Augmented unison

Augmented unison
Inverse	Diminished octave
Name
Other names	Chromatic semitone, minor semitone
Abbreviation	A1
Size
Semitones	1
Interval class	1
Just interval	25:24, 2187:2048
Cents
12-Tone equal temperament	100
Just intonation	71, 114

In modern Western tonal music theory an augmented unison or augmented prime^[3] is the interval between two notes on the same staff position, or denoted by the same note letter, whose alterations cause them, in ordinary equal temperament, to be one semitone apart. In other words, it is a unison where one note has been altered by a half-step, such as B♭ and B♮ or C♮ and C♯. The interval is often described as a chromatic semitone.^[4] The term, in its French form unisson superflu, appears to have been coined by Jean-Philippe Rameau in 1722, who also called this interval a minor semitone (semiton mineur).^[5] Historically, this interval, like the tritone, is described as being "mi contra fa", and therefore is the "diabolus in musica" (the Devil in music).^[6] In 12-tone equal temperament, it is the enharmonic equivalent of a diatonic semitone or minor second,^[1] although in other tunings the diatonic semitone is a different interval.

Diminished unison

The term diminished unison or diminished prime is also found occasionally. It is found once in Rameau's writings, for example,^[5] as well as subsequent French, German, and English sources.^{[diminished 1]} 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.^{[augmented 1]} The term is sometimes justified as a negative-numbered interval,^[7]^[8] and also in terms of violin double-stopping technique on analogy to parallel intervals found on other strings.^[9] Some theoreticians make a distinction for this diminished form of the unison, stating it is only valid as a melodic interval, not a harmonic one.^{[melodic 1]}

Notes

^
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. ISBN 978-3-598-10913-3 (cloth); ISBN 978-3-11-190694-2 (print/ebook); ISBN 978-3-11-150573-2 (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. ISBN 978-0-495-56593-2.
- 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.

^
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. ISBN 978-0-07-285260-8. "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. ISBN 978-0-7645-7838-0. "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. ISBN 0-7390-3635-1. "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. ISBN 978-0-87930-798-1. "In case you were wondering, there's no such thing as a diminished unison."
- Arthur Foote and Walter Raymond Spalding (1905). Modern Harmony in Its Theory and Practice, p. 5. Arthur P. Schmidt. "a diminished unison is unthinkable, and the diminished 2d and 9th are of no practical use:..."

^
Source for melodic interval:
- Nicolas Etienne Framery, Pierre Louis Ginguené, and Jérôme-Joseph Momigny. Encyclopédie méthodique: musique, 2 vols. (Paris: Mme. Veuve Agasse,1818): 2:19.
- Carl Edward Gardner, Essentials of Music Theory: Elementary (New York: Carl Fischer, Inc. 1912): 34.
- Johann Adam Hiller (ed.) "Fortsetzung zu dem musikalischen Wörterbuche", Wöchentliche Nachrichten und Anmerkungen, die Musik betreffend 3, no. 41 (10 April 1769): 315–22, citation on 318.
- E. Friedrich Richter, Traité de l'harmonie: théorique et pratique, translated from the German by Gustave Sandré (Leipzig and Brussels: Breitkopf & Härtel, Éditeurs, 1891): 3.

References

^ ^a ^b Porter, Steven (1986). Music, A Comprehensive Introduction, p. 66. ISBN 978-0-935016-81-9.
^ Burrows, Terry (1999). How To Read Music, p. 62. ISBN 978-0-312-24159-9.
^ Blood, Brian (12 September 2014). "Intervals". Music theory online. Dolmetsch Musical Instruments. Retrieved 30 August 2015.
^ Rushton, Julian. "Unison (prime)". Grove Music Online. Oxford Music Online. Retrieved 17 August 2011. (subscription needed)
^ ^a ^b 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.
^ 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.
^ Eytan Agmon, The Languages of Western Tonality, Computational Music Science (Berlin, Heidelberg, New York, Dordrecht, London: Springer-Verlag, 2013): 64, 151. ISBN 978-3-642-39586-4 (cloth); ISBN 978-3-642-39587-1 (ebook)
^ Steven Porter, Music: A Comprehensive Introduction: Workbook No. 1: Music Theory (New York: Excelsior Music Publishing, 1986): 8. ISBN 0-935016-83-X.
^ Karl Courvoisier, Die Violin-Technik (Cologne: Pet. Jos. Tonger, 1878): 26. English edition, as The Technics of Violin Playing, the Strad Library 1 (London: The Strad; New York: Charles Scribner's Sons, 1908): 49.

[7] 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. ISBN 978-3-598-10913-3 (cloth); ISBN 978-3-11-190694-2 (print/ebook); ISBN 978-3-11-150573-2 (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. ISBN 978-0-495-56593-2.

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.

[2] 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.]

[3] Henry Charles Banister, A Text-book of Music (London: George Bell and Sons, 1872): 34.

[4] 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

[5] Castil-Blaze [François-Henri-Joseph Blaze], Dictionnaire de musique moderne (Brussels: L'Academie de musique, 1828): 269.

[6] Anton Gräffer, Systematische Guitarre-Schule, Erster Theil (Vienna: Anton Strauß, 1811): 38.

[7] Oskar Kolbe, Kurzgefasste Generalbasslehre, second, enlarged and corrected edition (Leipzig: Breitkopf und Härtel, 1872): 12.

[8] 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.

[9] 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. ISBN 978-3-598-10913-3 (cloth); ISBN 978-3-11-190694-2 (print/ebook); ISBN 978-3-11-150573-2 (ebook).

[10] 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.

[11] Robert Middleton, Harmony in Modern Counterpoint (Boston: Allyn and Bacon, 1967): 20.

