View source for Tonality

{{Short description|Harmonic structure with a central pitch}}
{{About|the musical system|linguistic feature|tone (linguistics)|tone colour|timbre|use of this term in photography|tonal range}}
{{Use shortened footnotes|date=March 2021}}
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</score>|width=300|align=right|caption=[[Perfect authentic cadence]] (IV–V–I [[chord progression]], in which we see the chords [[F major]], [[G major]], and then [[C major]], in four-part harmony) in C major.<br />"Tonal music is built around these tonic and dominant arrival points [cadences], and they form one of the fundamental building blocks of musical structure".{{sfnp|Benjamin|Horvit|Nelson|2008|p=63}}}}

'''Tonality''' is the arrangement of [[pitch (music)|pitches]] and / or [[chord (music)|chords]] of a musical work in a hierarchy of perceived ''relations'', ''stabilities'', ''attractions'', and ''directionality''. 

In this hierarchy, the single pitch or the [[root (music)|root]] of a [[triad (music)|triad]] with the greatest ''stability'' in a melody or in its harmony is called the [[tonic (music)|''tonic'']]. In this context "stability" approximately means that a pitch occurs frequently in a melody – and usually is the final note – or that the pitch often appears in the harmony, even when it is not the pitch used in the melody.

The ''root'' of the tonic triad forms the name given to the [[key (music)|key]], so in the key of [[C major|C&nbsp;major]] the note&nbsp;C can be both the tonic of the [[scale (music)|scale]] and the root of the tonic triad. However, the tonic can be a different [[Musical tone|tone]] in the same scale, and then the work is said to be in one of the [[mode (music)|''modes'']] of that scale.{{sfnp|Kosta|2013|pp=454–455}} 

Simple [[folk music]] songs, as well as orchestral pieces, often start and end with the tonic note. The most common use of the term "tonality"
: "is to designate the arrangement of musical phenomena around a referential tonic in [[Classical music|European music]] from about 1600 to about 1910".{{sfnp|Hyer|2001a}}

[[Contemporary classical music]] from 1910 to the 2000s may seek to avoid any sort of tonality — but [[harmony]] in almost all Western [[popular music]] remains tonal.{{Vague|date=April 2016|reason=There are several; different senses of 'tonality' defined in this article (see the 'vague' flag on the Tagg quotation in the next paragraph, and the article's caution about context where the quotation is repeated in the body.}} Harmony in [[jazz music|jazz]] includes many but not all tonal characteristics of the European [[common practice period]], usually known as "[[classical music]]".

: "All harmonic idioms in popular music are tonal, and none is without [[diatonic function|function]]."{{sfnp|Tagg|2003|p=534}}{{Vague|date=March 2015|reason=There are eight senses of 'tonality' specified in the body of the article, all of which (including the modal practice of pre-modern church music and twelve-tone technique) could potentially fulfill this description. To which of these does Tagg refer?}}

Tonality is an organized system of tones (e.g., the tones of a [[Major scale|major]] or [[minor scale]]) in which one tone (the tonic) becomes the central point for the remaining tones. The other tones in a tonal piece are all defined in terms of their relationship to the tonic. In tonality, the tonic (tonal center) is the tone of complete relaxation and stability, the target toward which other tones lead.{{sfnp|Benward & Saker|2003|p=36}} The [[cadence (music)|cadence]] (a rest point) in which the [[dominant chord]] or [[dominant seventh]] chord resolves to the tonic chord plays an important role in establishing the tonality of a piece.
: "Tonal music is music that is ''unified'' and ''dimensional''. Music is 'unified' if it is exhaustively referable to a pre-compositional system generated by a single constructive principle derived from a basic scale-type; it is 'dimensional' if it can nonetheless be distinguished from that pre-compositional ordering".{{sfnp|Pitt|1995|p=299}}

The term ''tonalité'' originated with [[Alexandre-Étienne Choron]]{{sfnp|Choron|1810}} and was borrowed by [[François-Joseph Fétis]] in 1840.<ref>{{harvp|Simms|1975|p=119}}; {{harvp|Judd|1998a|p=5}}; {{harvp|Hyer|2001a}}; {{harvp|Brown|2005|p={{mvar|xiii}} }}.</ref> According to [[Carl Dahlhaus]], however, the term ''tonalité'' was only coined by [[Castil-Blaze]] in 1821.<ref>{{harvp|Dahlhaus|1967|p=960}}; {{harvp|Dahlhaus|1980|p=51}}.</ref> Although Fétis used it as a general term for a system of musical organization and spoke of ''types de tonalités'' rather than a single system, today the term is most often used to refer to [[Major and minor|major–minor]] tonality, the system of musical organization of the common practice period. Major-minor tonality is also called ''harmonic tonality'' (in the title of Carl Dahlhaus,{{sfnp|Dahlhaus|1990}} translating the German ''harmonische Tonalität''), ''diatonic tonality'', ''common practice tonality'', ''functional tonality'', or just ''tonality''.

== Characteristics and features ==
At least eight distinct senses of the word "tonality" (and corresponding adjective, "tonal"), some mutually exclusive, have been identified.{{sfnp|Hyer|2001a}}{{vague|date=March 2015|reason=Who identified these senses? Where did they find them used?}}

=== Systematic organization ===
The word tonality may describe any systematic organization of pitch phenomena in any music at all, including pre-17th century western music as well as much non-western music, such as music based on the [[slendro]] and [[pelog]] pitch collections of Indonesian [[gamelan]], or employing the modal nuclei of the [[Arabic maqam]] or the Indian [[raga]] system.

This sense also applies to the tonic/dominant/subdominant harmonic constellations in the theories of [[Jean-Philippe Rameau]] as well as the 144 basic transformations of [[twelve-tone technique]]. By the middle of the 20th century, it had become "evident that triadic structure does not necessarily generate a tone center, that non-triadic harmonic formations may be made to function as referential elements, and that the assumption of a twelve-tone complex does not preclude the existence of tone centers".{{sfnp|Perle|1991|p=8}}

For the composer and theorist [[George Perle]], tonality is not "a matter of 'tone-centeredness', whether based on a 'natural' hierarchy of pitches derived from the overtone series or an 'artificial' pre compositional ordering of the pitch material; nor is it essentially connected to the kinds of pitch structures one finds in traditional diatonic music".{{sfnp|Pitt|1995|p=291}} This sense (like some of the others) is susceptible to ideological employment, as Schoenberg, did by relying on the idea of a progressive development in musical resources "to compress divergent ''fin-de-siècle'' compositional practices into a single historical lineage in which his own music brings one historical era to a close and begins the next." From this point of view, twelve-tone music could be regarded "either as the natural and inevitable culmination of an organic motivic process ([[Anton Webern|Webern]]) or as a historical ''Aufhebung'' ([[Theodor W. Adorno|Adorno]]), the dialectical synthesis of late Romantic motivic practice on the one hand with a musical sublimation of tonality as pure system on the other".{{sfnp|Hyer|2001a}}

=== Theoretical arrangement of pitches ===
In another sense, tonality means any rational and self-contained [[Music theory|theoretical arrangement]] of musical pitches, existing prior to any concrete embodiment in music.

For example, "Sainsbury, who had Choron translated into English in 1825, rendered the first occurrence of tonalité as a 'system of modes' before matching it with the neologism 'tonality'. While tonality qua system constitutes a theoretical (and thus imaginative) abstraction from actual music, it is often hypostatized in musicological discourse, converted from a theoretical structure into a musical reality. In this sense, it is understood as a Platonic form or prediscursive musical essence that suffuses music with intelligible sense, which exists before its concrete embodiment in music, and can thus be theorized and discussed apart from actual musical contexts".{{sfnp|Hyer|2001a}}

=== Contrast with modal and atonal systems ===
To contrast with "[[Mode (music)|modal]]" and "[[Atonality|atonal]]", the term tonality is used to imply that tonal music is discontinuous as a form of cultural expression from modal music (before 1600) on the one hand and atonal music (after 1910) on the other.

=== Pre-modern concept ===
In some literature, tonality is a generic term applied to pre-modern music, referring to the eight modes of the Western church, implying that important historical continuities underlie music before and after the emergence of the [[common practice period]] around 1600, with the difference between ''tonalité ancienne'' (before 1600) and ''tonalité moderne'' (after 1600) being one of emphasis rather than of kind.

=== Referential tonic ===
In a general way, tonality can refer to a wide variety of musical phenomena (harmonies, cadential formulae, harmonic progressions, melodic gestures, formal categories) as arranged or understood in relation to a referential tonic.

=== Tonal theories ===
In a slightly different sense to the one above, tonality can also be used to refer to musical phenomena perceived or pre-interpreted in terms of the categories of tonal theories.

This is a psychophysical sense, where for example "listeners tend to hear a given pitch as, for instance, an<!--not a mistake--> A above middle C, an [[augmented fourth|augmented 4th]] above E{{sup|{{Music|flat}}}}, the minor 3rd in an F{{Music|sharp}} minor triad, a dominant in relation to D, or {{music|scale|2}} (where the caret designates a scale degree) in G major rather than a mere acoustical frequency, in this case [[440 Hz|440&nbsp;Hz]]".{{sfnp|Hyer|2001a}}

=== Synonym for "key" ===
The word tonality is sometimes used as a synonym for "[[key (music)|key]]", as in "the C-minor tonality of [[Symphony No. 5 (Beethoven)|Beethoven's Fifth Symphony]]".

