, however: What is classical music?; Who should be considered a composer of classical music?; and Who should be considered Jewish? The author, Lewis Stevens, has the perspicacity to answer all three questions at the outset, and while one may not be wholly satisfied with the answers, one must at least admire the clarity with which Stevens demarcates his territory. Classical music is "music that has sprung broadly from the European musical tradition, and is generally included in standard works on classical music" (p. 2)—yes to the motet, no to jazz and klezmer. He defines composers to the extent that musicians best known as performers or scholars are included if they composed within the classical music tradition. As for the matter of who is a Jew—certainly the question most likely to arouse passionate discussion—Stevens respectfully rejects Jewish law as too restrictive, and includes those with at least one Jewish grandparent, regardless of their religious practice or sense of Jewishness. Although he does not say so, this does strengthen his work considerably by allowing readers to compare the relationship of composers to their cultures and matters of faith in a given place or time. The book divides into two parts: a series of introductory essays running just shy of a hundred pages, and the biographical sketches themselves. The essays are well-meaning but otherwise have little to recommend them. Already the second sentence of chapter 1, in which the author feels compelled to footnote his observation that neumes were in use before the tenth century, raises the suspicion that Stevens is neither comfortable writing about music, nor especially equipped to do so. This is in fact one of the book's two fatal weaknesses; confirmation of the suspicion is delivered repeatedly in the next few pages. With regard to the relationship of notation and polyphony, he writes: An important change that occurred from the time of the Middle Ages was that musical tradition was no longer an oral tradition. Whilst monophonic music (a single melodic line) can be learned and handed down orally, it is all but impossible to memorize polyphonic music, which not only requires remembering each line, but also how they fit together. For the development of complex polyphonic music, a system of notation was a prerequisite. (pp. 12-13) Buried in this farrago of naïveté, false assumption, and non sequitur is a hint of the book's other fatal weakness: the absence of all but the most cursory attempt at editing beyond page layout ("change that occurred from the time"; "each line . . . they"). What should have been a useful description of the Jewish liturgical modes is an unintentionally virtuosic display of musical ignorance and terminological carelessness. Stevens notes (pp. 16-17) that there are five principal modes, two for use with scriptural texts and three for other devotional texts, and identifies the pitch sequences of all five, following to the letter the description in Alfred Sendrey's The Music of the Jews in the Disaspora (New York: Thomas Yoseloff, 1970). Both Stevens and Sendrey refer to the first two as "Pentateuch modes," one associated with the Sephardim, the other with the Ashkenazim. So far so good. Just a few pages earlier, however, Stevens refers to these two modes as "Pentatonic Sephardic" and "Pentatonic Ashkenazic" in a comparative graph of church, diatonic, and synagogue modes. They are, of course, not pentatonic at all, as they are formed by addition of tetrachords to form heptatonic scales. Stevens's confusion may have been caused by Sendrey's observation that Ashkenazic biblical motives "contain a sizable amount of intervallic patterns characteristic of the semitoneless pentatonic scale" (Sendrey, p. 175). But this confusion pales in comparison to...

Possible Influence of Linguistic Musical Background on Perceptual Pitch-Matching Tasks: A Pilot Study

Linguistic background has been identified as important in the perception of pitch, particularly between tonal versus nontonal languages. In addition, a link between native language and the perception of musical pitch has also been established. This pilot study examined the perception of pitch between listeners from tonal and nontonal linguistic cultures where two different styles of music originate. Listeners were 10 individuals born in China who ranged in age from 25 to 37 years and had spent on the average 30 mo. in the USA and 10 individuals, born on the Indian subcontinent, who ranged in age from 22 to 31 years, and had spent an average of 13 mo. in the USA. Listeners from both groups participated in two conditions. One condition involved listening to a selection of music characteristic of the individual's culture (China, pentatonic scale; Indian subcontinent, microtones), and one condition involved no music. All listeners within each condition participated in two voice pitch-matching tasks. One task involved matching the lowest and highest pitch of tape-recorded voices to a note on an electronic keyboard. Another task involved matching the voice pitch of tape-recorded orally read words to a note on the keyboard. There were no differences between the two linguistic groups. Methodological limitations preclude generalization but provide the basis for further research.

