Septimal whole tone: Difference between revisions

septimal major second
Inverse	harmonic seventh
Name
Other names	Septimal whole tone, Supermajor second
Abbreviation	M2
Size
Semitones	~2.5
Interval class	~2.5
Just interval	8:7
Cents
12-Tone equal temperament	200
24-Tone equal temperament	250
Just intonation	231

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File:Major second on C.png

3-limit 9:8 major tone Play.

In music, the septimal whole tone, septimal major second^[1], or supermajor second^[2]^[3] play^ⓘ is the musical interval exactly or approximately equal to a 8/7 ratio of frequencies or alternately 7/6^[4]. It is about 231 cents wide in just intonation^[5] and 250 cents in the quarter tone scale. The septimal whole tone may be derived from the harmonic series as the interval between the seventh and eighth harmonics and the term septimal refers to the fact that it utilizes the seventh harmonic.^[5]

This interval does not fit easily into equally-tempered tuning systems. The standard 12 equal temperament used in most western music does not come close to this interval. The 19 equal temperament offers a closer, but still poor, match for this interval, but it does not distinguish between this interval and the septimal minor third, which it has a better fit for. The 22 equal temperament distinguishes between these two intervals, but it still matches the septimal whole tone poorly. The 31 equal temperament is the smallest widely used equal temperament that matches this interval closely. In theory, 26 equal temperament provides an even closer match to the septimal whole tone (and its inversion, the harmonic seventh), but this tuning is little used due to the significant flatness of its major thirds and fifths.

Sources

^ Partch, Harry (1979). Genesis of a Music, p.68. ISBN 030680106X.
^ 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.
^ Andrew Horner, Lydia Ayres (2002). Cooking with Csound: Woodwind and Brass Recipes, p.131. ISBN 0895795078. "Super-Major Second".
^ ^a ^b Leta E. Miller, Fredric Lieberman (2006). Lou Harrison, p.72. ISBN 0252031202.

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[1] Partch, Harry (1979). Genesis of a Music, p.68. ISBN 030680106X.

[2] Royal Society (Great Britain) (1880, digitized Feb 26, 2008). Proceedings of the Royal Society of London, Volume 30, p.531. Harvard University.

[3] Society of Arts (Great Britain) (1877, digitized Nov 19, 2009). Journal of the Society of Arts, Volume 25, p.670. The Society.

[4] Andrew Horner, Lydia Ayres (2002). Cooking with Csound: Woodwind and Brass Recipes, p.131. ISBN 0895795078. "Super-Major Second".

[M&L-5] Leta E. Miller, Fredric Lieberman (2006). Lou Harrison, p.72. ISBN 0252031202.

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@@ Line 15: / Line 15: @@
 [[Image:Septimal major second on C.png|thumb|right|7-limit 8:7 septimal whole tone {{audio|Septimal major second on C.mid|Play}}.]]
-In music, the '''septimal whole tone''', '''septimal major second'''<ref>Partch, Harry (1979). ''Genesis of a Music'', p.68. ISBN 030680106X.</ref>, or '''supermajor second'''<ref>Royal Society (Great Britain) (1880, digitized Feb 26, 2008). ''Proceedings of the Royal Society of London, Volume 30'', p.531. Harvard University.</ref> {{Audio|Septimal major second on C.mid|play}} is the [[musical interval]] exactly or approximately equal to a 8/7 ratio of frequencies or alternately 7/6<ref>Andrew Horner, Lydia Ayres (2002). ''Cooking with Csound: Woodwind and Brass Recipes'', p.131. ISBN 0895795078. "Super-Major Second".</ref>. It is about 231 [[cent (music)|cents]] wide in [[just intonation]]<ref name="M&L">Leta E. Miller, Fredric Lieberman (2006). ''Lou Harrison'', p.72. ISBN 0252031202.</ref> and 250 cents in the [[quarter tone scale]]. The septimal whole tone may be derived from the [[Harmonic series (music)|harmonic series]] as the interval between the [[seventh harmonic|seventh]] and eighth harmonics and the term ''septimal'' refers to the fact that it utilizes the [[Harmonic seventh|seventh harmonic]].<ref name="M&L"/>
+In music, the '''septimal whole tone''', '''septimal major second'''<ref>Partch, Harry (1979). ''Genesis of a Music'', p.68. ISBN 030680106X.</ref>, or '''supermajor second'''<ref>Royal Society (Great Britain) (1880, digitized Feb 26, 2008). ''Proceedings of the Royal Society of London, Volume 30'', p.531. Harvard University.</ref><ref>Society of Arts (Great Britain) (1877, digitized Nov 19, 2009). ''Journal of the Society of Arts, Volume 25'', p.670. The Society.</ref> {{Audio|Septimal major second on C.mid|play}} is the [[musical interval]] exactly or approximately equal to a 8/7 ratio of frequencies or alternately 7/6<ref>Andrew Horner, Lydia Ayres (2002). ''Cooking with Csound: Woodwind and Brass Recipes'', p.131. ISBN 0895795078. "Super-Major Second".</ref>. It is about 231 [[cent (music)|cents]] wide in [[just intonation]]<ref name="M&L">Leta E. Miller, Fredric Lieberman (2006). ''Lou Harrison'', p.72. ISBN 0252031202.</ref> and 250 cents in the [[quarter tone scale]]. The septimal whole tone may be derived from the [[Harmonic series (music)|harmonic series]] as the interval between the [[seventh harmonic|seventh]] and eighth harmonics and the term ''septimal'' refers to the fact that it utilizes the [[Harmonic seventh|seventh harmonic]].<ref name="M&L"/>
 This interval does not fit easily into equally-tempered tuning systems.  The standard [[12 equal temperament]] used in most western music does not come close to this interval.  The [[19 equal temperament]] offers a closer, but still poor, match for this interval, but it does not distinguish between this interval and the [[septimal minor third]], which it has a better fit for.  The [[22 equal temperament]] distinguishes between these two intervals, but it still matches the septimal whole tone poorly. The [[31 equal temperament]] is the smallest widely used equal temperament that matches this interval closely. In theory, 26 equal temperament provides an even closer match to the septimal whole tone (and its inversion, the [[harmonic seventh]]), but this tuning is little used due to the significant flatness of its major thirds and fifths.