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<h2 id="secondary-dominant">Secondary dominant</h2> <p class="note">"V/V" redirects here. For other uses, see <a href="/facts/VV_(disambiguation)/mF4Blekm">VV (disambiguation)</a>.</p> <p>A secondary dominant (also applied dominant, artificial dominant, or borrowed dominant) is a major <a href="/facts/Triad_(music)/YIA2T6Y6">triad</a> or dominant <a href="/facts/Seventh_chord/XeWsnNrL">seventh chord</a> built and set to <a href="/facts/Resolution_(music)/5TLIIqFV">resolve</a> to a <a href="/facts/Degree_(music)/XooEJJya">scale degree</a> other than the <a href="/facts/Tonic_(music)/3YWh9zFV">tonic</a>. The dominant (seventh) of the dominant (written as V7/V or V7 of V) is the most frequently encountered.<a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a> The chord that the secondary dominant is the dominant of is said to be a temporarily <i><a href="/facts/Tonicized_chord/g61Tq6Ig">tonicized chord</a></i>. The secondary dominant is normally, though not always, followed by the tonicized chord. Tonicizations that last longer than a <a href="/facts/Phrase_(music)/bteKoAt6">phrase</a> are generally regarded as <a href="/facts/Modulation_(music)/qF2kCACj">modulations</a> to a new key (or new tonic). </p><p>According to music theorists David Beach and Ryan C. McClelland, "[t]he purpose of the secondary dominant is to place emphasis on a chord within the diatonic progression."<a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a> The secondary-dominant terminology is still usually applied even if the chord resolution is <a href="/facts/Diatonic_function/t3ekowqY">nonfunctional</a>. For example, the V/ii label is still used even if the V/ii chord is not followed by ii.<a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a> </p> <h3>Definition</h3> <p>The <a href="/facts/Major_scale/WtnkhIgv">major scale</a> contains seven basic chords, which are named with <a href="/facts/Roman_numeral_analysis/rwtlhyNE">Roman numeral analysis</a> in ascending order. Because tonic triads are either major or minor, one would not expect to find diminished chords (either the viio in major or the iio in minor) tonicized by a secondary dominant.<a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a> It would also not make sense for the tonic of the key itself to be tonicized. </p><p>In the <a href="/facts/Key_(music)/jo4UMbHp">key</a> of C major, the five remaining chords are: </p> Audio playback is not supported in your browser. You can download the audio file. <p>Of these chords, the V chord (G major) is said to be the <a href="/facts/Dominant_(music)/g5sd8AHg">dominant</a> of C major. However, each of the chords from ii to vi also has its own dominant. For example, V (G major) has a D major triad as its dominant. These extra dominant chords are not part of the key of C major as such because they include notes that are not part of the C major scale. Instead, they are secondary dominants. </p><p>The notation below shows the secondary-dominant chords for C major. Each chord is accompanied by its standard number in harmonic notation. In this notation, a secondary dominant is usually labeled with the formula "V of ..." (dominant chord of); thus "V of ii" stands for the dominant of the ii chord, "V of iii" for the dominant of iii, and so on. A shorter notation, used below, is "V/ii", "V/iii", etc. </p> Audio playback is not supported in your browser. You can download the audio file. <p>Like most chords, secondary dominants may be <a href="/facts/Seventh_chord/XeWsnNrL">seventh chords</a> or chords with other upper <a href="/facts/Extended_chord/83h8ttwM">extensions</a>.