Talk:Quartal and quintal harmony

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Rating[edit]

I have had to assess this as C only. Aside from the overabundance of musical examples, there is also a great deal of irrelevent material (or material that appears to be, at least):

...in [...] the Sinfonia no.9 there is an extreme density of imitation (very often at the interval of a fourth)... - I'm not convinced that imitation at the fourth counts as "quartal harmony" per se and if it does why the merely parenthetical "very often" and the unexplained example?

The subject of the fugue of the third movement of Beethoven's Piano sonata op. 110 opens with three ascending fourths (A♭ -> D♭ - B♭ -> E♭ - C -> F)... - That usage is melodic not harmonic: the harmony is clearly tertian.

...a connection between Richard Wagner's so-called Liebestod-Melody (Love-Death) from the second act of the opera Tristan und Isolde and Webern's work. Both works set in the leap of a fourth (E♭ - A♭) two semitones downwards (A♭ - G - G♭). - Again the Wagner usage is melodic, though, as I recall, the Tristan chord is quartal to a degree and is not actually mentioned!

All these sections (and others) are actually very well expressed and could be used in an article on "Quartal Melody" (if that is a real term!). Or the context needs to be better explained: "While composers avoided 4th chords in the Baroque, Classical and Early Romantic periods, they did use 4ths melodically and this usage often infomed the underlying harmonies." Or some such.

Any other thoughts? --Jubilee♫clipman 17:31, 20 November 2009 (UTC)

Addendum - This older comment makes the same point. --Jubilee♫clipman 17:36, 20 November 2009 (UTC)

Hm, I just re-read the lead: ...quartal harmony is the building of chordal and melodic structures with a distinct preference for intervals of fourths. - Harmony is based on the simultaneous sounding of notes in different parts, ie chords. Melody is a different concept based on the temporal relationship of the notes within one particular part. This statement in the lead is obviously the genesis of all the melodic discussion (!) found later. If the term really does include melody, then this needs to be clearly explained and sourced. However, the "Introduction" states: Harmony is that part of music theory concerned with the properties of simultaneously sounding tones. This contradicts the lead. There really is a lot of work to be done here... --Jubilee♫clipman 18:20, 20 November 2009 (UTC)

Further thoughts (From thoughs I sent to another user's talk page) - The article appears to have multiple issues which go way beyond the overabundance of musical examples. While the quality of writing, of itself, is excellent, the actual content appears to be full of inconsistencies and irrelevancies. As I understand it, Quartal Harmony relates to harmony that is based on fourths; the article discusses melody and uses Beethoven's 0p.110, Bach's Inventions and other music written in "Tertian Harmony" as examples of what might be called "Quartal Melody", to coin a phrase. Many of the musical examples are related to that; indeed the article itself contrasts Quartal and Tertian. I'm not even sure if Perotin's fourths and fifths are relevant here, since he mainly uses them in a melodic sense and only between two parts (the third part being a drone). In the sense I understand it, Quartal Harmony was first fully explored by Scriabin based on harmonic ideas he found in Liszt and Wagner (the Tristan chord, for example). It has been exploited ever since by Modernists and Postmodernists. If am right, then the article is full of errors and badly in need of an overhaul. Furthermore, the article is mainly a direct translation of the German page (accomplished by Rainwarrior) as it stood in 2006 - and as it still stands for the most part... Both articles appear to have been accepted as correct for all that time: for that reason I am reluctant to edit it yet. Maybe Quartal Harmony really does include melody? Two minds...! --Jubilee♫clipman 20:16, 21 November 2009 (UTC)

<copied over from Contemporary Music project talk page>The Perotin example needs to go. The harmonic intervals of the time are measured against the tenor (the drone). Perotin and esp. the substitute discant clausulae of the time could be used as examples of quartal harmony at times (as could the earliest parallel organum), but this example is totally wrong. -- Myke Cuthbert (talk) 10:09, 22 November 2009 (UTC)
That's just as I thought: the Notre Dame School did use a sort of proto-quartal technique at times, but the given example does not actually appear to show this. How about the purely melodic examples from Mozart, Beethoven, Wagner etc? And is all the discussion of Bach's "thick contrapuntal writing" using imitation at the fourth and fifth relevent? --Jubilee♫clipman 15:47, 22 November 2009 (UTC)
I think calling it proto-quartal is over stating it. The earliest organum seems to have been in parallel fourths with parallel fifths less common. Fifths quickly became the dominant intervallic force in the last century of the first millennium. By c. 1300 (maybe a bit before; we often put the date too late) the fifths began more and more commonly to be filled by thirds, though true tertial harmony (the idea that stacked thirds are both stable and better than 6-3 sonorities) will have to wait until the second half of the 15th century; and one could say that the seventh creates the first real tertial harmony as opposed to just the triad, so that's what, 1620? (A baroque specialist will know for sure). So to call Perotin proto-quartal is like calling a fish a proto-dolphin -- there's a lot of unrelated intermediate steps along the way.
Btw -- I disagree with the assessment at "C" though: despite some errors, there is a strong argument throughout and not just a bunch of facts. It covers a large swath of history, including non-classical repertories. I think unlike most Wikipedia theory entries which have too few, there are the right number of musical examples (maybe not formatted as well as they could be); compare with other music encyclopedias. The quotes from Hindemith are very important and relevant. Even though to get to GA or FA the article might have to be rewritten from scratch, as it is, it seems better than many if not most classical music "B" articles.
One note: in my reading, Quintal harmony is not considered indistinct from quartal harmony because it is the inversion of the fourth; rather it has seldom been used by composers, perhaps because both the interval is too wide and it has too many tonal implications; for instance, a quintal "triad" is likely to be heard as a ninth-chord with missing 3rd. But Schoenberg's Op. 19 no. 6 is a good example of true quintal harmony). Thanks for all the work, Jubilee, Rainwarrior, and our German colleagues! -- Myke Cuthbert (talk) 01:04, 23 November 2009 (UTC)
"...like calling a fish a proto-dolphin..." - I like it! Actually, you are right that Perotin is not really even proto-quartal: that's my point. Why is he there at all? Why is Beethoven there? Or Wagner? These examples do not relate to "Harmony" in the accepted sense. Perotin's fourths are more often a filling out of the melody, just as an orchestrator might use oboes in parallel thirds. The Beethoven has nothing at all to do with harmony. Worst of all, the Wagner example - ironically - discusses the melody of the Liebestod and fails to examine the all-important Tristan chord (F♮-B♮-D♯-G♯) which actually is "Proto-Quartal" (two fourths juxtaposed). The article cannot be assessed as B-class while these non-examples exist and pertinent examples are missed. (I'll get back to you on "Quintal" - though, FWIW, I think you may be right.)--Jubilee♫clipman 01:38, 23 November 2009 (UTC)

