Editing Major second (section)

==Major and minor tones<!--[[Major tone]] & [[minor tone]], etc. redirect directly here.-->==
[[Image:Origin of seconds and thirds in harmonic series.png|thumb|Origin of large and small seconds and thirds in harmonic series.<ref>Leta E. Miller, ed. (1988). ''Lou Harrison: Selected keyboard and chamber music, 1937–1994'', p.xliii. {{ISBN|978-0-89579-414-7}}.</ref>]]
[[Image:Major second on D.png|thumb|Lesser tone on D. {{audio|Lesser tone on D.mid|Play}}]]
In [[Musical tuning|tuning systems]] using [[just intonation]], such as [[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 '''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<ref name="Proceedings">Royal Society (Great Britain) (1880, digitized Feb 26, 2008). ''Proceedings of the Royal Society of London, Volume 30'', p.531. Harvard University.</ref> {{Audio|Major tone on C.mid|play}}, and it is an approximation thereof in other tuning systems, while the minor tone is the 10:9 ratio<ref name="Proceedings"/> {{Audio|Minor tone on C.mid|play}}. The major tone may be derived from the [[Harmonic series (music)|harmonic series]] as the interval between the eighth and ninth harmonics. The minor tone may be derived from the harmonic series as the interval between the ninth and tenth harmonics. The 10:9 minor tone arises in the C [[major scale]] between D & E and G & A, and is "a sharper dissonance" than 9:8.<ref name="Paul">Paul, Oscar (1885) {{Page needed|date=June 2017}}</ref><ref>{{cite web|url=https://books.google.com/books?id=4WEJAQAAMAAJ&q=musical+interval+%22pythagorean+major+third%22 |title=A Manual of Harmony for Use in Music-schools and Seminaries and for Self ... – Oscar Paul – Google Books |date=2010-05-25 |access-date=2015-02-25|last1=Paul |first1=Oscar }}{{Page needed|date=June 2017}}</ref> The 9:8 major tone arises in the C [[major scale]] between C & D, F & G, and A & B.<ref name="Paul"/> This 9:8 interval was named [[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 {{slink|Five-limit tuning|Size of intervals}}).

[[File:Comparison of major seconds.png|200px|right|thumb|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 equal temperament|15-ET]], [[22 equal temperament|22-ET]], [[34 equal temperament|34-ET]], [[41 equal temperament|41-ET]], [[53 equal temperament|53-ET]], and [[72 equal temperament|72-ET]].
Conversely, in [[Twelve tone equal temperament|twelve-tone equal temperament]], [[Pythagorean tuning]], and [[meantone temperament]] (including [[19 equal temperament|19-ET]] and [[31 equal temperament|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, [[major semitone]]s and [[minor semitone]]s are more often and more appropriately referred to as ''minor seconds'' (m2) and ''[[augmented unison]]s'' (A1), or ''diatonic'' and ''chromatic [[semitone]]s''.

Unlike most 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]].