<a class="footnote-ref" id="fnref:7" href="#fn:7"><sup>7</sup></a> <a href="/facts/Dominant_seventh_chord/E4EIVqmN">Dominant seventh chords</a> are commonly used as secondary dominants. The notation below shows the same secondary dominants as above but with dominant seventh chords. </p> Audio playback is not supported in your browser. You can download the audio file. <p>Note that the triad V/IV is the same as the I triad. When a <a href="/facts/Seventh_(chord)/1qzl63F9">seventh</a> is added (V7/IV), it becomes an altered chord because the seventh is not a diatonic pitch. <a href="/facts/Ludwig_van_Beethoven/eusBgBkA">Beethoven</a>'s <a href="/facts/Symphony_No._1_(Beethoven)/0528cdGU">Symphony No. 1</a> begins with a V7/IV chord:<a class="footnote-ref" id="fnref:8" href="#fn:8"><sup>8</sup></a> </p> Audio playback is not supported in your browser. You can download the audio file. <p>According to the principles exposed above, in fact, V7/IV, which means the C7 chord, i.e. the dominant seventh chord on the <a href="/facts/F_major/hSP9tBgs">F major scale</a> (C–E–G–B♭), does not represent the tonic because it contains a B♭, which isn't included in the main key, as Beethoven's Symphony No. 1 is written in the key of C major. The chord then resolves on the natural IV (<a href="/facts/F_major/hSP9tBgs">F major</a>) and in the following bar the V7, i.e. G7 (dominant seventh chord on the C major key), is presented. </p><p><a href="/facts/Chromatic_mediant/fbjbyhcH">Chromatic mediants</a>, for example VI is also a secondary dominant of ii (V/ii) and III is V/vi, are distinguished from secondary dominants with context and <a href="/facts/Musical_analysis/tq9UuN1V">analysis</a> revealing the distinction.<a class="footnote-ref" id="fnref:9" href="#fn:9"><sup>9</sup></a> </p> <h3>History</h3> <p>Before the 20th century, in the music of <a href="/facts/Johann_Sebastian_Bach/qA71yhEb">J.S. Bach</a>, <a href="/facts/Wolfgang_Amadeus_Mozart/2X5fm67T">Mozart</a>, <a href="/facts/Ludwig_van_Beethoven/eusBgBkA">Beethoven</a>, and <a href="/facts/Johannes_Brahms/wr1Qo5Jh">Brahms</a>, a secondary dominant, along with its chord of resolution, was considered a modulation. Since this was a rather self-contradictory description, theorists in the early 1900s, such as <a href="/facts/Hugo_Riemann/KmtMxEcw">Hugo Riemann</a> (who used the term "Zwischendominante"—"intermediary dominant", still the usual German term for a secondary dominant), searched for a better description of the phenomenon. </p><p><a href="/facts/Walter_Piston/JxnN7KXQ">Walter Piston</a> first used the analysis "V7 of IV" in a monograph entitled <i>Principles of Harmonic Analysis</i>.<a class="footnote-ref" id="fnref:10" href="#fn:10"><sup>10</sup></a><a class="footnote-ref" id="fnref:11" href="#fn:11"><sup>11</sup></a> In his 1941 book <i>Harmony</i>, Piston used the term "secondary dominant".<a class="footnote-ref" id="fnref:12" href="#fn:12"><sup>12</sup></a> At around the same time (1946–48), <a href="/facts/Arnold_Schoenberg/o9xuyDwC">Arnold Schoenberg</a> created the expression "artificial dominant" to describe the same phenomenon, in his posthumously published book <i>Structural Functions of Harmony</i>.<a class="footnote-ref" id="fnref:13" href="#fn:13"><sup>13</sup></a> </p><p>In the fifth edition of Walter Piston's <i>Harmony</i>, a passage from the last movement of <a href="/facts/Wolfgang_Amadeus_Mozart/2X5fm67T">Mozart</a>'s <a href="/facts/Piano_Sonata_No._5_(Mozart)/58rCpYQv">Piano Sonata K. 283 in G major</a> serves as one illustration of secondary dominants.<a class="footnote-ref" id="fnref:14" href="#fn:14"><sup>14</sup></a> This passage has three secondary dominants. The final four chords form a <a href="/facts/Circle_of_fifths/0aE2lkVq">circle of fifths</a> progression, ending in a standard dominant-tonic <a href="/facts/Cadence_(music)/9AuxqJD4">cadence</a>, which concludes the <a href="/facts/Phrase_(music)/bteKoAt6">phrase</a>. </p> Audio playback is not supported in your browser. You can download the audio file. <h3>In jazz and popular music</h3> <p>In <a href="/facts/Jazz_harmony/FrQyspN3">jazz harmony</a>, a secondary dominant is any dominant seventh chord on a weak beat and resolves downward by a perfect fifth. Thus, a chord is a secondary dominant when it functions as the dominant of some harmonic element other than the key's tonic and resolves to that element. This is slightly