In some languages, indeed, the word for "key" and that for "tonality" are the same, e.g. French ''tonalité''.

=== Other perspectives ===
There is a loose assortment of ideas associated with the term.

: "Tonal harmonies must always include the third of the chord".{{sfnp|Brown|2005|p=46}}

In major and minor harmonies, the [[perfect fifth]] is often implied and understood by the listener even if it is not present. To function as a tonic, a chord must be either a major or a minor triad. Dominant function requires a major-quality triad with a root a perfect fifth above the affiliated tonic and containing the leading tone of the key. This dominant triad must be preceded by a chord progression that establishes the dominant as the penultimate goal of a motion that is completed by moving on to the tonic. In this final dominant-to-tonic progression, the leading tone normally ascends by semitone motion to the tonic scale degree.<ref>{{harvp|Berry|1976|p=54}}; {{harvp|Brown|2005|p=4}}; {{harvp|Burnett|Nitzberg|2007|p=97}}; {{harvp|Rogers|2004|p=47}}.</ref> A dominant seventh chord always consist of a major triad with an added minor seventh above the root. To achieve this in minor keys, the seventh scale degree must be raised to create a major triad on the dominant.<ref>{{harvp|Duckworth|2015|p=225}}; {{harvp|Mayfield|2013|p=94}}.</ref>

[[David Cope]]{{sfnp|Cope|1997|p=12}} considers key, [[consonance and dissonance]] (relaxation and tension, respectively), and hierarchical relationships the three most basic concepts in tonality.

Carl Dahlhaus{{sfnp|Dahlhaus|1990|p=102}} lists the characteristic schemata of tonal harmony, "typified in the compositional formulas of the 16th and early 17th centuries," as the "complete cadence" I–[[ii–V–I]], [[I–IV–V–I]], I–IV–I–V–I; the [[circle of fifths]] progression I–IV–vii°–iii–[[vi–ii–V–I]]; and the major–minor parallelism: minor v–i–VII–III equals major iii–vi–V–I; or minor III–VII–i–v equals major I–V–vi–iii. The last of these progressions is characterized by "retrograde" harmonic motion.

=== Form ===
{{Main|Musical form}}

=== Consonance and dissonance ===
{{Main|Consonance and dissonance}}
The consonance and dissonance of different intervals plays an important role in establishing the tonality of a piece or section in [[common practice]] music and [[popular music]]. For example, for a simple [[folk music]] song in the key of C Major, almost all of the triadic chords in the song will be Major or minor chords which are stable and consonant (e.g., in the key of C Major, commonly used chords include D minor, F Major, G Major, etc.). The most commonly used dissonant chord in a pop song context is the [[dominant seventh]] chord built on the fifth scale degree; in the key of C Major, this would be a G dominant seventh chord, or G7 chord, which contains the pitches G, B, D and F. This dominant seventh chord contains a dissonant [[tritone]] interval between the notes B and F. In pop music, the listener will expect this tritone to be resolved to a consonant, stable chord (in this case, typically a C Major [[cadence (music)|cadence]] (coming to rest point) or a [[deceptive cadence]] to an A minor chord).

=== Tonal musics ===
"The larger portion of the world's folk and art music can be categorized as tonal," as long as the definition is as follows: "Tonal music gives priority to a single tone or tonic. In this kind of music all the constituent tones and resulting tonal relationships are heard and identified relative to their tonic".{{sfnp|Susanni|2012|p=66}} In this sense, "All harmonic idioms in popular music are tonal, and none is without function".{{sfnp|Tagg|2003|p=534}} However, "within the continuing hegemony of tonality there is evidence for a relatively separate tradition of genuine folk musics, which do not operate completely or even mainly according to the assumptions or rules of tonality. … throughout the reign of tonality there seem to have existed subterranean folk musical traditions organized on principles different from tonality, and often modal: Celtic songs and blues are obvious examples".{{sfnp|Shepherd|Virden|Vulliamy|Wishart|1977|p=156}}

According to Allan Moore,{{sfnp|Moore|1995|p=191}} "part of the heritage of rock lies within common-practice tonality"{{sfnp|Burns|2000|p=213}} but, because the [[leading-tone|leading-note]] / tonic relationship is "axiomatic to the definition of common-practice tonality", and a fundamental feature of rock music's identity is the absence of a diatonic leading tone, the harmonic practices of rock music, "while sharing many features with classical tonality, are nonetheless distinct".{{sfnp|Moore|1995|p=187}} Power chords are especially problematic when trying to apply classical functional tonality to certain varieties of popular music. Genres such as [[Heavy metal music|heavy metal]], [[New wave music|new wave]], [[punk rock]], and [[grunge music]] "took power chords into new arenas, often with a reduced emphasis on tonal function. These genres are often expressed in two parts—a bass line doubled in fifths, and a single vocal part. Power chord technique was often allied with modal procedure".{{sfnp|Everett|2000|p=331}}

Much jazz is tonal, but "functional tonality in jazz has different properties than that of common-practice classical music. These properties are represented by a unique set of rules dictating the unfolding of harmonic function, voice-leading conventions, and the overall behavior of chord tones and chordal extensions".{{sfnp|Terefenko|2014|p=26}}

== History and theory ==
=== 18th century ===
[[Jean-Philippe Rameau]]'s ''Treatise on Harmony'' (1722) is the earliest effort to explain tonal harmony through a coherent system based on acoustical principles,{{sfnp|Girdlestone|1969|p=520}} built upon the functional unit being the [[triad (music)|triad]], with inversions.

=== 19th century ===
The term ''tonalité'' (tonality) was first used in 1810 by Alexandre Choron in the preface ''Sommaire de l'histoire de la musique''{{sfnp|Brown|2005|loc=p. xiii}} to the ''Dictionnaire historique des musiciens artistes et amateurs'' (which he published in collaboration with [[:fr:François-Joseph-Marie Fayolle|François-Joseph-Marie Fayolle]]) to describe the arrangement of the dominant and subdominant above and below the tonic—a constellation that had been made familiar by Rameau. According to Choron, this pattern, which he called ''tonalité moderne'', distinguished modern music's harmonic organization from that of earlier [pre 17th century] music, including ''tonalité des Grecs'' (ancient Greek modes) and ''tonalité ecclésiastique'' (plainchant).<ref>{{harvp|Choron|1810|pp={{mvar|xxxvii–xl}} }}; {{harvp|Hyer|2001a}}.</ref> According to Choron, the beginnings of this modern tonality are found in the music of [[Claudio Monteverdi]] around the year 1595, but it was more than a century later that the full application of tonal harmony finally supplanted the older reliance on the melodic orientation of the church modes, in the music of the [[Neapolitan School]] — most especially that of [[Francesco Durante]].{{sfnp|Choron|1810|pp={{mvar|xxxviii, xl}} }}

François-Joseph Fétis developed the concept of ''tonalité'' in the 1830s and 1840s,{{sfnp|Brown|2005|loc=p. xiii}} finally codifying his theory of tonality in 1844, in his ''Traité complet de la théorie et de la pratique de l'harmonie''.<ref>{{harvp|Hyer|2001a}}; {{harvp|Wangermée|Ellis|2001}}.</ref> Fétis saw ''tonalité moderne'' as the historically evolving phenomenon with three stages: tonality of ''ordre transitonique'' ("transitonic order"), of ''ordre pluritonique'' ("pluritonic order") and, finally, ''ordre omnitonique'' ("omnitonic order"). The "transitonic" phase of tonality he connected with the late [[Claudio Monteverdi|Monteverdi]]. He described his earliest example of ''tonalité moderne'' thus: "In the passage quoted here from Monteverdi's madrigal (''Cruda amarilli'', mm. 9–19 and 24–30), one sees a tonality determined by the ''accord parfait'' [root position major chord] on the tonic, by the sixth chord assigned to the chords on the third and seventh degrees of the scale, by the optional choice of the ''accord parfait'' or the sixth chord on the sixth degree, and finally, by the ''accord parfait'' and, above all, by the unprepared seventh chord (with major third) on the dominant".{{sfnp|Fétis|1844|p=171}} Among most subtle representatives of "pluritonic order" there were Mozart and Rossini; this stage he saw as the culmination and perfection of ''tonalité moderne''. The romantic tonality of Berlioz and especially Wagner he related to "omnitonic order" with its "insatiable desire for modulation".{{sfnp|Hyer|2002|p=748}} His prophetic vision of the omnitonic order (though he didn't approve it personally) as the way of further development of tonality was a remarkable innovation to historic and theoretic concepts of the 19th century.{{sfnp|Simms|1975|p=132}}

''Tonalité ancienne'' Fetis described as tonality of ''ordre unitonique'' (establishing one key and remaining in that key for the duration of the piece). The principal example of this "unitonic order" tonality he saw in the Western plainchant.

