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The harmonic seventh interval , also known as the septimal minor seventh,〔Gann, Kyle (1998). ("Anatomy of an Octave" ), ''Just Intonation Explained''.〕〔Partch, Harry (1979). ''Genesis of a Music'', p.68. ISBN 0-306-80106-X.〕 or subminor seventh,〔Hermann L. F Von Helmholtz (2007). ''On the Sensations of Tone'', p.456. ISBN 1-60206-639-6.〕〔Royal Society (Great Britain) (1880, digitized Feb 26, 2008). ''Proceedings of the Royal Society of London, Volume 30'', p.531. Harvard University.〕〔Society of Arts (Great Britain) (1877, digitized Nov 19, 2009). ''Journal of the Society of Arts, Volume 25'', p.670. The Society.〕 is one with an exact 7:4 ratio〔Andrew Horner, Lydia Ayres (2002). ''Cooking with Csound: Woodwind and Brass Recipes'', p.131. ISBN 0-89579-507-8.〕 (about 969 cents).〔Bosanquet, Robert Holford Macdowall (1876). ''An elementary treatise on musical intervals and temperament'', pp. 41-42. Diapason Press; Houten, The Netherlands. ISBN 90-70907-12-7.〕 This is somewhat narrower than and is "sweeter in quality" than an "ordinary"〔"On Certain Novel Aspects of Harmony", p.119. Eustace J. Breakspeare. ''Proceedings of the Musical Association'', 13th Sess., (1886 - 1887), pp. 113-131. Published by: Oxford University Press on behalf of the Royal Musical Association.〕 minor seventh, which has a just-intonation ratio of 9:5〔"The Heritage of Greece in Music", p.89. Wilfrid Perrett. ''Proceedings of the Musical Association'', 58th Sess., (1931 - 1932), pp. 85-103. Published by: Oxford University Press on behalf of the Royal Musical Association.〕 (1017.596 cents), or an equal-temperament ratio of 1000 cents (25/6:1). The harmonic seventh may be derived from the harmonic series as the interval between the seventh harmonic and the fourth harmonic (octave of the fundamental). This note is often corrected to 16:9 (B, 996.09 cents) on the natural horn in just intonation or Pythagorean tunings, but the pure seventh harmonic was used in pieces including Britten's ''Serenade for tenor, horn and strings''.〔Fauvel, John; Flood, Raymond; and Wilson, Robin J. (2006). ''Music And Mathematics'', p.21-22. ISBN 9780199298938.〕 Composer Ben Johnston uses a small "7" as an accidental to indicate a note is lowered 49 cents (1018-969=49), or an upside-down "7" to indicate a note is raised 49 cents. Thus, in C major, "the seventh partial," or harmonic seventh, is notated as B with "7" written above the flat.〔Douglas Keislar; Easley Blackwood; John Eaton; Lou Harrison; Ben Johnston; Joel Mandelbaum; William Schottstaedt. p.193. "Six American Composers on Nonstandard Tunnings", ''Perspectives of New Music'', Vol. 29, No. 1. (Winter, 1991), pp. 176-211.〕〔Fonville, John. "Ben Johnston's Extended Just Intonation: A Guide for Interpreters", ''Perspectives of New Music'', Vol. 29, No. 2 (Summer, 1991), pp. 106-137.〕 Some theorists ((reference needed)) believe that the harmonic seventh is also used by Barbershop Quartet singers when they tune dominant seventh chords (harmonic seventh chord), and is an essential aspect of the Barbershop style; however this claim was not supported by the empirical data of Hagerman and Sundberg (1980), and the failure of other psychological studies on intonation to find evidence for the harmonic seventh casts doubt on its musical or psychological existence. Instead, Hagerman and Sundberg found that tuning of major and minor third intervals in Barbershop lies between just (4:5, 5:6) and equal temperament. The harmonic seventh differs from the augmented sixth by 224/225 (7.71 cents), or about one-third of a comma.〔"On Some Points in the Harmony of Perfect Consonances", p.153. R. H. M. Bosanquet. ''Proceedings of the Musical Association'', 3rd Sess., (1876 - 1877), pp. 145-153. Published by: Oxford University Press on behalf of the Royal Musical Association.〕 The harmonic seventh note is about one third of a semitone (≈ 31 cents) flatter than an equal tempered minor seventh. When this flatter seventh is used, the dominant seventh chord's "need to resolve" down a fifth is weak or non-existent. This chord is often used on the tonic (written as I7) and functions as a "fully resolved" final chord.〔Mathieu, W.A. (1997). ''Harmonic Experience'', pp. 318-319. Inner Traditions International; Rochester, Vermont. ISBN 0-89281-560-4.〕 The twenty-first harmonic (470.78 cents) is the harmonic seventh of the dominant, and would then arise in chains of secondary dominants (known as the Ragtime progression) in styles using harmonic sevenths, such as barbershop music. ==Notes== 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「harmonic seventh」の詳細全文を読む スポンサード リンク
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