different from the traditional use of the term, where a secondary dominant does not have to be a seventh chord, occur on a weak beat, or resolve downward. If a non-diatonic dominant chord is used on a strong beat, it is considered an extended dominant. If it doesn't resolve downward, it may be a <a href="/facts/Borrowed_chord/CbRg43yg">borrowed chord</a>. </p><p>Secondary dominants are used in jazz harmony in the <a href="/facts/Bebop_blues/NPuEjsWL">bebop blues</a> and other <a href="/facts/Twelve-bar_blues/NPuEjsWL">blues progression</a> variations, as are <a href="/facts/Substitute_dominant/hb06rvQF">substitute dominants</a> and <a href="/facts/Turnaround_(music)/fmFJwyol">turnarounds</a>.<a class="footnote-ref" id="fnref:15" href="#fn:15"><sup>15</sup></a> In some jazz tunes, all or almost all of the chords that are used are dominant chords. For example, in the standard jazz chord progression <a href="/facts/Ii%25E2%2580%2593V%25E2%2580%2593I_progression/WNMC6mjp">ii–V–I</a>, which would normally be Dm–G7–C in the key of C major, some tunes will use D7–G7–C7. Since jazz tunes are often based on the circle of fifths, this creates long sequences of secondary dominants. </p><p>Secondary dominants are also used in popular music. Examples include II7 (V7/V) in <a href="/facts/Bob_Dylan/WcaUqWBj">Bob Dylan</a>'s "<a href="/facts/Don%2527t_Think_Twice%2c_It%2527s_All_Right/sxCLQdoT">Don't Think Twice, It's All Right</a>" and III7 (V7/vi) in <a href="/facts/Betty_Everett/86DXH1BG">Betty Everett</a>'s "<a href="/facts/The_Shoop_Shoop_Song_(It%2527s_in_His_Kiss)/nejsgb8Q">The Shoop Shoop Song (It's in His Kiss)</a>".<a class="footnote-ref" id="fnref:16" href="#fn:16"><sup>16</sup></a> "<a href="/facts/Has_Anybody_Seen_My_Gal%253F_(song)/z2aoAeXG">Five Foot Two, Eyes of Blue</a>" features chains of secondary dominants.<a class="footnote-ref" id="fnref:17" href="#fn:17"><sup>17</sup></a> "<a href="/facts/Sweet_Georgia_Brown/6Ak72hRp">Sweet Georgia Brown</a>" opens with V/V/V–V/V–V–I. Playⓘ </p> <h3>Extended dominant</h3> <p class="note">For a chord with extensions past the seventh, see <a href="/facts/Extended_chord/83h8ttwM">Extended chord</a>.</p> <p>An extended dominant chord is a secondary dominant seventh chord that <a href="/facts/Resolution_(music)/5TLIIqFV">resolves</a> down by a fifth to another dominant seventh chord. A series of extended dominant chords continues to resolve downwards by the circle of fifths until it reaches the <a href="/facts/Tonic_chord/3YWh9zFV">tonic chord</a>. The most common extended dominant chord is the tertiary dominant, which resolves to a secondary dominant. For example, V/V/V (in C major, A(7)) resolves to V/V (D(7)), which resolves to V (G(7)), which resolves to I. Note that V/V/V is the same chord as V/ii, but differs in its resolution to a major dominant rather than a minor chord. </p><p>Quaternary dominants are rarer, but an example is the bridge section of the <a href="/facts/Rhythm_changes/CFa82SR8">rhythm changes</a>, which starts from V/V/V/V (in C major, E(7)). The example below from <a href="/facts/Fr%25C3%25A9d%25C3%25A9ric_Chopin/xWo0soVB">Chopin</a>'s <a href="/facts/Polonaises%2c_Op._26_(Chopin)/QxVLLaqu">Polonaises, Op. 26</a>, No. 1 (1835)<a class="footnote-ref" id="fnref:18" href="#fn:18"><sup>18</sup></a> has a quaternary dominant in the second beat (V/ii = V/V/V, V/vi = V/V/V/V). </p> Audio playback is not supported in your browser. You can download the audio file. <h2 id="secondary-leading-tone">Secondary leading-tone</h2> <p>In <a href="/facts/Music_theory/BoekvflP">music theory</a>, a secondary leading-tone chord is a secondary chord that is <a href="/facts/Root_(chord)/BzI7uzCG">rooted</a> on a tone that is a <a href="/facts/Leading-tone/oqelFQoq">leading-tone</a> of (in short, has a strong affinity to <a href="/facts/Resolution_(music)/5TLIIqFV">resolve</a> to) a tone just 1 semitone from that root (typically 1 semitone above, though <a href="/facts/Leading-tone/oqelFQoq">can be below</a>).