Fétis believed that tonality, ''tonalité moderne'', was entirely cultural, saying, "For the elements of music, nature provides nothing but a multitude of tones differing in pitch, duration, and intensity by the greater or least degree&nbsp;... The conception of the relationships that exist among them is awakened in the intellect, and, by the action of sensitivity on the one hand, and will on the other, the mind coordinates the tones into different series, each of which corresponds to a particular class of emotions, sentiments, and ideas. Hence these series become various types of tonalities."{{sfnp|Fétis|1844|pp=11–12}} "But one will say, 'What is the principle behind these scales, and what, if not acoustic phenomena and the laws of mathematics, has set the order of their tones?' I respond that this principle is purely metaphysical [anthropological]. We conceive this order and the melodic and harmonic phenomena that spring from it out of our conformation and education."{{sfnp|Fétis|1844|p=249}}

Fétis' ''Traité complet'' was very popular. In France alone the book was printed between 1844 and 1903 twenty times. The 1st edition was printed in Paris and Brussels in 1844, the 9th edition was printed in Paris in 1864,{{sfnp|Fétis|1864}} and the 20th edition was printed in Paris in 1903.

In contrast, [[Hugo Riemann]] believed tonality, "affinities between tones" or ''Tonverwandtschaften'', was entirely natural and, following [[Moritz Hauptmann]],{{sfnp|Hauptmann|1853|p={{Page needed|date=March 2021}}}} that the major third and perfect fifth were the only "directly intelligible" intervals, and that I, IV, and V, the tonic, subdominant, and dominant were related by the perfect fifths between their root notes.{{sfnp|Dahlhaus|1990|pp=101–102}}

It is in this era that the word ''tonality'' was popularized by Fétis.{{sfnp|Wangermée and Ellis|2001}}

Theorists such as Hugo Riemann, and later [[Edward Lowinsky]]{{sfnp|Lowinsky|1962}} and others, pushed back the date when modern tonality began, and the [[cadence (music)|cadence]] began to be seen as the definitive way that a tonality is established in a work of music.{{sfnp|Judd|1998b}}

In the music of some late-Romantic or [[post-Romantic]] composers such as [[Richard Wagner]], [[Hugo Wolf]], [[Pyotr Ilyich Tchaikovsky]], [[Anton Bruckner]], [[Gustav Mahler]], [[Richard Strauss]], [[Alexander Scriabin]], and others, we find a variety of harmonic and linear procedures that have the effect of weakening functional tonality. These procedures may produce a suspension of tonality or may create a sense of tonal ambiguity, even to the point that at times the sense of tonality is completely lost. [[Arnold Schoenberg|Schoenberg]] described this kind of tonality (with references to the music of Wagner, Mahler, and himself, amongst others) as "aufgehobene Tonalität" and "schwebende Tonalität",{{sfnp|Schoenberg|1922|pp=444, 459–460}} usually rendered in English as "suspended" ("not in effect", "cancelled") tonality and "fluctuating" ("suspended", "not yet decided") tonality, respectively.{{sfnp|Schoenberg|1978|p=383}}

=== 20th century ===
In the early 20th century, the tonality that had prevailed since the 17th century was seen to have reached a crisis or break down point. Because of the "...increased use of the ambiguous chords, the less probable harmonic progressions, and the more unusual melodic and rhythmic inflections,"{{sfnp|Meyer|1967|p=241}} the syntax of functional harmony loosened to the point where, "At best, the felt probabilities of the style system had become obscure; at worst, they were approaching a uniformity which provided few guides for either composition or listening."{{sfnp|Meyer|1967|p=241}}

Tonality may be considered generally, with no restrictions on the date or place the music was produced, and little restriction on the materials and methods used. This definition includes pre-17th century western music, as well as much non-western music. By the middle of the 20th century, it had become "evident that triadic structure does not necessarily generate a tone center, that non-triadic harmonic formations may be made to function as referential elements, and that the assumption of a twelve-tone complex does not preclude the existence of tone centers".{{sfnp|Perle|1991|p=8}} For the composer and theorist [[George Perle]], tonality is not "a matter of 'tone-centeredness', whether based on a 'natural' hierarchy of pitches derived from the overtone series or an 'artificial' pre compositional ordering of the pitch material; nor is it essentially connected to the kinds of pitch structures one finds in traditional diatonic music".{{sfnp|Pitt|1995|p=291}}

== Theoretical underpinnings ==

One area of disagreement going back to the origin of the term tonality is whether tonality is ''natural'' or inherent in acoustical phenomena, whether it is inherent in the human nervous system or a psychological construct, whether it is inborn or learned, and to what degree it is all these things.{{sfnp|Meyer|1967|p=236}} A viewpoint held by many theorists since the third quarter of the 19th century, following the publication in 1862 of the first edition of Helmholtz's ''On the Sensation of Tone'',{{sfnp|Helmholtz|1877}} holds that diatonic scales and tonality arise from natural overtones.<ref>{{harvp|Riemann|1872}}, {{harvp|Riemann|1875}}, {{harvp|Riemann|1882}}, {{harvp|Riemann|1893}}, {{harvp|Riemann|1905}}, {{harvp|Riemann|1914–15}}; {{harvp|Schenker|1906–35}}; {{harvp|Hindemith|1937–70}}.</ref>

[[Rudolph Réti]] differentiates between harmonic tonality of the traditional kind found in [[homophony]], and melodic tonality, as in [[monophony]]. In the harmonic kind, tonality is produced through the [[dominant (music)|V]]–[[tonic (music)|I]] [[chord progression]]. He argues that in the progression I–x–V–I (and all progressions), V–I is the only step "which ''as such'' produces the effect of tonality", and that all other chord successions, diatonic or not, being more or less similar to the tonic-dominant, are "the composer's free invention." He describes melodic tonality (the term coined independently and 10&nbsp;years earlier by [[Estonia]]n composer Jaan Soonvald{{sfnp|Rais|1992|p=46}}) as being "entirely different from the classical type," wherein, "the whole line is to be understood as a musical unit mainly through its relationship to this basic note [the tonic]," this note not always being the tonic as interpreted according to harmonic tonality. His examples are ancient Jewish and [[Gregorian chant]] and other Eastern music, and he points out how these melodies often may be interrupted at any point and returned to the tonic, yet harmonically tonal melodies, such as that from Mozart's ''[[The Magic Flute]]'' below, are actually "strict [[Harmonic rhythm|harmonic-rhythmic]] pattern[s]," and include many points "from which it is impossible, that is, illogical, unless we want to destroy the innermost sense of the whole line" to return to the tonic.{{sfnp|Reti|1958|p=16}}

{|
|[[File:Mozart-Reti - The Magic Flute.png|400px|The tonic feels more or less natural after each note of, for example, Mozart's ''The Magic Flute'']]
::x = return to tonic near inevitable
::ⓧ (circled x) = possible but not inevitable
::O (circle) = impossible
:::({{harvp|Reti|1958|p=133}})
|style="vertical-align:top;"|{{Listen|type=music|filename=Mozart-Reti - The Magic Flute.mid|title=Normally: "Ein Mädchen oder Weibchen" from ''The Magic Flute''|filename2=Mozart-Reti - The Magic Flute impossible.mid|title2=Impossible return after B{{music|natural}}<!-- This would be easier to follow with a score of the second sound file. -->}}
|}
Consequently, he argues, melodically tonal melodies resist harmonization and only reemerge in western music after, "harmonic tonality was abandoned," as in the music of [[Claude Debussy]]: "melodic tonality plus [[modulation (music)|modulation]] is [Debussy's] modern tonality".{{sfnp|Reti|1958|p=23}}

== Outside common-practice period ==
The noun "tonality" and adjective "tonal" are widely applied also, in studies of early and modern Western music, and in non-Western traditional music ([[Arabic maqam]], Indian [[raga]], Indonesian [[slendro]] etc.), to the "systematic arrangements of pitch phenomena and relations between them".<ref>{{harvp|Hyer|2001a}}; {{harvp|Hyer|2002}}.</ref> Felix Wörner, Ullrich Scheideler, and Philip Rupprecht in the introduction to a collection of essays dedicated to the concept and practice of tonality between 1900 and 1950 describe it generally as "the awareness of key in music".{{sfnp|Wörner|Scheideler|Rupprecht|2012|p=11}}

[[Harold Powers]], in a series of articles, used terms "sixteenth-century tonalities"<ref>{{harvp|Powers|1981|p=439}}; {{harvp|Powers|1992|p=12}}; {{harvp|Powers|1996|p=221}}.</ref> and "Renaissance tonality".{{sfnp|Powers|1996|p=226}} He borrowed German "Tonartentyp" from {{ill|Siegfried Hermelink|de}},{{sfnp|Hermelink|1960}} who related it to Palestrina, translated it into English as "tonal type",{{sfnp|Powers|1981|p=439}} and systematically applied the concept of "tonal types" to Renaissance sacred and paraliturgical polyphony. Cristle Collins Judd (the author of many articles and a thesis dedicated to the early pitch systems) found "tonalities" in this sense in motets of [[Josquin des Prez]].{{sfnp|Judd|1992}} Judd also wrote of "chant-based tonality",{{sfnp|Judd|1998c}} meaning "tonal" polyphonic compositions based on plainchant. Peter Lefferts found "tonal types" in the French polyphonic chanson of the 14th&nbsp;century,{{sfnp|Lefferts|1995}} Italian musicologists Marco Mangani and Daniele Sabaino in the late Renaissance music,{{sfnp|Mangani and Sabaino|2008}} and so on.

