In Western music theory, a semitone (also called a half step or half tone)Semitone, half step, half tone, halftone, and half-tone are all variously used in sources. Aaron Copland, Leonard Bernstein, and others use "half tone".
One source says that step is "chiefly US", and that half-tone is "chiefly N. Amer." is one of the two parts into which a whole tone is divided. Semitones are the smallest intervals commonly harmonically and melodically used in Western music, and are among the most dissonant intervals when sounded harmonically. A progression of semitones forms a chromatic scale, which informs the layout of many fixed-pitch instruments. For example, C is adjacent to D on a keyboard, so the interval between them is a semitone.
In musical notation, two types of semitones are distinguished. A diatonic semitone, or minor second, arises between two notes encompassing different staff positions, e.g. from C to D. A chromatic semitone, or augmented unison, arises between two notes at the same staff position, e.g. from D to D. The sum of these two intervals, the interval from C to D, is a whole tone, or major second.
The modern tuning system of 12-tone equal temperament divides the octave into twelve equal semitones, each with a frequency ratio of the twelfth root of two (100 cents). In this system, a given interval can be represented by a specific number of semitones from any starting note. For example, two semitones may represent a major second, four semitones a major third, and seven semitones a perfect fifth .
In tuning systems derived from stacking perfect fifths, i.e. Pythagorean tuning and the related meantone temperaments, diatonic semitones all have the same size, as do chromatic semitones, but the two sizes are distinct. For example, they are not the same size in Pythagorean tuning, where the diatonic semitone is distinguished from the larger chromatic semitone, or in quarter-comma meantone temperament, where the diatonic semitone is larger instead.
The condition of having semitones is called hemitonia; that of having no semitones is anhemitonia. A musical scale or chord containing semitones is called hemitonic; one without semitones is anhemitonic.
Minor second
The minor second (m2 or -2) occurs in the major scale, between the third and fourth degree, (mi (E) and fa (F) in C major), and between the seventh and eighth degree (ti (B) and do (C) in C major). It is also called the diatonic semitone because it occurs between steps in the diatonic scale. Its inversion is the major seventh (M7 or Ma7).
Melodically, this interval is very frequently used, and is of particular importance in cadences. In the authentic and deceptive cadences it appears as a resolution of the leading tone to the tonic. In the plagal cadence, it appears as the falling of the subdominant to the mediant. It also occurs in many forms of the imperfect cadence, wherever the tonic falls to the leading tone.
Harmonically, the interval usually occurs as some form of dissonance or a nonchord tone that is not part of the functional harmony. It may also appear in inversions of a major seventh chord, and in many added tone chords.
In unusual situations, the minor second can add a great deal of character to the music. For instance, Frédéric Chopin's Étude Op. 25, No. 5 opens with a melody accompanied by a line that plays fleeting minor seconds. These are used to humorous and whimsical effect, which contrasts with its more lyrical middle section. This eccentric dissonance has earned the piece its nickname: the "wrong note" étude. This kind of usage of the minor second appears in many other works of the Romantic period, such as Modest Mussorgsky's "Ballet of the Unhatched Chicks" from Pictures at an Exhibition. More recently, the music to the movie Jaws exemplifies the minor second.
Augmented unison
The augmented unison, augmented prime, or chromatic semitone is the interval between two notes on the same staff position (same letter name) that differ by one chromatic alteration. For example, the interval between B and B, or between C and C, is an augmented unison.
The term, in its French form , appears to have been coined by Jean-Philippe Rameau in 1722, who also called this interval a minor semitone ().Gene Henry Anderson, "Musical Terminology in J.-P. Rameau's Traité de l'harmonie: A Study and Glossary Based on an Index". PhD diss. (Iowa City: University of Iowa, 1981): 196. Historically, this interval, like the tritone, is described as being and was associated with the .Andreas Werckmeister, Harmonologia musica, oder kurze Anleitung zur musicalischen Composition (Frankfurt and Leipzig: Theodor Philipp Calvisius, 1702): 6, and Musicalische Paradoxal-Discourse, oder allgemeine Vorstellungen (Quedlinburg: Theodor Philipp Calvisius, 1707): 75–76.
Melodically, an augmented unison very frequently occurs when proceeding to a chromatic chord, such as a secondary dominant, a diminished seventh chord, or an augmented sixth chord. Its use is also often the consequence of a melody proceeding in semitones, regardless of harmonic underpinning, e.g. D, D, E, F, F. (Restricting the notation to only minor seconds is impractical, as the same example would have a rapidly increasing number of accidentals, written enharmonically as D, E, F, G, A).
Harmonically, augmented unisons are quite rare in tonal repertoire. In the example to the right, Liszt wrote an E against an E in the bass. Here E was preferred to a D to make the tone's function clear as part of an F dominant seventh chord, and the augmented unison is the result of superimposing this harmony upon an E pedal point.
In addition to this kind of usage, harmonic augmented unisons are frequently written in modern works involving tone clusters, such as Iannis Xenakis' Evryali for solo piano.