<a class="footnote-ref" id="fnref:19" href="#fn:19"><sup>19</sup></a> Like the secondary dominant it can be used as <a href="/facts/Tonicization/g61Tq6Ig">tonicization</a> of only one subsequent chord (which will be rooted in the resolution tone), or the music can continue with other chords/notes in the key of that chord's root for a phrase, or even longer to be considered a <a href="/facts/Modulation_(music)/qF2kCACj">modulation</a> to that key. This one-semitone-apart resolution of the secondary <i>leading-tone</i> is in contrast to the secondary <i>dominant</i> which <a href="/facts/Resolution_(music)/5TLIIqFV">resolves</a> through a wider distance of perfect fifth below or perfect fourth above the chord's root (as per the two distances between <a href="/facts/Dominant_(music)/g5sd8AHg">dominant</a> and tonic). </p><p>While the root of a secondary leading-tone chord needs to be the leading-tone, the other notes may vary and form with it one of: the <a href="/facts/Leading-tone/oqelFQoq">triad</a><a class="footnote-ref" id="fnref:20" href="#fn:20"><sup>20</sup></a> or one of the <a href="/facts/Leading-tone_seventh_chord/oqelFQoq">diminished sevenths</a> (as in seventh <a href="/facts/Degree_(music)/XooEJJya">scale degree</a><a class="footnote-ref" id="fnref:21" href="#fn:21"><sup>21</sup></a> or <a href="/facts/Leading-tone/oqelFQoq">leading-tone</a>, not necessarily seventh chord) where the type of the diminished seventh is typically related to the type of tonicized triad: </p> <ol><li>If the tonicized triad is minor, the leading-tone chord is fully diminished seventh chord.</li> <li>If it is major, the leading-tone chord may be either half-diminished or fully diminished, though fully diminished chords are used more often.<a class="footnote-ref" id="fnref:22" href="#fn:22"><sup>22</sup></a></li></ol> <p>Because of their symmetry, secondary leading-tone diminished seventh chords are also useful for <a href="/facts/Modulation_(music)/qF2kCACj">modulation</a>; all four notes may be considered the <a href="/facts/Root_(chord)/BzI7uzCG">root</a> of any diminished seventh chord. They may <a href="/facts/Resolution_(music)/5TLIIqFV">resolve</a> to these <a href="/facts/Major_chord/RwuuqKYS">major</a> or <a href="/facts/Minor_chord/XdLGImHS">minor</a> diatonic triads:<a class="footnote-ref" id="fnref:23" href="#fn:23"><sup>23</sup></a> </p> In <a href="/facts/Major_key/jo4UMbHp">major keys</a>: <a href="/facts/Supertonic/yrYUUqyS">ii</a>, <a href="/facts/Mediant/KjHgHP56">iii</a>, <a href="/facts/Subdominant/0lfRwEfa">IV</a>, V, <a href="/facts/Submediant/hLhXdzfM">vi</a> In <a href="/facts/Minor_key/KCv5M0yN">minor keys</a>: III, iv, V, VI <p>Especially in <a href="/facts/Four-part_harmony/9EjpzxvW">four-part writing</a>, the <a href="/facts/Seventh_(chord)/1qzl63F9">seventh</a> should resolve downwards by <a href="/facts/Steps_and_skips/Q6jCFRnB">step</a> and if possible the lower <a href="/facts/Tritone/fH2JqArb">tritone</a> should resolve appropriately, inwards if a <a href="/facts/Diminished_fifth/fH2JqArb">diminished fifth</a> and outwards if an <a href="/facts/Augmented_Fourth/fH2JqArb">augmented fourth</a>,<a class="footnote-ref" id="fnref:24" href="#fn:24"><sup>24</sup></a> as the example below<a class="footnote-ref" id="fnref:25" href="#fn:25"><sup>25</sup></a> shows. </p> Audio playback is not supported in your browser. You can download the audio file. <p>Secondary leading-tone chords were not used until the <a href="/facts/Baroque_music/UgrJnyTq">Baroque period</a> and are found more frequently and less conventionally in the <a href="/facts/Classical_period_(music)/HhEDbzVX">Classical period</a>. They are found even more frequently and freely in the <a href="/facts/Romantic_period_(music)/Smlk40jm">Romantic period</a>, but they began to be used less frequently with the breakdown of conventional harmony. </p><p>The chord progression viio7/V–V–I is quite common in <a href="/facts/Ragtime/hP0L6Jgr">ragtime</a> music.