Editing Major second

{{Short description|Musical interval}}
{{Redirect|Whole tones|the scale|Whole tone scale}}

[[Image:Major second on C.svg|thumb|right|Step: major second (major tone) {{audio|Major second on C.mid|Play}}.]]

{{Infobox Interval
|       main_interval_name = major second
|       inverse = [[minor seventh]]
|       complement = [[minor seventh]]
|       other_names = whole tone, whole step
|       abbreviation = M2
|       semitones = 2
|       interval_class = 2
|       just_interval = 9:8<ref name="Duffin">{{cite book|last1=Duffin|first1=Ross W.|title=How equal temperament ruined harmony : (and why you should care)|date=2008|publisher=W. W. Norton|location=New York|isbn=978-0-393-33420-3|pages=163|edition=First published as a Norton paperback.|url=https://books.google.com/books?id=i5LC7Csnw7UC&q=how+equal+temperament+ruined+harmony|access-date=28 June 2017}}</ref> or 10:9<ref name="Duffin" />
|       cents_equal_temperament = 200<ref name="Duffin" />
|       cents_24T_equal_temperament = 
|       cents_just_intonation = 204<ref name="Duffin" /> or 182<ref name="Duffin" />
}}

[[Image:Minor tone on C.png|thumb|right|Minor tone (10:9) {{audio|Minor tone on C.mid|Play}}.]]

In [[Western culture|Western]] [[music theory]], a '''major second''' (sometimes also called '''whole tone''' or a '''whole step''')  is a second spanning two [[semitone]]s ({{audio|Major second on C.mid|Play}}). A second is a [[interval (music)|musical interval]] encompassing two adjacent [[staff position]]s (see [[Interval number]] for more details). For example, the interval from C to D is a major second, as the note D lies two semitones above C, and the two notes are [[Musical notation|notated]] on adjacent staff positions. [[Diminished second|Diminished]], [[Minor second|minor]] and [[augmented second]]s are notated on adjacent staff positions as well, but consist of a different number of semitones (zero, one, and three).

{{Quote|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.<ref>Benward, Bruce & Saker, Marilyn (2003). ''Music: In Theory and Practice, Vol. I'', p.52. Seventh Edition. {{ISBN|978-0-07-294262-0}}.</ref>}}

The major second is the interval that occurs between the first and second [[Degree (music)|degrees]] of a [[major scale]], the [[Tonic (music)|tonic]] and the [[supertonic]]. On a [[musical keyboard]], a major second is the interval between two keys separated by one key, counting white and black keys alike. On a guitar string, it is the interval separated by two [[fret]]s. In moveable-do [[solfège]], it is the interval between ''do'' and ''re''. It is considered a [[Melody|melodic]] [[step (music)|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'''.<ref>{{cite web|url=http://www.merriam-webster.com/dictionary/whole%20step |title=Whole step – Definition and More from the Free Merriam-Webster Dictionary |publisher=Merriam-webster.com |access-date=2015-02-25}}</ref><ref>{{cite web|url=http://www.askoxford.com/concise_oed/tone |archive-url=https://web.archive.org/web/20071031074656/http://www.askoxford.com/concise_oed/tone |url-status=dead |archive-date=October 31, 2007 |title=Oxford Dictionaries – Dictionary, Thesaurus, & Grammar |publisher=Askoxford.com |date=2015-02-11 |access-date=2015-02-25}}</ref><ref>{{cite web|url=http://dictionary.reference.com/browse/whole%20step |title=Whole step &#124; Define Whole step at Dictionary.com |publisher=Dictionary.reference.com |access-date=2015-02-25}}</ref><ref>{{cite web|url=http://dictionary.reference.com/browse/whole%20tone |title=Whole tone &#124; Define Whole tone at Dictionary.com |publisher=Dictionary.reference.com |access-date=2015-02-25}}</ref><ref>{{cite book|url=https://books.google.com/books?id=sTMbuSQdqPMC&q=a+half+step+is+called+a+semitone&pg=PA19 |title=The Complete Idiot's Guide to Music Theory – Michael Miller – Google Books |isbn=9781592574377 |access-date=2015-02-25|last1=Miller |first1=Michael |year=2005 }}</ref><ref>{{cite book|url=https://books.google.com/books?id=iYgSJSxWW2sC |title=Music Theory For Dummies – Michael Pilhofer, Holly Day – Google Books |date=2011-02-25 |isbn=9781118054444 |access-date=2015-02-25|last1=Pilhofer |first1=Michael |last2=Day |first2=Holly }}</ref>
In [[just intonation]], major seconds can occur in at least two different [[frequency ratio]]s:<ref name="M&L">Leta E. Miller, Fredric Lieberman (2006). ''Lou Harrison'', p.72. {{ISBN|0-252-03120-2}}.</ref>
9:8 (about 203.9 cents) and 10:9 (about 182.4 cents). The largest (9:8) ones are called [[#Major and minor tones|major tones]] or greater tones, the smallest (10:9) are called [[#Major and minor tones|minor tone]]s or lesser tones. Their size differs by exactly one [[syntonic comma]] (81:80, or about 21.5 cents).
Some equal temperaments, such as [[15 equal temperament|15-ET]] and [[22 equal temperament|22-ET]], also distinguish between a greater and a lesser tone.

