A Biological Rationale for Musical Scales

Scales are collections of tones that divide octaves into specific intervals used to create music. Since humans can distinguish about 240 different pitches over an octave in the mid-range of hearing [1], in principle a very large number of tone combinations could have been used for this purpose. Nonetheless, compositions in Western classical, folk and popular music as well as in many other musical traditions are based on a relatively small number of scales that typically comprise only five to seven tones [2]–[6]. Why humans employ only a few of the enormous number of possible tone combinations to create music is not known. Here we show that the component intervals of the most widely used scales throughout history and across cultures are those with the greatest overall spectral similarity to a harmonic series. These findings suggest that humans prefer tone combinations that reflect the spectral characteristics of conspecific vocalizations. The analysis also highlights the spectral similarity among the scales used by different cultures

MYC Protein Expression in Primary Diffuse Large B-Cell Lymphoma of the Central Nervous System

Primary diffuse large B-cell lymphoma of the central nervous system (CNS DLBCL) is a rare, aggressive subtype of DLBCL, the biology of which is poorly understood. Recent studies have suggested a prognostic role of MYC protein expression in systemic DLBCL, but little is known about the frequency and significance of MYC protein expression in CNS DLBCL. Hence, we investigated MYC protein expression profiles of CNS DLBCL and assessed the relationship between MYC expression and a variety of histopathologic, immunophenotypic, genetic, and clinical features. Fifty-nine CNS DLBCL diagnosed at our institution over the past 13 years were evaluated. The majority of cases (80%) showed centroblastic morphology, and 12 (20%) displayed a perivascular pattern of infiltration. According to the Hans criteria, 41 (69%) cases had a non-germinal center B-cell and 18 (31%) had a germinal center B-cell cell-of-origin (COO) phenotype. Mean MYC protein expression was 50% (median: 50%, range: 10-80%). Forty-three cases (73%) showed MYC overexpression (≥40%), and 35 (60%) showed MYC/BCL2 coexpression. MYC overexpression was seen in the single case harboring MYC translocation and in the cases showing increased copies of MYC (27%); however, no significant difference in mean MYC expression was seen between groups harboring or lacking MYC aberrations. In our series, age was associated with a significantly increased risk of death, and the perivascular pattern of infiltration was associated with a significantly increased risk of disease progression. Neither MYC expression (with or without BCL2 coexpression) nor other variables, including COO subtype were predictive of clinical outcome. Our findings indicate that the proportion of CNS DLBCL overexpressing MYC is higher compared to systemic DLBCL, and MYC overexpression appears to be independent of genetic MYC abnormalities. Thus, MYC expression and other immunophenotypic markers used for prognostication of systemic DLBCL might not apply to CNS DLBCL due to differences in disease biology

The harmonic structure of a tonal dyad (a major third in this example) compared to a harmonic series.

<p>The fundamental frequency of the harmonic series used for comparison with the dyad is given by the greatest common divisor (100 Hz). In this case, the dyad comprises 8 out of the 20 harmonic frequencies in the harmonic series (percentage similarity  = 40%).</p

The 60 intervals with the greatest percentage similarity to a harmonic series.

<p>Interval size is the distance from a fixed tonic in cents. See <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0008144#s2" target="_blank">Methods</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0008144#pone-0008144-g002" target="_blank">Figure 2</a> for further explanation.</p

The 50 heptatonic scales whose intervals conform most closely to a harmonic series out of ∼4×10⁷ possibilities examined.

<p>The 50 heptatonic scales whose intervals conform most closely to a harmonic series out of ∼4×10⁷ possibilities examined.</p

The 50 pentatonic scales whose intervals conform most closely to a harmonic series out of ∼4×10⁵ possibilities examined.

<p>Scale degrees are indicated as frequency ratios with respect to a fixed tonic; the ordering of scale degrees is based on decreasing percentage similarity both here and in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0008144#pone-0008144-t003" target="_blank">Table 3</a>.</p

Pentatonic and heptatonic scales (included tones are indicated by red dots).

<p>The five pentatonic scales are modes of the same set of notes, the only difference being the starting note or tonic. Seven of the nine heptatonic scales shown are also modes that entail the same notes in different arrangements (the exceptions are the harmonic and melodic minor scales). There are three unique forms of the minor heptatonic scale: the natural, harmonic and melodic (the melodic minor scale shown is designated as ascending since this scale is identical to the natural minor scale when descending). Although the scales shown begin and end on specific notes of the keyboard, each could begin on any note and retain its identity as long as all intervals between notes remained the same. Scale tones are represented on keyboards for didactic purposes only in this and subsequent figures and should not be interpreted as being tuned in equal temperament (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0008144#s2" target="_blank">Methods</a>).</p

Survival curve showing a trend toward shorter progression-free survival of CNS DLBCL manifesting a perivascular pattern of infiltration.

<p>Survival curve showing a trend toward shorter progression-free survival of CNS DLBCL manifesting a perivascular pattern of infiltration.</p

Representative examples of CNS DLBCL harboring or lacking chromosome 8/<i>MYC</i> aberrations.

<p>H&E-stained section of a case exhibiting morphologic features intermediate between DLBCL and Burkitt lymphoma (A), 80% MYC expression by the neoplastic cells (B), non-GCB COO subtype - BCL6+ (C) and MUM1/IRF4+ (D), and displaying two normal <i>MYC</i> loci by FISH (two fused signals) (E). H&E-stained section of a case showing immunoblastic morphology (F), 50% MYC expression by the neoplastic cells (G), non-GCB COO subtype - BCL6+ (H) and MUM1/IRF4+ (I), and displaying <i>MYC</i> rearrangement by FISH (one split signal, red and green, and one fused signal) (J). H&E-stained section of a DLBCL showing anaplastic morphology (K), 60% MYC expression by the neoplastic cells (L), GCB COO subtype - CD10+ (M) and BCL6+ (N), and increased copies of <i>MYC</i> by FISH (5 fused signals) (O). Photomicrographs of all H&E-stained sections were taken at 400x magnification and all others at 40x magnification.</p

Clinical Characteristics of CNS DLBCL.

<p>Abbreviations: MXT, methotrexate. WBRT, whole brain radiation therapy. R-MVP, rituximab, methotrexate, procarbazine, and vincristine.</p><p>*Normal range of LDH: 115–221 units/L.</p><p>Clinical Characteristics of CNS DLBCL.</p