<a class="footnote-ref" id="fnref:26" href="#fn:26"><sup>26</sup></a> </p> <h2 id="secondary-supertonic">Secondary supertonic</h2> <p>The secondary supertonic chord, or secondary second, is a secondary chord that is on the <a href="/facts/Supertonic/yrYUUqyS">supertonic</a> <a href="/facts/Degree_(music)/XooEJJya">scale degree</a>. Rather than <a href="/facts/Tonicization/g61Tq6Ig">tonicizing</a> a degree other than the <a href="/facts/Tonic_(music)/3YWh9zFV">tonic</a>, as does a secondary dominant, it creates a temporary dominant.<a class="footnote-ref" id="fnref:27" href="#fn:27"><sup>27</sup></a> Examples include ii7/III (F♯min.7, in C major), ii7/II (Amin.7, in F major), ii7/V (Emin.7, in G major), and ii7/IV (Bmin.7, in E major).<a class="footnote-ref" id="fnref:28" href="#fn:28"><sup>28</sup></a> </p> <h2 id="secondary-subdominant">Secondary subdominant</h2> <p>The secondary subdominant is the <a href="/facts/Subdominant/0lfRwEfa">subdominant</a> (IV) of the tonicized chord. For example, in G major, the supertonic chord is A minor and the IV of ii chord is D major. </p> <h2 id="others">Others</h2> <p>The other secondary functions are the secondary mediant, the secondary submediant, and the secondary subtonic. </p> <h2 id="see-also">See also</h2> <ul><li><a href="/facts/Barbershop_seventh_chord/PcKKGkTp">Barbershop seventh chord</a> – A major triad plus the harmonic seventh intervalPages displaying short descriptions of redirect targets</li> <li><a href="/facts/Backdoor_progression/CEGS9et9">Backdoor progression</a> – Jazz chord progression</li> <li><a href="/facts/Circle_progression/BW2UVyYT">Circle progression</a> – Type of chord progressionPages displaying short descriptions of redirect targets</li> <li><a href="/facts/Common-tone_diminished_seventh_chord/BsyETryS">Common-tone diminished seventh chord</a> – Musical chordPages displaying short descriptions of redirect targets</li> <li><a href="/facts/Ii%25E2%2580%2593V%25E2%2580%2593I_progression/WNMC6mjp">ii–V–I progression</a> – Common chord progression</li> <li><a href="/facts/Secondary_development/eI5Xb0dK">Secondary development</a> – Section in some classical musical works</li> <li><a href="/facts/Subtonic/nA0NBIkR">Subtonic</a> – the lowered or minor seventh degree of the scale, a whole step below the tonic and a half step below the leadingPages displaying wikidata descriptions as a fallback</li></ul> <h2 id="notes">Notes</h2> <h2 id="bibliography">Bibliography</h2> <ul><li>Beach, David; McClelland, Ryan C. (2012). <i>Analysis of 18th- and 19th-century Musical Works in the Classical Tradition</i>. Routledge. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 9780415806657.</li> <li>Benward, Bruce; Saker, Marilyn Nadine (2003). <a href="https://archive.org/details/musicintheorypra0001benw_b9i1"><i>Music: In Theory and Practice</i></a>. Vol. I (7th ed.). McGraw-Hill. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-07-294262-0.</li> <li>Blatter, Alfred (2007). <i>Revisiting Music Theory: A Guide to the Practice</i>. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-415-97440-2.</li> <li>Boyd, Bill (1997). <i>Jazz Chord Progressions</i>. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-7935-7038-7.</li> <li>Everett, Walter (2009). <a href="https://archive.org/details/foundationsofroc0000ever"><i>The Foundations of Rock</i></a>. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-19-531023-8.</li> <li>Kostka, Stefan; Payne, Dorothy (2004). <a href="https://archive.org/details/tonalharmonywith0000kost"><i>Tonal Harmony</i></a> (5th ed.). Boston: McGraw-Hill. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0072852607. <a href="/facts/OCLC_(identifier)/Yqad8waq">OCLC</a> <a href="https://search.worldcat.org/oclc/51613969">51613969</a>.</li> <li>Ottman, Robert W. (1992) [1961]. <a href="https://archive.org/details/advancedharmonyt00ottm"><i>Advanced Harmony: Theory and Practice</i></a> (4th ed.). Englewood Cliffs, NJ: <a href="/facts/Prentice_Hall/bynWAuat">Prentice Hall</a>. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-13-006016-X.