The wide usage of "tonality" and "tonal" has been supported by several other musicologists (of diverse provenance).<ref>It can be traced, e.g., in the articles collected in {{harvp|Judd|1998a}}.</ref> A possible reason for this broader usage of terms "tonality" and "tonal" is the attempt to translate German "Tonart" as "tonality" and "Tonarten-" prefix as "tonal" (for example, it is rendered so in the seminal ''[[New Grove]]'' article "Mode",<ref>{{harvp|Powers et al.|2001|loc=§V, 1, et passim}}; {{harvp|Powers|1981|p=441}}; {{harvp|Powers|1982|pp=59, 61}}.</ref> etc.). Therefore, two different German words "Tonart" and "Tonalität" have sometimes been translated as "tonality" although they are not the same words in German.

[[File:Hugo Riemann, "Tonalität," Musik-Lexikon (1882).png|thumb|Riemann's illustration of a non-diatonic cadence possessing ''Tonalität'' without ''Tonart''{{sfnp|Kopp|2011|p=401}} [[File:Hugo Riemann, "Tonalität," Musik-Lexikon (1882).mid|thumb]]]]
In 1882, Hugo Riemann defined the term ''Tonalität'' specifically to include chromatic as well as diatonic relationships to a tonic, in contrast to the usual diatonic concept of ''Tonart''. In the [[neo-Riemannian theory]] of the late 20th century, however, the same chromatic chord relations cited by Riemann came to be regarded as a fundamental example of nontonal triadic relations, reinterpreted as a product of the hexatonic cycle (the six-pitch-class set forming a scale of alternating minor thirds and semitones, [[Forte number|Forte's set-type]] 6–20, but manifested as a succession of from four to six alternating major and minor triads), defined without reference to a tonic.<ref>{{harvp|Cohn|1996|p=18, et passim}}; {{harvp|Kopp|2011|p=401}}.</ref>

In the 20th century, music that no longer conformed to the strict definition of common-practice tonality could nevertheless still involve musical phenomena (harmonies, cadential formulae, harmonic progressions, melodic gestures, formal categories) arranged or understood in relation to a referential tonic.{{sfnp|Hyer|2001a}} For example, the closing bars of the first movement of [[Béla Bartók]]'s ''[[Music for Strings, Percussion and Celesta]]'' do not involve a composed-out triad, but rather a diverging-converging pair of chromatic lines moving from a unison A to an octave E{{Music|flat}} and back to a unison A again, providing a framing "deep structure" based on a tritone relationship that nevertheless is not analogous to a tonic-dominant axis, but rather remains within the single functional domain of the tonic, A.{{sfnp|Agawu|2009|p=72}} To distinguish this species of tonality (found also, for example, in the music of [[Samuel Barber|Barber]], [[Alban Berg|Berg]], [[Leonard Bernstein|Bernstein]], [[Benjamin Britten|Britten]], [[Irving Fine|Fine]], [[Paul Hindemith|Hindemith]], [[Francis Poulenc|Poulenc]], [[Sergei Prokofiev|Prokofiev]], and, especially, Stravinsky) from the stricter kind associated with the 18th century, some writers use the term "[[neotonality]]",<ref>({{harvp|Burkholder, Grout, and Palisca|2009|pp=838, 885}}; {{harvp|Silberman|2006|pp={{mvar|v}}, 2, 33, 37, 58, 65, 108}}.</ref> while others prefer to use the term ''centricity'',{{sfnp|Straus|2000|pp=112–114}} and still others retain the term ''tonality'',{{sfnp|White|1979|p=558}} in its broader sense or use word combinations like ''extended tonality''.{{sfnp|Schoenberg|1942}}{{sfnp|Schoenberg|1950}}

== Computational methods to determine the key ==
In [[music information retrieval]], techniques have been developed to determine the key of a piece of [[Classical music|classical Western music]] (recorded in audio data format) automatically. These methods are often based on a compressed representation of the pitch content in a 12-dimensional [[pitch-class]] profile (chromagram) and a subsequent procedure that finds the best match between this representation and one of the prototype vectors of the 24 minor and major keys.{{sfnp|Purwins, Blankertz, and Obermayer|2000|pp=270–272}} For implementation, often the [[constant-Q transform]] is used, displaying the musical signal on a log frequency scale. Although a radical (over)simplification of the concept of tonality, such methods can predict the key of classical Western music well for most pieces. Other methods also take into consideration the sequentiality of music.

== See also ==
{{Portal|Music}}
* [[History of music]]
* [[Harry Partch]]' [[Otonality and utonality]]
* [[Peter Westergaard's tonal theory]]
* [[Polytonality]]
* [[Tonality diamond]]
* [[Schenkerian analysis]]