Diminished unison
The term diminished unison or diminished prime is also found occasionally. It is found once in Rameau's writings, for example, as well as subsequent French, German, and English sources.Sources for diminished unison Johann Georg Albrechtsberger, Methods of Harmony, Figured Base, and Composition: Adapted for Self-Instruction, Volume 1, edited by Ignaz Seyfried (Ritter von), and Alexandre Choron (London: R. Cocks & Co., 1834): 4 [Translated from Méthodes d'harmonie et de composition: à l'aide desquelles on peut apprendre soi-même à accompagner la basse chiffrée et à composer toute espèce de musique, par J.-Georges Albrechtsberger. Nouvelle éd., mise en ordre et considérablement augmentée d'après l'enseignement de l'auteur, et formant la collection complète de ses OEuvres de théorie musicale, par le chevalier de Seyfried, son élève. Traduite de l'allemand, avec des notes, par M. Choron. Paris: Bachelier, 1830.] Henry Charles Banister, A Text-book of Music (London: George Bell and Sons, 1872): 34. Alexandre Choron, Principes de Composition des Ecoles d'Italie: Adoptés par le Gouvernement Français pour servir à l'instruction des Elèves des Maîtrises de Cathédrales: ouvrage classique formé de la réunion des modèles les plus parfaits en tout genre, enrichi d'un texte méthodique rédigé selon l'enseignement des Ecoles les plus célèbres et des Ecrivains didactiques les plus estimés, Tome premier, Contenant la préface & les Trois premiers Livres (Paris, 1808): 2 Castil-Blaze [François-Henri-Joseph Blaze], Dictionnaire de musique moderne (Brussels: L'Academie de musique, 1828): 269. Anton Gräffer, Systematische Guitarre-Schule, Erster Theil (Vienna: Anton Strauß, 1811): 38. Oskar Kolbe, Kurzgefasste Generalbasslehre, second, enlarged and corrected edition (Leipzig: Breitkopf und Härtel, 1872): 12. Alexander Lehr, Campanology Textbook: The Musical and Technical Aspect of Swinging Bells and Carillons, constituting Bulletin of the Guild of Carillonneurs in North America Volume 54 (2005): 51. The Guild of Carillonneurs in North America. Horst Leuchtmann, Dictionary of Terms in Music / Wörterbuch Musik: English–German, German–English, fourth, revised and enlarged edition (Munich, London, New York, and Paris: K. G. Saur; Berlin: Walter De Gruyter, 1992): 324. (cloth); (print/ebook); (ebook). Frederic Allison Lyman, The Normal Music Course in the Schoolroom: Being a Practical Exposition of the Normal Music Course, Together with Its Complemental Series, The Cecilian Series of Study and Song, by John W. Tufts, Designed to Aid Those who Teach Vocal Music (Boston, New York, Chicago: Silver, Burdett, and Company, 1896): 47–48. Robert Middleton, Harmony in Modern Counterpoint (Boston: Allyn and Bacon, 1967): 20. Cesar-Auguste Monti-Punti, Les secrets de la musique ou théorie musicale, edited by Pierre Rigaud (Paris: Leduc, 1846): 63, 72, 77. Robert Nelson and Carl J. Christensen, Foundations of Music, seventh edition (Boston: Schirmer Cengage Learning, 2008): 169. . Gustav Schilling, Musikalische Didaktik; oder, Die Kunst des Unterrichts in der Musik: Ein nothwendiges Hand- und Hülfsbuch für alle lehrer und lernende der Musik, Erzieher, Schulvorsteher, Organisten, Volkschullehrer &c. (Eisleben: Ferdinand Kuhnt. 1851): 315. Daniel Gottlob Türk, Anweisung zum Generalbaßspielen, second edition (Halle: Hemmerde und Schwetschte; Leipzig: Schwickert, 1800): 16. William Alfred White (1907). Harmony and Ear-Training (New York, Boston [etc.]: Silver, Burdett & Company): 35. Other sources reject the possibility or utility of the diminished unison on the grounds that any alteration to the unison increases its size, thus augmenting rather than diminishing it.Sources for augmented unison Friedrich Wilhelm Marpurg, Anfangsgründe der theoretischen Musik (Leipzig: Johann Gottlieb Immanuel Breitkopf, 1757): 34. Friedrich Wilhelm Marpurg, Handbuch bey dem Generalbasse und der Composition: mit zwo- drey- vier- fünf- sechs- sieben- acht und mehreren Stimmen für Anfänger und Geübtere, second, expanded and corrected edition (Berlin: Gottlieb August Lange. 1762): 14. Stefan Kostka and Dorothy Payne (2004). Tonal Harmony (Boston: McGraw-Hill): 21. . "There is no such thing as a diminished unison." Michael Pilhofer and Holly Day (2006). Music Theory for Dummies (Hoboken, NJ: John Wiley & Sons, Inc.): 113. . "There is no such thing as a diminished unison, because no matter how you change the unisons with accidentals, you are adding half steps to the total interval." Andrew Surmani, Karen Farnum Surmani, and Morton Manus (2009). Alfred's Essentials of Music Theory: A Complete Self-Study Course for All Musicians ([s.l.]: Alfred Music Publishing): 135. . "Since lowering either note of a perfect unison would actually increase its size, the perfect unison cannot be diminished, only augmented." W. S. B. Mathews (1909). "Editorial: Prof. White's Harmony and Ear-Training", The Journal of School Music 1, no. 9 (June): 260–63. Citation on 263: "What he [Prof. White in Harmony and Ear Training] calls the 'diminished prime or unison' cannot possibly occur. It is simply an augmented unison. Because unison is 'the relation of two tones at the same pitch,' and when one of these is chromatically distanced, it creates the contradiction in terms known as 'augmented' unison; but the other term, 'diminished unison' is impossible on the face of it, because the 'same pitch' cannot be made less." Smith, Uselma Clarke (1916). Keyboard Harmony, p. 15. The Boston Music Company. "Note that the diminished unison and octave are not commonly used." Jim Aikin (2004). A Player's Guide to Chords & Harmony (San Francisco: Backbeat Books): 32. . "In case you were wondering, there's no such thing as a diminished unison."