</li> <li><a href="/facts/Walter_Piston/JxnN7KXQ">Piston, Walter</a> (1933). <a href="https://archive.org/details/principlesofharm0000walt_i7h6"><i>Principles of Harmonic Analysis</i></a>. Boston: E. C. Schirmer. [ISBN unspecified]</li> <li><a href="/facts/Walter_Piston/JxnN7KXQ">Piston, Walter</a> (1941). <i>Harmony</i>. New York: W. W. Norton & Company, Inc. [ISBN unspecified]</li> <li><a href="/facts/Walter_Piston/JxnN7KXQ">Piston, Walter</a> (1987) [First published 1941]. <a href="https://archive.org/details/harmony0000pist_l8w3"><i>Harmony</i></a>. Revised and expanded by Mark Devoto (5th ed.). New York: W. W. Norton & Company, Inc. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-393-95480-7.</li> <li>Rawlins, Robert; Bahha, Nor Eddine (2005). <a href="https://archive.org/details/jazzologyencyclo0000rawl"><i>Jazzology: The Encyclopedia of Jazz Theory for All Musicians</i></a>. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-634-08678-2.</li> <li>Lawn, Richard; Hellmer, Jeffrey L. (1996). <i>Jazz: Theory and Practice</i>. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-88284-722-1.</li> <li><a href="/facts/William_Russo_(musician)/aCYmsjMQ">Russo, William</a> (2015) [1961]. <i>Composing for the Jazz Orchestra</i>. University of Chicago. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-226-73209-1.</li> <li><a href="/facts/Arnold_Schoenberg/o9xuyDwC">Schoenberg, Arnold</a> (1954). <a href="/facts/Humphrey_Searle/SYLJUSoC">Searle, Humphrey</a> (ed.). <i>Structural Functions of Harmony</i>. New York: W. W. Norton & Company, Inc.</li> <li>Shepherd, John (2003). <i>Continuum Encyclopedia of Popular Music of the World</i>. Vol. II: Performance and Production. <a href="/facts/A%2526C_Black/1DDWvrln">A&C Black</a>. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 9780826463227.</li> <li>Spitzer, Peter (2001). <i>Jazz Theory Handbook</i>. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-7866-5328-0.</li> <li>White, John D. (1976). <a href="https://archive.org/details/analysisofmusic00whit"><i>The Analysis of Music</i></a>. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-13-033233-X.</li></ul> <h2 id="further-reading">Further reading</h2> <ul><li>Nettles, Barrie & Graf, Richard (1997). <i>The Chord Scale Theory and Jazz Harmony</i>. Advance Music, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 3-89221-056-X</li> <li>Thompson, David M. (1980). <i>A History of Harmonic Theory in the United States</i>. Kent, Ohio: The Kent State University Press.</li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>Kostka & Payne 2004, p. 246. - Kostka, Stefan; Payne, Dorothy (2004). Tonal Harmony (5th ed.). Boston: McGraw-Hill. ISBN 0072852607. OCLC 51613969. <a href="https://archive.org/details/tonalharmonywith0000kost" target="_blank">https://archive.org/details/tonalharmonywith0000kost</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Benward & Saker 2003, pp. 273–277. - Benward, Bruce; Saker, Marilyn Nadine (2003). Music: In Theory and Practice. Vol. I (7th ed.). McGraw-Hill. ISBN 978-0-07-294262-0. <a href="https://archive.org/details/musicintheorypra0001benw_b9i1" target="_blank">https://archive.org/details/musicintheorypra0001benw_b9i1</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>Kostka & Payne 2004, p. 250. - Kostka, Stefan; Payne, Dorothy (2004). Tonal Harmony (5th ed.). Boston: McGraw-Hill. ISBN 0072852607. OCLC 51613969. <a href="https://archive.org/details/tonalharmonywith0000kost" target="_blank">https://archive.org/details/tonalharmonywith0000kost</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>Beach & McClelland 2012, p. 32. - Beach, David; McClelland, Ryan C. (2012). Analysis of 18th- and 19th-century Musical Works in the Classical Tradition. Routledge. ISBN 9780415806657. <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> <li id="fn:5"><p>Rawlins & Bahha 2005, p. 59. - Rawlins, Robert; Bahha, Nor Eddine (2005). Jazzology: The Encyclopedia of Jazz Theory for All Musicians. ISBN 0-634-08678-2. <a