[12] Cesar-Auguste Monti-Punti, Les secrets de la musique ou théorie musicale, edited by Pierre Rigaud (Paris: Leduc, 1846): 63, 72, 77.

[13] Robert Nelson and Carl J. Christensen, Foundations of Music, seventh edition (Boston: Schirmer Cengage Learning, 2008): 169. ISBN 978-0-495-56593-2.

[14] 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.

[15] Daniel Gottlob Türk, Anweisung zum Generalbaßspielen, second edition (Halle: Hemmerde und Schwetschte; Leipzig: Schwickert, 1800): 16.

[16] William Alfred White (1907). Harmony and Ear-Training (New York, Boston [etc.]: Silver, Burdett & Company): 35.

[8] 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. ISBN 978-0-07-285260-8. "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. ISBN 978-0-7645-7838-0. "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. ISBN 0-7390-3635-1. "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. ISBN 978-0-87930-798-1. "In case you were wondering, there's no such thing as a diminished unison."

Arthur Foote and Walter Raymond Spalding (1905). Modern Harmony in Its Theory and Practice, p. 5. Arthur P. Schmidt. "a diminished unison is unthinkable, and the diminished 2d and 9th are of no practical use:..."

[18] Friedrich Wilhelm Marpurg, Anfangsgründe der theoretischen Musik (Leipzig: Johann Gottlieb Immanuel Breitkopf, 1757): 34.

[19] 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.

[20] Stefan Kostka and Dorothy Payne (2004). Tonal Harmony (Boston: McGraw-Hill): 21. ISBN 978-0-07-285260-8. "There is no such thing as a diminished unison."

[21] Michael Pilhofer and Holly Day (2006). Music Theory for Dummies (Hoboken, NJ: John Wiley & Sons, Inc.): 113. ISBN 978-0-7645-7838-0. "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."

[22] 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. ISBN 0-7390-3635-1. "Since lowering either note of a perfect unison would actually increase its size, the perfect unison cannot be diminished, only augmented."

[23] 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."

[24] Smith, Uselma Clarke (1916). Keyboard Harmony, p. 15. The Boston Music Company. "Note that the diminished unison and octave are not commonly used."

[25] Jim Aikin (2004). A Player's Guide to Chords & Harmony (San Francisco: Backbeat Books): 32. ISBN 978-0-87930-798-1. "In case you were wondering, there's no such thing as a diminished unison."

[26] Arthur Foote and Walter Raymond Spalding (1905). Modern Harmony in Its Theory and Practice, p. 5. Arthur P. Schmidt. "a diminished unison is unthinkable, and the diminished 2d and 9th are of no practical use:..."

[12] Source for melodic interval:

Nicolas Etienne Framery, Pierre Louis Ginguené, and Jérôme-Joseph Momigny. Encyclopédie méthodique: musique, 2 vols. (Paris: Mme. Veuve Agasse,1818): 2:19.

Carl Edward Gardner, Essentials of Music Theory: Elementary (New York: Carl Fischer, Inc. 1912): 34.

Johann Adam Hiller (ed.) "Fortsetzung zu dem musikalischen Wörterbuche", Wöchentliche Nachrichten und Anmerkungen, die Musik betreffend 3, no. 41 (10 April 1769): 315–22, citation on 318.

E. Friedrich Richter, Traité de l'harmonie: théorique et pratique, translated from the German by Gustave Sandré (Leipzig and Brussels: Breitkopf & Härtel, Éditeurs, 1891): 3.

[28] Nicolas Etienne Framery, Pierre Louis Ginguené, and Jérôme-Joseph Momigny. Encyclopédie méthodique: musique, 2 vols. (Paris: Mme. Veuve Agasse,1818): 2:19.

[29] Carl Edward Gardner, Essentials of Music Theory: Elementary (New York: Carl Fischer, Inc. 1912): 34.

[30] Johann Adam Hiller (ed.) "Fortsetzung zu dem musikalischen Wörterbuche", Wöchentliche Nachrichten und Anmerkungen, die Musik betreffend 3, no. 41 (10 April 1769): 315–22, citation on 318.

[31] E. Friedrich Richter, Traité de l'harmonie: théorique et pratique, translated from the German by Gustave Sandré (Leipzig and Brussels: Breitkopf & Härtel, Éditeurs, 1891): 3.

[Porter-1] Porter, Steven (1986). Music, A Comprehensive Introduction, p. 66. ISBN 978-0-935016-81-9.

[Burrows-2] Burrows, Terry (1999). How To Read Music, p. 62. ISBN 978-0-312-24159-9.

[blood-3] Blood, Brian (12 September 2014). "Intervals". Music theory online. Dolmetsch Musical Instruments. Retrieved 30 August 2015.

[grove-4] Rushton, Julian. "Unison (prime)". Grove Music Online. Oxford Music Online. Retrieved 17 August 2011. (subscription needed)

[Anderson-5] 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.

[6] 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.

[9] Eytan Agmon, The Languages of Western Tonality, Computational Music Science (Berlin, Heidelberg, New York, Dordrecht, London: Springer-Verlag, 2013): 64, 151. ISBN 978-3-642-39586-4 (cloth); ISBN 978-3-642-39587-1 (ebook)

[10] Steven Porter, Music: A Comprehensive Introduction: Workbook No. 1: Music Theory (New York: Excelsior Music Publishing, 1986): 8. ISBN 0-935016-83-X.

[11] Karl Courvoisier, Die Violin-Technik (Cologne: Pet. Jos. Tonger, 1878): 26. English edition, as The Technics of Violin Playing, the Strad Library 1 (London: The Strad; New York: Charles Scribner's Sons, 1908): 49.

[1]

[2]

[3]

[4]

[5]

[6]

[diminished 1]

[augmented 1]

[7]

[8]

[9]

[melodic 1]

Diminished unison

See also

Notes

References