Major second

Source: Wikipedia, the free encyclopedia.
"Whole tones" redirects here. For the scale, see
Whole tone scale
.
Step: major second (major tone) Playⓘ.
major second
Inverse
minor seventh
Name
Other nameswhole tone, whole step
AbbreviationM2
Size
Semitones2
Interval class2
Just interval9:8[1] or 10:9[1]
Cents
12-Tone equal temperament200[1]
Just intonation204[1] or 182[1]
Minor tone (10:9) Playⓘ.

In

minor and augmented seconds
are notated on adjacent staff positions as well, but consist of a different number of semitones (zero, one, and three).

The intervals from the tonic (keynote) in an upward direction to the second, to the third, to the sixth, and to the seventh scale degrees (of a major scale are called major.[2]

The major second is the interval that occurs between the first and second

step
, as opposed to larger intervals called skips.

Intervals composed of two semitones, such as the major second and the diminished third, are also called tones, whole tones, or whole steps.[3][4][5][6][7][8] In

frequency ratios:[9]
9:8 (about 203.9 cents) and 10:9 (about 182.4 cents). The largest (9:8) ones are called major tones or greater tones, the smallest (10:9) are called minor tones or lesser tones. Their size differs by exactly one syntonic comma (81:80, or about 21.5 cents). Some equal temperaments, such as 15-ET and 22-ET, also distinguish between a greater and a lesser tone.

The major second was historically considered one of the most

diatonic and pentatonic
scales.

Listen to a major second in equal temperament

middle C is followed by D, which is a tone 200 cents
sharper than C, and then by both tones together.

Major and minor tones

Origin of large and small seconds and thirds in harmonic series.[10]
Lesser tone on D. Playⓘ

In

5-limit tuning, in which major seconds occur in two different sizes, the wider of them is called a major tone or greater tone, and the narrower a minor tone or, lesser tone. The difference in size between a major tone and a minor tone is equal to one syntonic comma
(about 21.51 cents).

The major tone is the 9:8 interval

epogdoon
(meaning 'one eighth in addition') by the Pythagoreans.

Notice that in these tuning systems, a third kind of whole tone, even wider than the major tone, exists. This interval of two semitones, with ratio 256:225, is simply called the diminished third (for further details, see Five-limit tuning § Size of intervals).

Comparison, in cents, of intervals at or near a major second

Some equal temperaments also produce major seconds of two different sizes, called greater and lesser tones (or major and minor tones). For instance, this is true for 15-ET, 22-ET, 34-ET, 41-ET, 53-ET, and 72-ET. Conversely, in

twelve-tone equal temperament, Pythagorean tuning, and meantone temperament (including 19-ET and 31-ET
) all major seconds have the same size, so there cannot be a distinction between a greater and a lesser tone.

In any system where there is only one size of major second, the terms greater and lesser tone (or major and minor tone) are rarely used with a different meaning. Namely, they are used to indicate the two distinct kinds of whole tone, more commonly and more appropriately called major second (M2) and diminished third (d3). Similarly,

minor semitones are more often and more appropriately referred to as minor seconds (m2) and augmented unisons (A1), or diatonic and chromatic semitones
.

Unlike almost all uses of the terms major and minor, these intervals span the same number of semitones. They both span 2 semitones, while, for example, a major third (4 semitones) and minor third (3 semitones) differ by one semitone. Thus, to avoid ambiguity, it is preferable to call them greater tone and lesser tone (see also greater and lesser diesis).

Two major tones equal a ditone.

Epogdoon

Diagram showing relations between epogdoon, diatessaron, diapente, and diapason
Translation
Detail of Raphael's School of Athens showing Pythagoras with epogdoon diagram

In

Ancient Greek: ἐπόγδοον) is the interval
with the ratio 9 to 8. The word is composed of the prefix epi- meaning "on top of" and ogdoon meaning "one eighth"; so it means "one eighth in addition". For example, the natural numbers are 8 and 9 in this relation (8+(×8)=9).

According to Plutarch, the Pythagoreans hated the number 17 because it separates the 16 from its Epogdoon 18.[14]

"[Epogdoos] is the 9:8 ratio that corresponds to the tone, [hêmiolios] is the 3:2 ratio that is associated with the musical fifth, and [epitritos] is the 4:3 ratio associated with the musical fourth. It is common to translate epogdoos as 'tone' [major second]."[15]

Further reading

See also

References

  1. ^
    ISBN 978-0-393-33420-3
    . Retrieved 28 June 2017.
  2. ISBN 978-0-07-294262-0
    .
  3. ^ "Whole step – Definition and More from the Free Merriam-Webster Dictionary". Merriam-webster.com. Retrieved 2015-02-25.
  4. ^ "Oxford Dictionaries – Dictionary, Thesaurus, & Grammar". Askoxford.com. 2015-02-11. Archived from the original on October 31, 2007. Retrieved 2015-02-25.
  5. ^ "Whole step | Define Whole step at Dictionary.com". Dictionary.reference.com. Retrieved 2015-02-25.
  6. ^ "Whole tone | Define Whole tone at Dictionary.com". Dictionary.reference.com. Retrieved 2015-02-25.
  7. ISBN 9781592574377
    . Retrieved 2015-02-25.
  8. ISBN 9781118054444
    . Retrieved 2015-02-25.
  9. ISBN 0-252-03120-2
    .
  10. ISBN 978-0-89579-414-7
    .
  11. ^ a b Royal Society (Great Britain) (1880, digitized Feb 26, 2008). Proceedings of the Royal Society of London, Volume 30, p.531. Harvard University.
  12. ^ a b Paul, Oscar (1885) [page needed]
  13. ^ Paul, Oscar (2010-05-25). "A Manual of Harmony for Use in Music-schools and Seminaries and for Self ... – Oscar Paul – Google Books". Retrieved 2015-02-25.[page needed]
  14. ^ "Plutarch • Isis and Osiris (Part 3 of 5)". Penelope.uchicago.edu. Retrieved 2015-02-25.
  15. ^ "Proclus : Commentary on Plato's Timaeus". Philpapers.org. Retrieved 25 February 2015.
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