Septimal whole tone

septimal major second
Inverse harmonic seventh
Name
Other names Septimal whole tone, Supermajor second
Abbreviation S2, SM2
Size
Semitones ~2.5
Interval class ~2.5
Just interval 8:7[1]
Cents
Equal temperament 200
24 equal temperament 250
Just intonation 231

In music, the septimal whole tone, septimal major second[2], or supermajor second[3][4] is the musical interval exactly or approximately equal to a 8/7 ratio of frequencies[5]. It is about 231 cents wide in just intonation[6]. Although 24 equal temperament does not match this interval particularly well, its nearest representation is at 250 cents, approximately 19 cents sharp. 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.[6] It can also be thought of as the octave inversion of the 7/4 interval, the harmonic seventh.

No close approximation to this interval exists in the standard 12 equal temperament used in most modern western music. 26 equal temperament matches this interval almost perfectly with an error of only 0.4 cents, but at the cost of the significant flatness of its major thirds and fifths.

Sources

  1. ^ Haluska, Jan (2003). The Mathematical Theory of Tone Systems, p.xxiii. ISBN 0824747143. Septimal whole tone.
  2. ^ Partch, Harry (1979). Genesis of a Music, p.68. ISBN 030680106X.
  3. ^ Royal Society (Great Britain) (1880, digitized Feb 26, 2008). Proceedings of the Royal Society of London, Volume 30, p.531. Harvard University.
  4. ^ Society of Arts (Great Britain) (1877, digitized Nov 19, 2009). Journal of the Society of Arts, Volume 25, p.670. The Society.
  5. ^ Andrew Horner, Lydia Ayres (2002). Cooking with Csound: Woodwind and Brass Recipes, p.131. ISBN 0895795078. "Super-Major Second".
  6. ^ a b Leta E. Miller, Fredric Lieberman (2006). Lou Harrison, p.72. ISBN 0252031202.
  7. ^ Leta E. Miller, ed. (1988). Lou Harrison: Selected keyboard and chamber music, 1937-1994, p.xliii. ISBN 9780895794147.
Numbers in brackets are the number of semitones in the interval.
Fractional semitones are approximate.
Twelve-semitone
(Western)
Perfect
unison (0) · fourth (5) · fifth (7) · octave (12) · fifteenth (24)
Major
second (2) · third (4) · sixth (9) · seventh (11)
Minor
second (1) · third (3) · sixth (8) · seventh (10)
Augmented
unison (1) · second (3) · third (5) · fourth (6) · fifth (8) · sixth (10) · seventh (12) · octave (13)
Diminished
unison (-1) · second (0) · third (2) · fourth (4) · fifth (6) · sixth (7) · seventh (9) · octave (11)
Compound
ninth (13 or 14) · tenth (15 or 16) · eleventh (17) · thirteenth (18 or 19)
Other systems
Supermajor
second (2⅓) · third (4⅓) · sixth (9⅓) · seventh (11⅓)
Neutral
second (1½) · third (3½) · sixth (8½) · seventh (10½)
Subminor
second (⅔) · third (2⅔) · sixth (7⅔) · seventh (9⅔)
7-limit
chromatic semitone (⅔) · diatonic semitone (1⅙) · whole tone (2⅓) · subminor third (2⅔) · supermajor third (4⅓) · harmonic (subminor) seventh (9⅔)
Other intervals
Groups
Measurement
Others