The major second was historically considered one of the most [[Consonance and dissonance|dissonant]] intervals of the [[diatonic scale]], although much [[20th-century music]] saw it reimagined as a consonance.{{citation needed|date=August 2021}} It is common in many different musical systems, including [[Arabic music]], [[Turkish music]] and music of the [[Balkans]], among others.  It occurs in both [[diatonic]] and [[Pentatonic scale|pentatonic]] scales.

{{audio|Second_ET.ogg|Listen to a major second in equal temperament}}. Here, [[middle C]] is followed by D, which is a tone 200 [[Cent (music)|cents]] sharper than C, and then by both tones together.

==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]].

==''Epogdoon''<!--[[Epogdoon]] redirects directly here-->==
{{multiple image
| align = right
| direction = vertical
| width = 200
| image1 = Epogdoon.jpg
| caption1 = Diagram showing relations between ''epogdoon'', ''[[perfect fourth|diatessaron]]'', ''[[perfect fifth|diapente]]'', and ''[[octave|diapason]]''
| image2 = Epogdoon translation.png
| caption2 = Translation
}}
[[Image:Epogdoon-Raphael.JPG|thumb|left|200px|Detail of Raphael's ''[[The School of Athens|School of Athens]]'' showing Pythagoras with ''epogdoon'' diagram ]]

In [[Pythagorean tuning|Pythagorean]] music theory, the '''''epogdoon''''' ({{langx|grc|ἐπόγδοον}}) is the [[interval (music)|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 ({{nowrap|8+(<math>\tfrac{1}{8}</math>×8){{=}}9}}).

According to [[Plutarch]], the Pythagoreans hated  the number 17 because it separates the 16 from its Epogdoon 18.<ref>{{cite web|url=https://penelope.uchicago.edu/Thayer/E/Roman/Texts/Plutarch/Moralia/Isis_and_Osiris*/C.html |title=Plutarch • Isis and Osiris (Part 3 of 5) |publisher=Penelope.uchicago.edu |access-date=2015-02-25}}</ref>

"[''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]."<ref>{{cite web|url=http://philpapers.org/archive/BALPCO |title=Proclus : Commentary on Plato's Timaeus |publisher=Philpapers.org |access-date=25 February 2015}}</ref>

===Further reading===
* [[Andrew Barker (classicist)|Barker, Andrew]] (2007). ''The Science of Harmonics in Classical Greece''. Cambridge University Press. {{ISBN|9780521879514}}.
* Plutarch (2005). ''Moralia''. Translated by Frank Cole Babbitt. Kessinger Publishing. {{ISBN|9781417905003}}.

==See also==
*[[Diminished third]]
*[[List of meantone intervals]]
*[[Minor second]]
*[[Pythagorean interval]]
*[[Whole tone scale]]
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==References==
{{Reflist}}

{{Intervals}}
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{{DEFAULTSORT:Major Second}}
[[Category:Major intervals]]
[[Category:Seconds (music)]]
[[Category:Units of level]]