Comparison of erzincan central town ballads to Idil-Ural “Tataristan-Baskurdistan-Cuvasistan” region

As we study the pentatonic characteristics in the melodies of ballads of different cultures we may encounter some similarities in the melodies of Idil-Ural and Erzincan Central Town ballads of which people share a common background in the past. Some ballads from Erzincan region are similar from the view of pentatonic form to Idil-Ural region. But, we can notice that there are differences in the pentatonic scale of the two regions.

What Is Old and What Is New in the Traditional Music of the Volga-Kama Region

The theory based on the similarity of melody types in the Hungarian, Cheremis and Chuvash folk music and observed first by Bela Bartok, then Zoltan Kodaly emerged roughly 60 years ago. According to it, this musical congruence points to an origin preceding the conquest of the territory of Hungary by the Magyars: Thus the counterparts of the supposedly oldest Hungarian fifth-shift melodies can still be found among the present-day inhabitants of the one-time country of origin. In the thirties the musical material collected among the related (Finno-Ugrian and Turkic) peoples and available for comparative research some 600 to 700 melodies was published, except for 24 phonographed songs, in foreign collections. As a result, the melodies were not within easy reach for Hungarian scholars and none of the items was associated with Hungarian field experiences. Unfortunately, even the specific knowledge of musical notation was missing in several cases. Nevertheless, on the basis of mainly Mountain Cheremis and Northern Chuvash melodies it became obvious that a relationship, however distant in time and space, could be demonstrated by means of the pentatonic scale and the fifth-shift structure, respectively. This theory was apparently supported by historical facts and the already two hundred-year old linguistic research. In addition to the similarity of melody types there emerged some closely related Hungarian, Cheremis and Chuvash melodies as well. This circumstance strengthened the theory of musical relationship which seemed to be almost incontestable by then. We also have to take into consideration that the Hungarian pentatonic music which was meant to improve the whole Hungarian musical culture, and the

Interval-Class Content in Equally Tempered Pitch-Class Sets: Common Scales Exhibit Optimum Tonal Consonance

Pitch-class sets (such as scales) can be characterized according to the inventory of possible intervals that can be formed by pairing all pitches in the set. The frequency of occurrence of various interval classes in a given pitch-class set can be correlated with corresponding measures of perceived consonance for each interval class. If a goal of music-making is to promote a euphonious effect, then those sets that exhibit a plethora of consonant intervals and a paucity of dissonant intervals might be of particular interest to musicians. In this paper, it is shown that the pitch-class sets that provide the most consonant interval-class inventories are the major diatonic scale, the harmonic and melodic minor scales, and equally tempered equivalents of the Japanese Ritsu mode, the common pentatonic scale, and the common "blues" scale. Consonant harmonic intervals are more readily available in these sets than in other possible sets that can be drawn from the 12 equally tempered pitch chromas.

An interactive experimental method for the determination of musical scales in oral cultures

The contrapuntal vocal polyphony of the Aka Pygmies is based on a pentatonic scale but the nature of this scale is difficult to determine by ear. To overcome this problem and to circumvent difficulties of articulating such abstract concepts as musical scales which, for the Aka, are not subject to verbalisation, a method based on the use of a synthesiser was conceived and applied in a series of experiments among the Pygmies. In these experiments, polyphonic music of their own culture was simulated with different underlying scale models and submitted to their cultural judgment. This method was shown not only to cope with the initial problem but also to provoke a series of non-verbal interactions that open new dimensions for the study of cognitive aspects of musical systems in oral traditions.

Discrimination of melodies from the first and fifth serials of the pentatonic scale

A basic aspect of music is the scale or set of tones that is used to generate melodic and rhythmic patterns. There is one scale that has a prominent place in the music of many cultures. This scale, the pentatonic, dates back as far as 1300 B.C. and extends to the present. Data are presented on the discrimination of melodies randomly generated from the first and fifth serials of the pentatonic scale. The question is: does the part of the scale used to generate a melody give a distinct quality to the melody? The results show that such melodies can be discriminated independently of melodic line, rhythm, frequency range, and tone color. This suggests that melodies can be heard as being from two different serials, indicating that each of these serials possesses a quality, a tonality, that yields perceptually different melodies. The results are related to Orff’s theory of musical development.