==Footnotes==
{{reflist|18em}}

===Sources===
{{refbegin|colwidth=25em|small=yes}}
* {{cite book
 |last=Agawu |first=Kofi
 |year=2009
 |title=Music as Discourse: Semiotic adventures in romantic music
 |series=Oxford Studies in Music Theory
 |place=Oxford, UK / New York, NY
 |publisher=Oxford University Press
 |isbn=978-0-19-537024-9
}}
* {{cite book
 |last1=Benjamin |first1=Thomas
 |last2=Horvit   |first2=Michael M.
 |last3=Nelson   |first3=Robert
 |year=2008
 |title=Techniques and Materials of Music: From the common practice period through the twentieth century |edition=7th
 |place=Belmont, CA |publisher=Thomson Schirmer
 |isbn=978-0-495-18977-0
}}
* {{cite book
 |last1=Benward |first1=Bruce
 |last2=Saker   |first2=Marilyn
 |year=2003
 |title=Music: In theory and practice |edition=7th
 |volume=I
 |place=New York, NY |publisher=McGraw Hill
 |isbn=978-0-07-294262-0
}}
* {{cite book
 |last=Berry |first=Wallace
 |year=1976
 |title=Structural Functions in Music |edition=original
 |place=Englewood Cliffs, NJ |publisher=Prentice-Hall
}}
: {{cite book
 |last=Berry |first=Wallace
 |year=1987 |orig-year=1976
 |title=Structural Functions in Music |edition=reprint pbk
 |place=Mineola NY |publisher=Dover Publications
 |isbn=0-486-25384-8
}}
* {{cite book
 |last=Brown |first=Matthew
 |year=2005
 |url=https://books.google.com/books?id=aQ2HuqGVzn0C&dq=Choron+Tonality&pg=PR13
 |title=Explaining Tonality: Schenkerian theory and beyond
 |series=Eastman Studies in Music |volume=27
 |place=Rochester, NY |publisher=University of Rochester Press
 |isbn = 1-58046-160-3
}}
* {{cite book
 |last1=Burkholder |first1=J. Peter
 |last2=Grout      |first2=D.J.     |author2-link=Donald Jay Grout
 |last3=Palisca    |first3=Claude V.
 |year=2009
 |title=A History of Western Music |edition=8th
 |place=New York, NY  |publisher=W.W. Norton
 |isbn=978-0-393-93125-9
}}
* {{cite book
 |last1=Burnett |first1=Henry
 |first2=Roy |last2=Nitzberg
 |year=2007
 |title=Composition, Chromaticism and the Developmental Process: A new theory of tonality
 |place=Aldershot / Burlington VT  |publisher=Ashgate Publishing
 |isbn = 978-0-7546-5162-8
}}
* {{cite book
 |last=Burns |first=Lori
 |year=2000
 |section=Analytic methodologies for rock music: Harmonic and voice-leading strategies in Tori Amos's "Crucify"
 |title=Expression in Pop-rock Music: A collection of critical and analytical essays
 |editor-first=Walter |editor-last=Everett
 |pages=213–246
 |place=New York, NY |publisher=Garland Publishing
 |isbn=978-0-8153-3160-5
}}
* {{cite book
 |last=Choron |first=A.-E. |author-link=Alexandre-Étienne Choron
 |year=1810 |orig-year=1810–1811
 |section=Introduction: Sommaire de l'histoire de la musique |lang=fr
 |trans-section=Introduction: A summary of the history of music 
 |editor1-first=A.E. |editor1-last=Choron
 |editor2-first=François |editor2-last=Fayolle
 |section-url=https://www.digitale-sammlungen.de/en/view/bsb10599980?page=1
 |title=Dictionnaire historique des musiciens artistes et amateurs, morts ou vivants
 |quote=qui se sont illustrés en une partie quelconque de la musique et des arts qui y sont relatifs ... ; précédé d'un sommaire de l'histoire de la musique
 |volume=1 |pages={{mvar|xi–xcii}}
 |place=Paris, FR |publisher=Valade et Lenormant
}}
:: published in English translation as
: {{cite book
 |last=Choron |first=A.-E. |author-link=Alexandre-Étienne Choron
 |year=1827 |orig-year=1810–1811
 |section=Summary of the history of music (introduction)
 |editor-first=John S. |editor-last=Sainsbury
 |title=A Dictionary of Musicians, from the Earliest Ages to the Present Time
 |edition=2nd Engl.
 |place=London, UK |publisher=Sainsbury & Co.
 |pages={{mvar|xxxvj}} & ''passim''
}}
* {{cite journal
 |last=Cohn |first=Richard
 |date=March 1996
 |title=Maximally smooth cycles, hexatonic systems, and the analysis of late-Romantic triadic progressions
 |journal=Music Analysis
 |volume=15 |number=1 |pages=9–40
|doi=10.2307/854168
 |jstor=854168
 }}
* {{cite book
 |last=Cope |first=D. |author-link=David Cope
 |year=1997
 |title=Techniques of the Contemporary Composer
 |place=New York, NY |publisher=Schirmer Books
 |isbn=0-02-864737-8
}}
* {{cite book
 |last=Dahlhaus |first=Carl |author-link=Carl Dahlhaus
 |year=1967
 |section=Tonalität
 |title=[[Riemann Musiklexikon]]: Sachteil
 |editor-first=H.H. |editor-last=Eggebrecht |editor-link=Hans Heinrich Eggebrecht
 |pages=960–962 |place=Mainz, DE |publisher=B. Schott's Söhne
}}
* {{cite book
 |last=Dahlhaus |first=Carl |author-link=Carl Dahlhaus
 |year=1980
 |section=Tonality
 |editor1-first=S. |editor1-last=Sadie   |editor1-link=Stanley Sadie
 |editor2-first=J. |editor2-last=Tyrrell |editor2-link=John Tyrrell (professor of music) 
 |title=The New Grove Dictionary of Music and Musicians  |edition=2nd
 |title-link=The New Grove Dictionary of Music and Musicians 
 |volume=19 |pages=51–55
 |place=London, UK |publisher=Macmillan Publishers
 |isbn=0-333-23111-2  |postscript=none
}} (cloth); {{ISBN|978-0-333-60800-5}}; {{ISBN|978-0195170672}} (hc) 
* {{cite book
 |last=Dahlhaus |first=Carl |author-link=Carl Dahlhaus
 |year=1990
 |title=Studies in the Origin of Harmonic Tonality
 |translator-first=Robert O. |translator-last=Gjerdingen
 |place=Princeton, NJ |publisher=Princeton University Press
 |isbn=0-691-09135-8
}}
* {{cite book
 |last=Duckworth |first=William |author-link=William Duckworth (composer)
 |year=2015
 |title=A Creative Approach to Music Fundamentals |edition=11th
 |series=Cengage Advantage Books
 |place=Stamford, CT |publisher=Engage Learning
 |isbn=978-1-285-44620-2
}}
* {{cite book
 |last=Everett |first=Walter
 |year=2000
 |section=Confessions from Blueberry Hell, or, pitch can be a sticky substance
 |title=Expression in Pop-Rock Music: A collection of critical and analytical essays
 |editor-first=Walter |editor-last=Everett
 |pages=269–346
 |place=New York, NY |publisher=Garland Publishing
 |isbn=0-8153-3160-6
}}
* {{cite book
 |ref={{harvid|Fétis|1844}}
 |last=Fétis |first=François-Joseph |author-link=François-Joseph Fétis
 |orig-year=1844, 1864 |year=2008
 |title=Traité complet de la théorie et de la pratique de l'harmonie contenant la doctrine de la science et de l'art
 |lang=fr
 |trans-title=Complete Treatise on the Theory and Practice of Harmony
 |edition=English
 |translator-first=Peter M. |translator-last=Landey
 |series=Harmonologia: Studies in Music Theory |volume=13
 |place=Hillsdale, NY  |publisher=Pendragon Press
 |isbn=978-1-57647-111-1
}} Brussels, BG: Conservatoire de Musique<br /> Paris, FR: Maurice Schlesinger
* {{cite book
 |last=Fétis |first=François-Joseph |author-link=François-Joseph Fétis
 |year=1864
 |title=Traité complet |edition=9th
 |place=Paris, FR |publisher=Brandus et Dufour
 |oclc=9892650 |url=https://archive.org/details/traitcompletde00ft
}} — for bibliographical information, see {{OCLC|9892650}}.
* {{cite book
 |last=Girdlestone |first=Cuthbert |author-link=Cuthbert Girdlestone
 |year=1969 |title=Jean-Philippe Rameau: His life and work
 |edition=revised and enlarged, reprint
 |place=New York, NY |publisher=Dover Publications
}}
* {{cite book
 |last=Hauptmann |first=M. |author-link=Moritz Hauptmann
 |year=1853
 |title=Die Natur der Harmonik und der Metrik |lang=de
 |trans-title=The Nature of Harmony and Metre
 |place=Leipzig, DE |publisher=Breitkopf und Härtel
}}
* {{cite book
 |last=von&nbsp;Helmholtz |first=Hermann |author-link=Hermann von Helmholtz
 |year=1877
 |title=Die Lehre von den Tonempfindungen als physiologische Grundlage für die Theorie der Musik
 |lang=de
 |trans-title=On the Sensations of Tone as a Physiological Basis for the Theory of Music
 |edition=4te
 |place=Braunschweig, DE |publisher=F. Vieweg
}}
:: expanded and published in English as
: {{cite book
 |last=von&nbsp;Helmholtz |first=Hermann             |author-link=Hermann von Helmholtz
 |editor-last=Ellis       |editor-first=Alexander J. |editor-link=Alexander J. Ellis
 |year=1954  |orig-year=1877, 1885
 |title=On the Sensations of Tone as a Physiological Basis for the Theory of Music
 |edition=reprinted 2nd English
 |quote=translated, thoroughly revised and corrected, rendered conformal to the 4th (and last) German ed. of 1877, with numerous additional notes and a new additional appendix bringing down information to 1885, and especially adapted to the use of music students
 |place=New York, NY |publisher=Dover Publications
 |others=Margenau, Henry (1954 introduction)
}}
* {{cite book
 |last=Hermelink |first=Siegfried
 |year=1960
 |title=Dispositiones modorum: die Tonarten in der Musik Palestrinas und seiner Zeitgenossen
 |series=Münchner Veröffentlichungen zur Musikgeschichte |volume=4
 |place=Tutzing, DE |publisher=Hans Schneider
}}
* {{cite book
 |last=Hindemith |first=Paul |author-link=Paul Hindemith
 |date=1937–1970
 |title=Unterweisung im Tonsatz |lang=de
 |trans-title=Instruction in Musical Composition
 |place=Mainz, DE |publisher=B. Schott's Söhne
}} 3&nbsp;vols.;
:: first two volumes translated and published as
: {{cite book
 |last=Hindemith |first=Paul |author-link=Paul Hindemith
 |orig-date=1937–1970 |date=1941–1942
 |title=The Craft of Musical Composition |lang=en
 |translator1-first=Arthur |translator1-last=Mendel
 |translator2-first=Otto   |translator2-last=Ortmann
 |place=New York, NY / London, UK
 |publisher=Associated Music Publishers (NY) / Schott (UK)
}}
* {{cite book
 |last=Hyer |first=Brian |year=2001a
 |section=Tonality
 |editor1-first=S. |editor1-last=Sadie   |editor1-link=Stanley Sadie
 |editor2-first=J. |editor2-last=Tyrrell |editor2-link=John Tyrrell (professor of music) 
 |title=The New Grove Dictionary of Music and Musicians  |edition=2nd
 |title-link=The New Grove Dictionary of Music and Musicians 
 |place=London, UK |publisher=Macmillan Publishers
 |isbn=978-1-56159-239-5  |postscript=none
}} (cloth); {{ISBN|978-0-333-60800-5}}; {{ISBN|978-0195170672}} (hc) 
* {{cite book
 |last=Hyer |first=Brian
 |year=2002b
 |section=Tonality
 |title=The Cambridge History of Western Music Theory
 |editor-first=Thomas |editor-last=Christensen
 |place=Cambridge, UK |publisher=Cambridge University Press
 |isbn=0-521-62371-5
 |pages=726–752
}} – mostly a reprint of {{harvp|Hyer|2001a}}, but with some essential edits 
* {{cite journal
 |last=Judd |first=Cristle Collins
 |year=1992
 |title=Modal types and "ut, re, mi" tonalities: Tonal coherence in sacred vocal polyphony from about 1500
 |journal=Journal of the American Musicological Society
 |volume=45 |issue=3
 |pages=428–467
|doi=10.2307/831714
 |jstor=831714
 }}
* {{cite book
 |last=Judd |first=Cristle Collins
 |year=1998a
 |title=Tonal Structures in Early Music
 |place=New York, NY / London, UK |publisher=Garland Publishing
 |isbn = 0-8153-2388-3
}}
* {{cite book
 |last=Judd |first=Cristle Collins
 |year=1998b
 |section=Introduction: Analyzing early music
 |title=Tonal Structures of Early Music
 |editor-first=Cristle Collins |editor-last=Judd
 |pages=3–13
 |place=New York, NY |publisher=Garland Publishing
 |isbn=0-8153-2388-3
}}
*  {{cite book
 |last=Judd |first=Cristle Collins
 |year=1998c
 |section=Josquin's gospel motets and chant-based tonality
 |title=Tonal Structures of Early Music
 |editor-first=Cristle Collins |editor-last=Judd
 |pages=3–13
 |place=New York, NY |publisher=Garland Publishing
 |isbn=0-8153-2388-3
}}
* {{wikicite|ref={{harvid|Kholopov}}|reference=[[Yuri Kholopov|Kholopov, Yuri]].{{Full citation needed|date=April 2018}}.}} 
* {{wikicite|ref={{harvid|Kopp|2011}}|reference=Kopp, David. 2011. "Chromaticism and the Question of Tonality. ''The Oxford Handbook of Neo-Riemannian Music Theories'', edited by Edward Gollin and Alexander Rehding, 400–418. Oxford and New York: Oxford University Press. {{ISBN|978-0-19-532133-3}}.}}
* {{cite book
 |last=Kostka |first=S.M. |author-link=Stefan Kostka
 |year=2013
 |title=Tonal Harmony: With an introduction to twentieth-century music |edition=7th
 |others=Payne, Dorothy & Almén, Byron
 |place=New York, NY |publisher=McGraw-Hill
 |oclc=812454417 |isbn=978-0-07-802514-3
 |pages=454–455
}}
* {{wikicite|ref={{harvid|Lefferts|1995}}|reference=Lefferts, Peter. 1995. "Signature-Systems and Tonal Types in the Fourteenth-Century French Chanson". ''Plainsong and Medieval Music'' 4:117–147.}}