href="https://archive.org/details/jazzologyencyclo0000rawl" target="_blank">https://archive.org/details/jazzologyencyclo0000rawl</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li> <li id="fn:6"><p>Kostka & Payne 2004, p. 246. - Kostka, Stefan; Payne, Dorothy (2004). Tonal Harmony (5th ed.). Boston: McGraw-Hill. ISBN 0072852607. OCLC 51613969. <a href="https://archive.org/details/tonalharmonywith0000kost" target="_blank">https://archive.org/details/tonalharmonywith0000kost</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li> <li id="fn:7"><p>For example, Ottman 1992, p. 308 discusses secondary dominant ninth chords, such as V9/V. - Ottman, Robert W. (1992) [1961]. Advanced Harmony: Theory and Practice (4th ed.). Englewood Cliffs, NJ: Prentice Hall. ISBN 0-13-006016-X. <a href="https://archive.org/details/advancedharmonyt00ottm" target="_blank">https://archive.org/details/advancedharmonyt00ottm</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li> <li id="fn:8"><p>White 1976, p. 5. - White, John D. (1976). The Analysis of Music. ISBN 0-13-033233-X. <a href="https://archive.org/details/analysisofmusic00whit" target="_blank">https://archive.org/details/analysisofmusic00whit</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></p></li> <li id="fn:9"><p>Benward & Saker 2003, pp. 201–204. - Benward, Bruce; Saker, Marilyn Nadine (2003). Music: In Theory and Practice. Vol. I (7th ed.). McGraw-Hill. ISBN 978-0-07-294262-0. <a href="https://archive.org/details/musicintheorypra0001benw_b9i1" target="_blank">https://archive.org/details/musicintheorypra0001benw_b9i1</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></p></li> <li id="fn:10"><p>Piston 1933. - Piston, Walter (1933). Principles of Harmonic Analysis. Boston: E. C. Schirmer. <a href="https://archive.org/details/principlesofharm0000walt_i7h6" target="_blank">https://archive.org/details/principlesofharm0000walt_i7h6</a> <a href="#fnref:10" class="footnote-back-ref">↩</a></p></li> <li id="fn:11"><p>Notably, Piston's analytical symbol always used the word "of"—e.g. "V7 of IV" rather than the virgule V7/IV. <a href="/wiki/Slash_chord" target="_blank">/wiki/Slash_chord</a> <a href="#fnref:11" class="footnote-back-ref">↩</a></p></li> <li id="fn:12"><p>Piston 1941, p. 151: "These temporary dominant chords have been referred to by theorists as attendant chords, parenthesis chords, borrowed chords, etc. We shall call them secondary dominants, in the belief that the term is slightly more descriptive of their function." - Piston, Walter (1941). Harmony. New York: W. W. Norton & Company, Inc. <a href="#fnref:12" class="footnote-back-ref">↩</a></p></li> <li id="fn:13"><p>Schoenberg 1954, pp. 15–29, 197. The term "artificial", however, appears to refer to the alteration by which a chord changes into another: "By substituting for [altering] the third in minor triads, they produce 'artificial' major triads and 'artificial' dominant seventh chords. Substituting for [altering] the fifth changes minor triads to 'artificial' diminished triads, commonly used with an added seventh, and changes major triads to augmented. Artificial dominants, artificial dominant seventh chords, and artificial diminished seventh chords are normally used in progressions according to the models V–I, V—VI and V—IV. (p. 16.) - Schoenberg, Arnold (1954). Searle, Humphrey (ed.). Structural Functions of Harmony. New York: W. W. Norton & Company, Inc. <a href="#fnref:13" class="footnote-back-ref">↩</a></p></li> <li id="fn:14"><p>Piston 1987, p. 257. - Piston, Walter (1987) [First published 1941]. Harmony. Revised and expanded by Mark Devoto (5th ed.). New York: W. W. Norton & Company, Inc. ISBN 978-0-393-95480-7. <a href="https://archive.org/details/harmony0000pist_l8w3" target="_blank">https://archive.org/details/harmony0000pist_l8w3</a> <a href="#fnref:14" class="footnote-back-ref">↩</a></p></li> <li id="fn:15"><p>Spitzer 2001, p. 62. - Spitzer, Peter (2001). Jazz Theory Handbook. ISBN 0-7866-5328-0. <a href="#fnref:15" class="footnote-back-ref">↩</a></p></li> <li id="fn:16"><p>Everett 2009, p. 198. Everett notates major-minor