Twelve Nasca Panpipes: A Study

aithful production of sound, as originally intended, is achieved with instruments that have not undergone any significant change since their construction. Instruments made of clay or stone meet this requirement of preservation over long periods. The dry climate prevalent on the Peruvian coast has preserved fragile textiles and also musical instruments (found among the contents of graves). Museum and private collections retain such artifacts, and panpipes made by craftsmen of the Nasca culture have been preserved in sufficient numbers for comparative studies. Studies covering Nasca panpipes were reviewed by Stevenson (1968:245-255). The pentatonic scale originally postulated for the Precolumbian period in what today is Peru has recently been questioned. About one-third of the samples covered in two investigations were labeled twins, or pairs, such as those on Moche vase paintings from the North Coast, which frequently show two panpipes linked by a cord. Dawson (1964) demonstrated slip casting to be the technique used by craftsmen of the Paracas and Nasca cultures of the Peruvian South Coast for producing pipes for panpipes. Essentially all the published pitch data pertaining to Nasca panpipes are expressed in Western notation with plus and minus signs to denote deviation from the written pitches. It was intended that the present study would use this information to determine the scale system used for the tuning of these instruments, but this plan was abandoned when results differing from the ones using frequency measurements were arrived at by using Western notation for the instruments to be described below. The purpose of this study is to describe twelve Nasca panpipes, to present tonometric measurements, and to analyze the determined frequency intervals in order to establish the scale system intended for the tuning of these panpipes.

The natural evolution of musical scales

The 12‐tone chromatic scale shall be shown to be a natural and evolutionary phenomenon, due to the pitch/interval responses of human hearing and the integral harmonic series of vibrating strings, air columns, and vocal chords. The important implication is that if music were to begin all over again, from day one, the same scale system of 12 chromatic tones would result. Credibility is gained by considering the origins of the pentatonic scale, in use since primitive times and precursor to the major and chromatic scales. The pentatonic scale is polytenetic, having evolved independently in the earliest cultures of Europe, Japan, Africa, Americas, Oceania, etc. Historically the Pythagoreans suspected the universality of such musical scales which consequently influenced their search for a numerical universal “harmony” (i.e., harmony of the spheres). Specific examples of vibrating strings under uniform tension (rates of vibration being reciprocal to respective lengths) can be seen in relationship to Pythagorean efforts ot represent the universe in simple numeric/geometric expressions. Beyond such historical considerations, comprehensive evidence supports the premise that the 12‐tone scale system of music, rather than being invented or contrived, is a natural, evolutionary and universal manifestation.

Markovian Versus Rhomboidal Patterning in the Song of Swainson's Thrush

1. This paper examines a claim of NELSON (1973) of rhomboidal patterning in the songs of Swainson's Thrushes reflecting supposed holistic control of the sequences. 2. The subjects were six Swainson's Thrushes recorded in the wild in Quebec. Samples from the six birds ranged from 40 to 346 songs. 3. We used a Ubiquitous Spectrum Analyzer, and Sonagraph to produce frequency-time displays, and the former to produce also amplitude-frequency spectra. 4. The songs consist of 5 to 7 consecutive syllables given in fixed sequence, except for occasional errors. Each bird had 3 to 7 song types, or particular sequences of syllables, also sung in fixed order. 5. Similar syllables may occur in different songs of individual birds. No convincing evidence of recombination units of syllable pairs was found. 6. Evidence essential to support the claim of rhomboidal pattern was found wanting. In particular a) the frequencies (pitches) of successive syllables do not fit a pentatonic scale; b) the validity of a keynote is doubted; c) the definition of rhomboidal patterning is so vague that even pseudorandom numbers yield results similar to those claimed for the thrushes. 7. Alternatively the Markovian model of sequences of events appears more suited to the songs of Swainson's Thrushes, based on the evidence of sequences of syllables and songs, and errors in these sequences.

A Positive Analysis on the Road from Nucleus to Pentatonic Scale

A Positive Analysis on the Road from Nucleus to Pentatonic Scale