A Biological Rationale for Musical Scales
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{"title"=>"A biological rationale for musical scales", "type"=>"journal", "authors"=>[{"first_name"=>"Kamraan Z.", "last_name"=>"Gill", "scopus_author_id"=>"55144615500"}, {"first_name"=>"Dale", "last_name"=>"Purves", "scopus_author_id"=>"7005389069"}], "year"=>2009, "source"=>"PLoS ONE", "identifiers"=>{"issn"=>"19326203", "isbn"=>"1932-6203", "pmid"=>"19997506", "scopus"=>"2-s2.0-77954056827", "doi"=>"10.1371/journal.pone.0008144", "sgr"=>"77954056827", "pui"=>"359087426"}, "id"=>"8e71b35a-8831-314e-a9c1-fe1c481e2c2d", "abstract"=>"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, 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. 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.", "link"=>"http://www.mendeley.com/research/biological-rationale-musical-scales", "reader_count"=>244, "reader_count_by_academic_status"=>{"Unspecified"=>4, "Professor > Associate Professor"=>9, "Librarian"=>2, "Researcher"=>53, "Student > Doctoral Student"=>9, "Student > Ph. D. Student"=>67, "Student > Postgraduate"=>6, "Other"=>14, "Student > Master"=>31, "Student > Bachelor"=>19, "Lecturer"=>2, "Lecturer > Senior Lecturer"=>2, "Professor"=>26}, "reader_count_by_user_role"=>{"Unspecified"=>4, "Professor > Associate Professor"=>9, "Librarian"=>2, "Researcher"=>53, "Student > Doctoral Student"=>9, "Student > Ph. D. Student"=>67, "Student > Postgraduate"=>6, "Other"=>14, "Student > Master"=>31, "Student > Bachelor"=>19, "Lecturer"=>2, "Lecturer > Senior Lecturer"=>2, "Professor"=>26}, "reader_count_by_subject_area"=>{"Unspecified"=>6, "Agricultural and Biological Sciences"=>58, "Arts and Humanities"=>23, "Philosophy"=>6, "Business, Management and Accounting"=>1, "Computer Science"=>22, "Earth and Planetary Sciences"=>3, "Energy"=>1, "Engineering"=>4, "Environmental Science"=>4, "Biochemistry, Genetics and Molecular Biology"=>3, "Nursing and Health Professions"=>1, "Medicine and Dentistry"=>7, "Neuroscience"=>21, "Physics and Astronomy"=>7, "Psychology"=>63, "Social Sciences"=>12, "Linguistics"=>2}, "reader_count_by_subdiscipline"=>{"Medicine and Dentistry"=>{"Medicine and Dentistry"=>7}, "Social Sciences"=>{"Social Sciences"=>12}, "Physics and Astronomy"=>{"Physics and Astronomy"=>7}, "Psychology"=>{"Psychology"=>63}, "Unspecified"=>{"Unspecified"=>6}, "Environmental Science"=>{"Environmental Science"=>4}, "Arts and Humanities"=>{"Arts and Humanities"=>23}, "Engineering"=>{"Engineering"=>4}, "Neuroscience"=>{"Neuroscience"=>21}, "Energy"=>{"Energy"=>1}, "Earth and Planetary Sciences"=>{"Earth and Planetary Sciences"=>3}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>58}, "Computer Science"=>{"Computer Science"=>22}, "Business, Management and Accounting"=>{"Business, Management and Accounting"=>1}, "Nursing and Health Professions"=>{"Nursing and Health Professions"=>1}, "Linguistics"=>{"Linguistics"=>2}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>3}, "Philosophy"=>{"Philosophy"=>6}}, "reader_count_by_country"=>{"Hong Kong"=>1, "United States"=>18, "Portugal"=>2, "Austria"=>1, "Netherlands"=>1, "Sweden"=>2, "Luxembourg"=>1, "Brazil"=>2, "Chile"=>1, "France"=>1, "Japan"=>1, "Philippines"=>1, "United Kingdom"=>3, "Switzerland"=>3, "Spain"=>1, "India"=>3, "Canada"=>2, "Belgium"=>1, "Norway"=>2, "Taiwan"=>1, "Denmark"=>1, "Italy"=>3, "South Africa"=>1, "Germany"=>4, "Indonesia"=>1}, "group_count"=>8}