* {{wikicite|ref={{harvid|Lowinsky|1962}}|reference=[[Edward Lowinsky|Lowinsky, Edward]]. 1962. ''Tonality and Atonality in Sixteenth-Century Music''. Berkeley and Los Angeles: University of California Press.}}<!--
* {{wikicite|ref={{harvid|Lyzhov}}|reference=Lyzhov.{{Full citation needed|date=April 2018}}.}} -->
* {{wikicite|ref={{harvid|Mangani and Sabaino|2008}}|reference=Mangani, Marco, and Daniele Sabaino. 2008. "Tonal Types and Modal Attribution in Late Renaissance Polyphony: New Observations". ''Acta Musicologica'' 80:231–250.}}
* {{wikicite|ref={{harvid|Mayfield|2013}}|reference=Mayfield, Connie. 2013. ''Theory Essentials'', second edition. Boston: Schirmer Cengage Learning.}}
* {{wikicite|ref={{harvid|Meyer|1967}}|reference=[[Leonard B. Meyer|Meyer, Leonard B.]] 1967. ''Music, the Arts, and Ideas: Patterns and Predictions in Twentieth-Century Culture''. Chicago and London: University of Chicago Press.}}
* {{wikicite|ref={{harvid|Moore|1995}}|reference=Moore, Allan F. 1995. "The So-called 'Flattened Seventh' in Rock". ''Popular Music'' 14, no. 2:185–201. Reprinted in Allan F. Moore, ''Critical Essays in Popular Musicology'', 283–300. Aldershot: Ashgate, 2007. {{ISBN|978-0-7546-2647-3}}.}}
* {{wikicite|ref={{harvid|Perle|1991}}|reference=[[George Perle|Perle, George]]. 1991. ''Serial Composition and Atonality: An Introduction to the Music of Schoenberg, Berg, and Webern'', sixth edition, revised. Berkeley and Los Angeles: University of California Press. {{ISBN|0-520-07430-0}}.}}
* {{cite journal
 |last=Pitt |first=David
 |year=1995
 |title=What is tonality?
 |journal=International Journal of Musicology
 |volume=4 |pages=291–300
 |quote=A Birthday Offering for George Perle (edited by Gary S. Karpinski)
 |url=http://web.calstatela.edu/faculty/dpitt/tonality.pdf
 |via=[[California State University, Los Angeles|Cal State LA]] (calstatela.edu)
}}
* {{cite journal
 |last=Powers |first=H.  |author-link=Harold Powers 
 |date=Autumn 1981
 |title=Tonal types and modal categories in Renaissance polyphony
 |journal=Journal of the American Musicological Society
 |volume=34 |issue=3 |pages=428–470
|doi=10.2307/831189 |jstor=831189 }}
* {{cite journal
 |last=Powers |first=H.  |author-link=Harold Powers 
 |year=1982
 |title=Modal representations in polyphonic offertories
 |journal=Early Music History
 |volume=2 |pages=43–86
|doi=10.1017/S0261127900002084 }}
* {{cite journal
 |last=Powers |first=H.  |author-link=Harold Powers 
 |year=1992
 |title=Is mode real? Pietro Aron, the octenary system and polyphony
 |journal=Basler Jahrbuch für historische Musikpraxis
 |volume=16 |pages=9–52
}}
* {{cite book
 |last=Powers |first=H.  |author-link=Harold Powers 
 |year=1996
 |section=Anomalous modalities
 |title=Orlando di Lasso in der Musikgeschichte
 |trans-title=Orlando di Lasso in Musical History
 |editor-first=Bernhold  |editor-last=Schmid
 |pages=221–242
 |place=Munich, DE  |publisher=Verlag der Bayerischen Akademie der Wissenschaften
}}
*  {{cite book
 |first1=Harold  |last1=Powers  |author1-link=Harold Powers 
 |first2=James       |last2=Cowdery     |first3=Ruth       |last3=Davis
 |first4=RuthStephen |last4=Jones       |first5=RuthAllan  |last5=Marett
 |first6=RuthMarc    |last6=Perlman     |first7=RuthJames  |last7=Porter
 |first8=RuthRichard |last8=Widdess     |first9=RuthFrans  |last9=Wiering
 |display-authors = 6
 |year=2001
 |section=Mode
 |editor1-first=S. |editor1-last=Sadie   |editor1-link=Stanley Sadie
 |editor2-first=J. |editor2-last=Tyrrell |editor2-link=John Tyrrell (professor of music) 
 |title=The New Grove Dictionary of Music and Musicians  |edition=2nd
 |title-link=The New Grove Dictionary of Music and Musicians 
 |place=London, UK |publisher=Macmillan Publishers
 |isbn=978-1-56159-239-5 |postscript=none
}} (cloth); {{ISBN|978-0-333-60800-5}}; {{ISBN|978-0195170672}} (hc) 
* {{cite conference
 |last1=Purwins    |first1=Hendrik
 |last2=Blankertz  |first2=Benjamin
 |last3=Obermayer  |first3=Klaus
 |year=2000
 |title=A new method for tracking modulations in tonal music in audio data format
 |conference=International Joint Conference on Neural Networks
 |volume=6  |pages=270–275
 |url=http://mtg.upf.edu/files/publications/Purwins_IJCNN_2000_ModulTrack.pdf
 |via=[[Universitat Pompeu Fabra]], Barcelona (upf.edu)
}}
* {{cite journal
 |last=Rais |first=Mark
 |year=1992
 |title=Jaan Soonvald and his musical system
 |journal=Leonardo Music Journal
 |volume=2 |issue=1 |pages=45–47
|doi=10.2307/1513209
 |jstor=1513209
 }}
* {{cite book
 |last=Reti |first=Rudolph |author-link=Rudolph Reti
 |year=1958
 |title=Tonality, Atonality, Pantonality: A study of some trends in twentieth century music
 |place=Westport, CT  |publisher=Greenwood Press
 |isbn=0-313-20478-0
}}
* {{cite journal
 |last=Riemann |first=Hugo  |author-link=Hugo Riemann
 |year=1872
 |title=Üeber Tonalität  |lang=de
 |trans-title=On tonality
 |journal=Neue Zeitschrift für Musik
 |volume=68 |pages=443–445, 451–454
}}
:: English translation published as
: {{cite journal
 |last=Riemann |first=Hugo  |author-link=Hugo Riemann
 |year=1985 |orig-year=1872
 |translator-last=McCune    |translator-first=Mark
 |title=Hugo Riemann's 'Ueber Tonalität': A translation
 |journal=Theoria |volume=1 |pages=132–150
}}
* {{cite journal
 |last=Riemann |first=Hugo  |author-link=Hugo Riemann
 |year=1875
 |title=Die objective Existenz der Untertöne in der Schallwelle  |lang=de
 |trans-title=The objective existence of the undertones in sound waves
 |journal=Allgemeine Musikzeitung
 |volume=2  |pages=205–206, 213–215
}}
* {{cite book
 |last=Riemann |first=Hugo  |author-link=Hugo Riemann
 |year=1882
 |title=Die Natur der Harmonik |lang=de
 |trans-title=The Nature of Harmony
 |series=Sammlung musikalischer Vorträge |volume=40
 |editor-first=Paul Graf |editor-last=Waldersee
 |place=Leipzig, DE  |publisher=Breitkopf und Härtel
}}
* {{cite book
 |last=Riemann |first=Hugo  |author-link=Hugo Riemann
 |orig-year=1893 |year=1903 
 |title=Vereinfachte Harmonielehre oder die Lehre von den tonalen Funktionen der Akkorde
 |trans-title=Harmony Simplified, or the Theory of the Tonal Functions of Chords
 |lang=de |edition=2nd
 |place=London, UK / New York, NY |publisher=Augener
}}
:: English translation published as
: {{cite book
 |last=Riemann |first=Hugo  |author-link=Hugo Riemann
 |orig-year=1893  |year=1895
 |title=Harmony Simplified, or the Theory of the Tonal Functions of Chords
 |place=London, UK  |publisher=Augener
}}
* {{cite journal
 |last=Riemann |first=Hugo  |author-link=Hugo Riemann
 |year=1905
 |title=Das Problem des harmonischen Dualismus |lang=de
 |trans-title=The problem of harmonic duality
 |journal=Neue Zeitschrift für Musik
 |volume=101 |pages=3–5, 23–26, 43–46, 67–70
}}
* {{cite book
 |last=Riemann |first=Hugo  |author-link=Hugo Riemann
 |year=1914–1915
 |section=Ideen zu einer 'Lehre von den Tonvorstellungen'  |lang=de
 |trans-section=Ideas towards a 'theory of tone concepts'
 |title=Jahrbuch der Musikbibliothek Peters 1914–15
 |trans-title=1914–1915 Yearbook of the Peters Music Library 
 |pages=1–26
}}
* {{wikicite|ref={{harvid|Rogers|2004}}|reference=Rogers, Michael R. 2004. ''Teaching Approaches in Music Theory: An Overview of Pedagogical Philosophies'', second edition. [Carbondale]: Southern Illinois University Press. {{ISBN|0-8093-1147-X}} (cloth); {{ISBN|0-8093-2595-0}} (pbk).}}
* {{wikicite|ref={{harvid|Schenker|1906–35}}|reference=[[Heinrich Schenker|Schenker, Heinrich]]. 1906–35. ''Neue musikalische Theorien und Phantasien''. 3 vols. in 4. Vienna and Leipzig: Universal Edition.}}
* {{cite book
 |last=Schoenberg |first=A.  |author-link=Arnold Schoenberg
 |year=1942
 |title=Models for Beginners in Composition
 |place=New York, NY |publisher=Schirmer
 |page=14
}} {{cite book
 |last=Schoenberg |first=A.  |author-link=Arnold Schoenberg
 |year=1950
 |title=Style and Idea
 |place=New York, NY |publisher=Philosophical Library
 |page=103
}}
* {{cite book
 |last=Schoenberg |first=A.  |author-link=Arnold Schoenberg
 |year=1922
 |title=Harmonielehre |lang=de |edition=3rd
 |trans-title=Harmony Lessons
 |place=Vienna, AU |publisher=Universal-Edition
}}
* {{wikicite|ref={{harvid|Schoenberg|1978}}|reference=Schoenberg, Arnold. 1978. ''Theory of Harmony'', translated by Roy E. Carter. Berkeley & Los Angeles: University of California Press. {{ISBN|0-520-03464-3}}. Reprinted 1983, {{ISBN|0-520-04945-4}}. Pbk ed. 1983, {{ISBN|0-520-04944-6}}.}}
* {{cite book
 |last1=Shepherd |first1=John
 |first2=Phil |last2=Virden
 |first3=Graham |last3=Vulliamy
 |first4=Trevor |last4=Wishart
 |orig-year=1977 |year=2008
 |title=Whose Music? A sociology of musical languages |edition=reprint
 |place=London, UK (1977) / Picataway, NJ (2008)
 |publisher=Latimer (1977) / Transaction Publishers (2008)
 |isbn = 978-0-87855-384-6
 |postscript=none
}} (cloth); {{ISBN|978-0-87855-815-5}} (pbk).
* {{cite thesis
 |last=Silberman |first=Peter Scott
 |year=2006
 |title=Neighbor Spaces: A theory of harmonic embellishment for twentieth-century neotonal music
 |degree=PhD 
 |place=Rochester, NY
 |publisher=[[University of Rochester]]
 |series=[[Eastman School of Music]]
}}
* {{cite journal
 |last=Simms |first=Bryan
 |date=Spring 1975
 |title=Choron, Fétis, and the theory of tonality
 |journal=Journal of Music Theory
 |volume=19 |issue=1 |pages=112–138
|doi=10.2307/843752
 |jstor=843752
 }}
* {{cite book
 |last1=Straus |first1=Joseph N.
 |year=2000
 |title=Introduction to Post-Tonal Theory |edition=2nd
 |place=Upper Saddle River, NJ |publisher=Prentice-Hall
 |isbn=0-13-014331-6
}}
* {{cite book
 |last1=Susanni     |first1=Paolo
 |last2=Antokoletz  |first2=Elliott
 |year=2012
 |title=Music and Twentieth-Century Tonality: Harmonic progression based on modality and the interval cycles
 |place=New York, NY / London, UK  |publisher=Routledge
 |isbn=978-0-415-80888-0 |postscript=none}} (cloth); {{ISBN|978-1-136-31421-6}} (ebook); {{ISBN|978-0-203-11929-7}} (ebook)
* {{cite book
 |last=Tagg |first=Philip |author-link=Philip Tagg
 |year=2003
 |section=Harmony
 |volume=Part&nbsp;1 Performance and production
 |editor1-first=John  |editor1-last=Shepherd
 |editor2-first=David |editor2-last=Horn
 |editor3-first=Dave  |editor3-last=Laing
 |editor4-first=Paul  |editor4-last=Oliver
 |editor5-first=Peter |editor5-last=Wicke  |editor5-link=Peter Wicke
 |title=Continuum Encyclopedia of Popular Music of the World
 |place=London, UK / New York, NY |publisher={{nobr|A & C Black}}
 |isbn=978-1-84714-472-0
}}
* {{wikicite|ref={{harvid|Terefenko|2014}}|reference=Terefenko, Dariusz. 2014. ''Jazz Theory: From Basic to Advanced Study''. New York: Routledge. {{ISBN|978-0-415-53759-9}} (cloth); {{ISBN|978-0-415-53761-2}} (pbk); {{ISBN|978-0-203-38000-0}} (ebook).}}
* {{cite book
 |last1=Wangermée |first1=Robert
 |last2=Ellis     |first2=Katherine  |author2-link=Katharine Ellis
 |year=2001
 |section=Fétis: (1) François-Joseph Fétis
 |editor1-first=S. |editor1-last=Sadie   |editor1-link=Stanley Sadie
 |editor2-first=J. |editor2-last=Tyrrell |editor2-link=John Tyrrell (professor of music) 
 |title=The New Grove Dictionary of Music and Musicians  |edition=2nd
 |title-link=The New Grove Dictionary of Music and Musicians 
 |place=London, UK |publisher=Macmillan Publishers
 |isbn=978-1-56159-239-5  |postscript=none
}} (cloth); {{ISBN|978-0-333-60800-5}}; {{ISBN|978-0195170672}} (hc) 
* {{cite book
 |last1=White |first1=Eric Walter
 |year=1979
 |title=Stravinsky: The composer and his works |edition=2nd
 |place=Berkeley, CA / Los Angeles, CA |publisher=The University of California Press
 |isbn=0-520-03985-8
}}
* {{cite book
 |last1=Wörner     |first1=Felix
 |last2=Scheideler |first2=Ulrich
 |last3=Rupprecht  |first3=Philip Ernst
 |year=2012
 |section=Introduction
 |editor1-last=Wörner     |editor1-first=Felix
 |editor2-last=Scheideler |editor2-first=Ulrich
 |editor3-last=Rupprecht  |editor3-first=Philip Ernst
 |title=Tonality 1900–1950: Concept and practice
 |pages=11–24
 |series=Musikwissenschaft
 |place=Stuttgart, DE |publisher=Steiner Verlag
 |isbn=978-3-515-10160-8
}}
{{refend}}