sevenths Xm7. - Everett, Walter (2009). The Foundations of Rock. ISBN 978-0-19-531023-8. <a href="https://archive.org/details/foundationsofroc0000ever" target="_blank">https://archive.org/details/foundationsofroc0000ever</a> <a href="#fnref:16" class="footnote-back-ref">↩</a></p></li> <li id="fn:17"><p>Shepherd 2003, p. 10. - Shepherd, John (2003). Continuum Encyclopedia of Popular Music of the World. Vol. II: Performance and Production. A&C Black. ISBN 9780826463227. <a href="#fnref:17" class="footnote-back-ref">↩</a></p></li> <li id="fn:18"><p>Benward & Saker 2003, p. 276. - Benward, Bruce; Saker, Marilyn Nadine (2003). Music: In Theory and Practice. Vol. I (7th ed.). McGraw-Hill. ISBN 978-0-07-294262-0. <a href="https://archive.org/details/musicintheorypra0001benw_b9i1" target="_blank">https://archive.org/details/musicintheorypra0001benw_b9i1</a> <a href="#fnref:18" class="footnote-back-ref">↩</a></p></li> <li id="fn:19"><p>Benward & Saker 2003, p. 271. - Benward, Bruce; Saker, Marilyn Nadine (2003). Music: In Theory and Practice. Vol. I (7th ed.). McGraw-Hill. ISBN 978-0-07-294262-0. <a href="https://archive.org/details/musicintheorypra0001benw_b9i1" target="_blank">https://archive.org/details/musicintheorypra0001benw_b9i1</a> <a href="#fnref:19" class="footnote-back-ref">↩</a></p></li> <li id="fn:20"><p>Blatter 2007, pp. 132–133. - Blatter, Alfred (2007). Revisiting Music Theory: A Guide to the Practice. ISBN 0-415-97440-2. <a href="#fnref:20" class="footnote-back-ref">↩</a></p></li> <li id="fn:21"><p>Blatter 2007, pp. 132–133. - Blatter, Alfred (2007). Revisiting Music Theory: A Guide to the Practice. ISBN 0-415-97440-2. <a href="#fnref:21" class="footnote-back-ref">↩</a></p></li> <li id="fn:22"><p>Kostka & Payne 2004, p. 263. - Kostka, Stefan; Payne, Dorothy (2004). Tonal Harmony (5th ed.). Boston: McGraw-Hill. ISBN 0072852607. OCLC 51613969. <a href="https://archive.org/details/tonalharmonywith0000kost" target="_blank">https://archive.org/details/tonalharmonywith0000kost</a> <a href="#fnref:22" class="footnote-back-ref">↩</a></p></li> <li id="fn:23"><p>Benward & Saker 2003, p. 271. - Benward, Bruce; Saker, Marilyn Nadine (2003). Music: In Theory and Practice. Vol. I (7th ed.). McGraw-Hill. ISBN 978-0-07-294262-0. <a href="https://archive.org/details/musicintheorypra0001benw_b9i1" target="_blank">https://archive.org/details/musicintheorypra0001benw_b9i1</a> <a href="#fnref:23" class="footnote-back-ref">↩</a></p></li> <li id="fn:24"><p>Benward & Saker 2003, p. 272. - Benward, Bruce; Saker, Marilyn Nadine (2003). Music: In Theory and Practice. Vol. I (7th ed.). McGraw-Hill. ISBN 978-0-07-294262-0. <a href="https://archive.org/details/musicintheorypra0001benw_b9i1" target="_blank">https://archive.org/details/musicintheorypra0001benw_b9i1</a> <a href="#fnref:24" class="footnote-back-ref">↩</a></p></li> <li id="fn:25"><p>Benward & Saker 2003, p. 270. - Benward, Bruce; Saker, Marilyn Nadine (2003). Music: In Theory and Practice. Vol. I (7th ed.). McGraw-Hill. ISBN 978-0-07-294262-0. <a href="https://archive.org/details/musicintheorypra0001benw_b9i1" target="_blank">https://archive.org/details/musicintheorypra0001benw_b9i1</a> <a href="#fnref:25" class="footnote-back-ref">↩</a></p></li> <li id="fn:26"><p>Benward & Saker 2003, p. 271. - Benward, Bruce; Saker, Marilyn Nadine (2003). Music: In Theory and Practice. Vol. I (7th ed.). McGraw-Hill. ISBN 978-0-07-294262-0. <a href="https://archive.org/details/musicintheorypra0001benw_b9i1" target="_blank">https://archive.org/details/musicintheorypra0001benw_b9i1</a> <a href="#fnref:26" class="footnote-back-ref">↩</a></p></li> <li id="fn:27"><p>Blatter 2007, pp. 132–133. - Blatter, Alfred (2007). Revisiting Music Theory: A Guide to the Practice. ISBN 0-415-97440-2. <a href="#fnref:27" class="footnote-back-ref">↩</a></p></li> <li id="fn:28"><p>Russo 2015, p. 80. - Russo, William (2015) [1961]. Composing for the Jazz Orchestra. University of Chicago. ISBN 978-0-226-73209-1. <a href="#fnref:28" class="footnote-back-ref">↩</a></p></li> </ol>