2001:468:C80:4292:EDBF:74CA:F96:F6ED: /* Specific heat capacity */

2014-10-01T20:59:35Z

Specific heat capacity

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	~~{{mergefrom\|date=July 2013\|discuss=Talk~~:~~Major second#Merge: Epogdoon\|Epogdoon}}~~		[http://pleased.org Pleased] to meet you! My husband and my name is Eusebio furthermore I think it voice overs quite good when buyers say it. As a man what While i really like is representing but I'm thinking through to starting something new. I work as an get clerk. My house is asap in South Carolina in addition I don't plan using changing it. You can also find my website here: http://prometeu.net<br><br>
	~~{{See~~ also~~\|Minor second\|Diminished third}}~~
	~~{{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 or 10~~:9\|
	~~cents_equal_temperament = 200\|~~
	~~cents_24T_equal_temperament = 200\|~~
	~~cents_just_intonation = 204 or 182~~
	}}

	~~[[Image:Major second on C.svg\|thumb\|right\|Step: major second (major tone) {{audio\|Major second on C.mid\|Play}}.]]~~		Feel free to visit my blog; [http://prometeu.net astuces clash of clans]
	~~[[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''') 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 (music)#Number\|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).

	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>''Whole step'', ''whole tone'', and ''tone'' are all variously used in sources.[http://www.merriam-webster.com/dictionary/whole%20step][http://www.askoxford.com/concise_oed/tone][http://dictionary.reference.com/browse/whole%20step][http://dictionary.reference.com/browse/whole%20tone][http://books.google.com/books?id=sTMbuSQdqPMC&pg=PA19&vq=a+half+step+is+called+a+semitone&source=gbs_search_r&cad=1_1&sig=ACfU3U3wGz6xpxqful9Y_uiLLKGXVokauw][http://books.google.com/books?id=iYgSJSxWW2sC]
	~~<br>One source says ''step'' is "chiefly US."[http://www.askoxford.com/concise_oed/step]~~
	~~<br>The preferred usage has been argued since the 19th century:~~
	*"Mr. M. in teaching the Diatonic scale calls a tone a step, and a semitone a half step; now, who ever heard of a step in music, or in sound ? Can any one suppose that a pupil will understand the meaning of tone and semitone any sooner by calling them step or half step, … ?" [http://books.google.com/books?id=sJQPAAAAYAAJ&pg=PA115&vq=who+ever+heard+of+a+step+in+music,+or+in+sound+%3F&source=gbs_search_r&cad=1_1 (1853)]
	*"… to use the term tone for a whole step is certainly objectionable …" [http://books.google.com/books?id=IG4PAAAAYAAJ&pg=PA401&vq=to+use+the+term+tone+for+a+whole+step+is+certainly+objectionable&source=gbs_search_r&cad=1_1 (1897)]</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. 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 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<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 and e and G and A, and is "a sharper dissonance" than 9:8.<ref name="Paul">Paul, Oscar (1885). ''[http://books.google.com/books?id=4WEJAQAAMAAJ&dq=musical+interval+%22pythagorean+major+third%22&source=gbs_navlinks_s A manual of harmony for use in music-schools and seminaries and for self-instruction]'', p.165. Theodore Baker, trans. G. Schirmer.</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 [[Five-limit tuning#Size of intervals]]).

	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 [[Equal temperament#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'' (A2), or ''diatonic'' and ''chromatic [[semitone]]s''.

	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''<!--[[Epogdoon]] redirects directly here-->==~~
	~~[[Image:Epogdoon.jpg\|thumb\|left\|200px\|Diagram showing relations between ''epogdoon'', ''[[perfect fourth\|diatessaron]]'', ''[[perfect fifth\|diapente]]'', and ''[[octave\|diapason]]'' ]]~~
	~~[[Image:Epogdoon-Raphael.JPG\|thumb\|200px\|right\|Detail of Raphael's ''[[The School of Athens\|School of Athens]]'' showing ''epogdoon'' diagram ]]~~

	~~In [[Pythagorean tuning\|Pythagorean]] music theory, the '''''epogdoon''''' ({{lang-grc\|ΕΠΟΓΔΟΩΝ}}) is the [[interval (music)\|interval]] with the ratio 9~~ to ~~8. The word is composed of the prefix '''epi''-' meaning 'on top of' and '''ogdo''' 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>http://penelope.uchicago.edu/Thayer/E/Roman/Texts/Plutarch/Moralia/Isis_and_Osiris*/C.html{{Bare inline\|date=July 2013}}</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>{{PDFlink\|http://~~philpapers.org/archive/BALPCO}}{{Bare inline\|date=July 2013}}</ref>~~

	~~===Further reading===~~
	* 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==~~
	*[[Whole tone scale]]
	*[[Pythagorean interval]]
	*[[List of meantone intervals]]

	~~==Sources==~~
	~~{{Reflist}}~~

	~~{{Intervals}}~~
	~~<br>~~

	~~{{DEFAULTSORT:Major Second}}~~
	~~[[Category:Major intervals]]~~
	~~[[Category:Seconds]]~~

	~~[[fr:Ton (musique)]~~]

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2001:468:C80:4292:EDBF:74CA:F96:F6ED: /* Specific heat capacity */

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