== Further reading ==
{{refbegin|25em|small=yes}}
* {{wikicite|ref={{harvid|Alembert|1752}}|reference=[[Jean le Rond d'Alembert|Alembert, Jean le Rond d']]. 1752. ''{{lang|fr|Elémens de musique, theorique et pratique, suivant les principes de m. Rameau}}''. Paris: David l'aîné. Facsimile reprint, New York: Broude Bros., 1966. Translated by {{harvp|Marpurg|1757}} }}
* Benjamin, Thomas. 2003. ''The Craft of Tonal Counterpoint, with Examples from the Music of Johann Sebastian Bach'', 2nd edition. New York: Routledge. {{ISBN|0-415-94391-4}}.
* [[Stephen Blum|Blum, Stephen]]. 2006. "Navā'i: A Musical Genre of Northeastern Iran". In ''Analytical Studies in World Music'', edited by [[Michael Tenzer]], 41–57. Oxford and New York: Oxford University Press. {{ISBN|978-0-19-517788-6}} (cloth); {{ISBN|978-0-19-517789-3}} (pbk)
* [[Castil-Blaze]]. 1821. ''{{lang|fr|Dictionnaire de musique moderne}}''. Paris: Au magazin de musique de la Lyre moderne.
* Cohn, Richard. 2012. ''Audacious Euphony: Chromatic Harmony and the Triad's Second Nature''. Oxford Studies in Music Theory. Oxford and New York: Oxford University Press. {{ISBN|978-0-19-977269-8}}.
* DeVoto, Mark. 2004. ''Debussy and the Veil of Tonality: Essays on His Music''. Dimension and Diversity: Studies in 20th-century Music 4. N.p.: Pendragon Press. {{ISBN|1-57647-090-3}}.
* [[Alfred Einstein|Einstein, Alfred]]. 1954. ''A Short History of Music'', fourth American edition, revised. New York: Vintage Books.
* Gustin, Molly. 1969. ''Tonality''. New York: Philosophical Library. {{LCCN|68018735}}.
* [[Lou Harrison|Harrison, Lou]]. 1992. "Entune." ''Contemporary Music Review'' 6, no. 2:9–10.
* Janata, Petr, Jeffery L. Birk, John D. Van Horn, Marc Leman, Barbara Tillmann, and Jamshed J. Bharucha. 2002. "The Cortical Topography of Tonal Structures Underlying Western Music." ''Science'' 298, no. 5601 (December 13): 2167–2170.
* [[Johannes Kepler|Kepler, Johannes]]. 1619. ''Harmonices mundi'' [Latin: The Harmony of the World]. Linz: Godofredo Tampechi.
* Kilmer, Anne Draffkorn, Richard L. Crocker, and Robert R. Brown. 1976. ''Sounds from Silence, Recent Discoveries in Ancient Near Eastern Music''. LP sound recording, 33⅓ rpm, 12&nbsp;inch, with bibliography (23 p. ill.) laid in container. [n.p.]: Bit Enki Records. LCC#75-750773 /R.
* Manuel, Peter. 2006. "Flamenco in Focus: An Analysis of a Performance of Soleares". In ''Analytical Studies in World Music'', edited by Michael Tenzer, 92–119. Oxford and New York: Oxford University Press. {{ISBN|978-0-19-517788-6}} (cloth); {{ISBN|978-0-19-517789-3}} (pbk)
* [[Friedrich Wilhelm Marpurg|Marpurg, Friedrich Wilhelm]]. 1753–1754. ''Abhandlung von der Fuge nach dem Grundsätzen der besten deutschen und ausländischen Meister''. 2 vols. Berlin: A. Haude, und J. C. Spener.
* {{wikicite|ref={{harvid|Marpurg|1757}}|reference=Marpurg, Friedrich Wilhelm. 1757. ''Systematische Einleitung in die musikalische Setzkunst, nach den Lehrsätzen des Herrn Rameau'', Leipzig: J. G. I. Breitkopf. Translation of {{harvp|Alembert|1752}}}}
* [[George Perle|Perle, George]]. 1978. ''Twelve-Tone Tonality''. Berkeley and Los Angeles: University of California Press. {{ISBN|978-0-520-03387-0}} (first edition reprinted 1996, {{ISBN|0-520-20142-6}}; second edition 1995, {{ISBN|978-0-520-20142-2}}).
* [[Henry Pleasants (music critic)|Pleasants, Henry]]. 1955 ''The Agony of Modern Music''. New York: Simon & Schuster. LCC#54-12361.
* {{cite book |author-link=Jean-Philippe Rameau |last=Rameau |first=J-P |year=1722 |title=Traité de l'harmonie réduite à ses principes naturels |place=Paris, FR |publisher=Ballard |url=https://books.google.com/books?id=kM85AAAAIAAJ }}
* Rameau, Jean-Philippe. 1726. ''Nouveau Systême de Musique Theorique, où l'on découvre le Principe de toutes les Regles necessaires à la Pratique, Pour servir d'Introduction au Traité de l'Harmonie''. Paris: L'Imprimerie de Jean-Baptiste-Christophe Ballard.
* Rameau, Jean-Philippe. 1737. ''Génération harmonique, ou Traité de musique théorique et pratique''. Paris: Prault fils.
* Rameau, Jean-Philippe. 1750. ''Démonstration du Principe de L'Harmonie, Servant de base à tout l'Art Musical théorique et pratique''. Paris: Durand et Pissot.
* Reichert, Georg. 1962. "Tonart und Tonalität in der älteren Musik". ''Musikalische Zeitfragen'', edited by [[Walter Wiora]], 10. Kassel: Bärenreiter Verlag, pp.&nbsp;97–104.<!--check 'Walter Wiora' in MGG 1, 'Schriftenreihen' in the last section of this article; this is not just 'a book', it is a Schriftenreihe, that is ''periodical''; see [http://www.worldcat.org/oclc/611817836] -->
* [[Miguel Roig-Francolí|Roig-Francolí, Miguel A.]] 2008. ''Understanding Post-Tonal Music''. New York: McGraw-Hill. {{ISBN|0-07-293624-X}}.
* [[Jim Samson|Samson, Jim]]. 1977. ''Music in Transition: A Study of Tonal Expansion and Atonality, 1900–1920''. New York: W. W. Norton. {{ISBN|0-393-02193-9}}. Samson suggests the following discussions of tonality as defined by Fétis, Helmholtz, Riemann, D'Indy, Adler, Yasser, and others:
** Beswick, Delbert M. 1950. "The Problem of Tonality in Seventeenth Century Music". Ph.D. thesis. Chapel Hill: University of North Carolina. p.&nbsp;1–29. {{OCLC|12778863}}.
** Shirlaw, Matthew. 1917. ''The Theory of Harmony: An Inquiry into the Natural Principles of Harmony; with an Examination of the Chief Systems of Harmony from Rameau to the Present Day''. London: Novello. (Reprinted New York: Da Capo Press, 1969. {{ISBN|0-306-71658-5}}.)
* Rings, Steven. 2011. ''Tonality and Transformation''. Oxford Studies in Music Theory. Oxford and New York: Oxford University Press. {{ISBN|978-0-19-538427-7}}.
* [[Glenn Schellenberg|Schellenberg, E. Glenn]], and [[Sandra Trehub|Sandra E. Trehub]]. 1996. "Natural Musical Intervals: Evidence from Infant Listeners" ''[[Psychological Science]]'', vol. 7, no. 5 (September): 272–277.
* [[Heinrich Schenker|Schenker, Heinrich]]. 1954. ''Harmony'', edited and annotated by [[Oswald Jonas]]; translated by [[Elisabeth Mann-Borgese]]. Chicago: University of Chicago Press. {{oclc|280916}}. Translation of ''Neue musikalische Theorien und Phantasien'' 1: ''Harmonielehre''. (Reprinted Cambridge, Massachusetts: MIT Press, 1973, {{ISBN|0-262-69044-6}}.)
* Schenker, Heinrich. 1979. ''Free Composition'', translated and edited by Ernst Oster. New York: Longman. Translation of ''Neue musikalische Theorien und Phantasien'' 3: ''Der freie Satz''. {{ISBN|0-582-28073-7}}.{{Full citation needed|date=February 2014|reason=Place, publisher, and year of this German edition needed. Presumably the ISBN is false, since for German books ISBNs begin with a 3.}}
* Schenker, Heinrich. 1987. ''Counterpoint'', translated by John Rothgeb and Jürgen Thym; edited by John Rothgeb. 2 vols. New York: Schirmer Books; London: Collier Macmillan. Translation of ''Neue musikalische Theorien und Phantasien'' 2: ''Kontrapunkt''. {{ISBN|0-02-873220-0}}.
* Stegemann, Benedikt. 2013. ''Theory of Tonality'', translated by David LeClair. Theoretical Studies. Wilhelmshaven: Noetzel. {{ISBN|978-3-7959-0963-5}}.
* [[William Ennis Thomson|Thomson, William]]. 1999. ''Tonality in Music: A General Theory''. San Marino, California: Everett Books. {{ISBN|0-940459-19-1}}.
* [[Dmitri Tymoczko|Tymoczko, Dmitri]]. 2011. ''A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice''. Oxford Studies in Music Theory. Oxford and New York: Oxford University Press. {{ISBN|978-0-19-533667-2}}.
* [[Martin Litchfield West|West, Martin Litchfield]]. 1994. "The Babylonian Musical Notation and the Hurrian Melodic Texts". ''[[Music & Letters]]'' 75, no. 2 (May): 161–179.
{{refend}}