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  • {"files"=>["https://ndownloader.figshare.com/files/872938"], "description"=>"<p>The 50 heptatonic scales whose intervals conform most closely to a harmonic series out of ∼4×10<sup>7</sup> possibilities examined.</p>", "links"=>[], "tags"=>["50", "heptatonic", "scales", "intervals", "conform", "harmonic", "possibilities"], "article_id"=>543392, "categories"=>["Neuroscience"], "users"=>["Kamraan Z. Gill", "Dale Purves"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0008144.t003", "stats"=>{"downloads"=>1, "page_views"=>14, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_50_heptatonic_scales_whose_intervals_conform_most_closely_to_a_harmonic_series_out_of_4_10_7_possibilities_examined_/543392", "title"=>"The 50 heptatonic scales whose intervals conform most closely to a harmonic series out of ∼4×10<sup>7</sup> possibilities examined.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-02-21 03:35:10"}
  • {"files"=>["https://ndownloader.figshare.com/files/872781"], "description"=>"<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>", "links"=>[], "tags"=>["harmonic", "tonal", "dyad", "compared"], "article_id"=>543241, "categories"=>["Neuroscience"], "users"=>["Kamraan Z. Gill", "Dale Purves"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0008144.g002", "stats"=>{"downloads"=>1, "page_views"=>20, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_harmonic_structure_of_a_tonal_dyad_a_major_third_in_this_example_compared_to_a_harmonic_series_/543241", "title"=>"The harmonic structure of a tonal dyad (a major third in this example) compared to a harmonic series.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 03:34:24"}
  • {"files"=>["https://ndownloader.figshare.com/files/872656"], "description"=>"<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>", "links"=>[], "tags"=>["heptatonic", "scales", "tones", "indicated"], "article_id"=>543111, "categories"=>["Neuroscience"], "users"=>["Kamraan Z. Gill", "Dale Purves"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0008144.g001", "stats"=>{"downloads"=>1, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Pentatonic_and_heptatonic_scales_included_tones_are_indicated_by_red_dots_/543111", "title"=>"Pentatonic and heptatonic scales (included tones are indicated by red dots).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 03:33:40"}
  • {"files"=>["https://ndownloader.figshare.com/files/872971"], "description"=>"<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>", "links"=>[], "tags"=>["50", "pentatonic", "scales", "intervals", "conform", "harmonic", "possibilities"], "article_id"=>543426, "categories"=>["Neuroscience"], "users"=>["Kamraan Z. Gill", "Dale Purves"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0008144.t002", "stats"=>{"downloads"=>5, "page_views"=>15, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_50_pentatonic_scales_whose_intervals_conform_most_closely_to_a_harmonic_series_out_of_4_10_5_possibilities_examined_/543426", "title"=>"The 50 pentatonic scales whose intervals conform most closely to a harmonic series out of ∼4×10<sup>5</sup> possibilities examined.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-02-21 03:35:22"}
  • {"files"=>["https://ndownloader.figshare.com/files/873008"], "description"=>"<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>", "links"=>[], "tags"=>["60", "intervals", "harmonic"], "article_id"=>543467, "categories"=>["Neuroscience"], "users"=>["Kamraan Z. Gill", "Dale Purves"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0008144.t001", "stats"=>{"downloads"=>2, "page_views"=>16, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_60_intervals_with_the_greatest_percentage_similarity_to_a_harmonic_series_/543467", "title"=>"The 60 intervals with the greatest percentage similarity to a harmonic series.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-02-21 03:35:33"}
  • {"files"=>["https://ndownloader.figshare.com/files/872853"], "description"=>"<p>A) The 15 possible intervals between the tones of this scale. B) The percentage similarity of each scalar interval compared to a harmonic series (see <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0008144#pone-0008144-g002\" target=\"_blank\">Figure 2</a>) and the mean percentage similarity of the full scale are indicated. Scale degrees are conventionally indicated as frequency ratios with respect to a fixed tonic.</p>", "links"=>[], "tags"=>["pentatonic"], "article_id"=>543321, "categories"=>["Neuroscience"], "users"=>["Kamraan Z. Gill", "Dale Purves"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0008144.g003", "stats"=>{"downloads"=>0, "page_views"=>14, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Determination_of_the_mean_percentage_similarity_of_a_scale_using_the_pentatonic_minor_scale_as_an_example_/543321", "title"=>"Determination of the mean percentage similarity of a scale, using the pentatonic minor scale as an example.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 03:34:49"}

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Relative Metric

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