== External links ==
{{Wikiquote}}
* {{cite web |title=Key signatures, part&nbsp;1 |department=Tonal music fundamentals |website=BigComposer.com |type=lecture notes |url=http://www.bigcomposer.com/module/lectures/keysignatures1.pdf }}
* {{cite web |last=Kelly |first=Robert, Ph.D. |title=Reference materials for the undergraduate theory student |department=Tonal harmony |website=RobertKelleyPhd.com |url=http://www.robertkelleyphd.com/tonalharmony.htm }}
* {{cite web |title=Tonality, modality, and atonality |website=SolomonsMusic.net |url=http://solomonsmusic.net/tonality.htm |url-status=dead <!-- presumed --> |archive-url=https://web.archive.org/web/20071115223321/http://solomonsmusic.net/tonality.htm |archive-date=2007-11-15 }}
* {{cite web |title=Reference guide to tonal music |website=TonalityGUIDE.com |url=http://www.tonalityguide.com/index.php }}
* {{cite web |title=Main page |website=Tonalcentre.org |url=http://www.tonalcentre.org/ }} — website has explanations and demonstrations of some of the key concepts of tonality
* {{cite web |title=Algebra of tonal functions |website=Sonantometry.blogspot.com |url=http://sonantometry.blogspot.com/2007_05_01_archive.html }}
* {{cite web |title=A model of analysis for tonal harmonic discourse |website=BW.Musique.UMontreal.ca |publisher=[[University of Montreal]] |place=Montreal, CA |url=http://bw.musique.umontreal.ca/nm/index-en.html }}

{{Tonality}}
{{Timbre}}
{{Authority control}}

[[Category:Tonality| ]]
[[Category:Harmony]]
[[Category:Music theory]]