I think I'll have to be bold soon and delete all the material that has nothing to do with harmony, including most of the middle section of the article (Perotin, Renaisance, Baroque, Bach, Mozart, Beethoven, Wagner), and add things that I think have been missed out (eg the Tristan chord). I'll wait another week or so though (but draft things in my sandboxes). --Jubilee♫clipman 04:30, 24 November 2009 (UTC) BTW, our project will probably drop C-class, so this has to go down one for now... --Jubilee♫clipman 04:33, 24 November 2009 (UTC)

Started editing[edit]

I've started the editing process on this article. For the most part I will restrict the edits to the mirror on my user subpage: User:Jubileeclipman/(mirror) Quartal and quintal harmony. I've also created a "shadow" copy of the article prior to my edits: User:Jubileeclipman/(shadow) Quartal and quintal harmony. Several less objectionable edits will be made live to this article itself, where these either tidy up the language or (in the case of the lead) come closer to modern scholarship and terminology. For example, the word "harmony" now tends to be used of music built on chords of three or more notes rather than of "diadic" music, as it were, ie that built on chords of only two notes. Furthermore, because of its modern connotations, the term, though used in the Middle Ages and Renaissance, seems to be an anachronism when used to describe Renaissance polyphony - especially when we try to talk about "Renaissance triadic harmony" or the like. Feel free to comment on my non-live edits on my talk page: User talk:Jubileeclipman. I won't submit these edits to the article itself until: a) I have finished them; and b) any objections are responded to and acted upon. Thank you for your understanding. --Jubilee♫clipman 00:13, 2 December 2009 (UTC)

This is going to be a nightmare... A lot of the statements need to be verified but none of the the translated material has been sourced from English texts. Worse the vast majority of the book list is in German, which most of us do not read! Even worse, the books are not cited in the text, but simply plonked at the bottom as further reading. For example: "Quartal chord sounds have a somewhat "erratic" function, in that they have a tendency to forget which key they are in." Do they? Who pointed this out? Does anyone disagree with this? Etc... I feel I might simply have to purge unverified statements like that when the time comes to purge the stuff I highlighted above (ie the non-harmonic stuff), unless anyone can help source it. We'll see.

Moreover, the translation, has produced some odd phrasing which I have had to clarify. There is also a huge section at the top explaining guitar chords and other tertian usage, but I can't yet see any point to these being there. Maybe I'll move them to the relevent articles. In fact, I might just do that with all the purged material: some of it is insightful and therefore useful to someone, but it is not helpful here. Eek... quite a challenge! --Jubilee♫clipman 02:18, 2 December 2009 (UTC)

Finished basics[edit]

Any objection to replacing the text of the present article with the text of User:Jubileeclipman/(mirror) Quartal and quintal harmony? I have removed several sections and placed them in User:Jubileeclipman/(removed) Quartal and quintal harmony. Indeed the last three on that page have been incorporated into their respective articles and so have not been lost. There are several other major changes, mainly as regards the actual usage of the word "quartal" and the implications of that usage. One cannot truly call Perotin's music "quartal" nor even Wagner's for that matter. I have also included a section on the Tristan chord in my version of the article. I have also made the usage of US/UK english consistant in favour of UK (which was more used anyway, I think). I feel the US usage of "tone" is ambiguous in a musical context that discusses harmony and have put a note (!) in the intro to explain this. Any thoughts welcome before I dump the text over... --Jubilee♫clipman 22:52, 2 December 2009 (UTC)

You might consider disambiguating these terms:
YesY Done and removed excess. Dabbed "sixth" with major sixth and minor sixth; also, rmved over use of wikied "cadence", which solved that one; rmved the POV stuff about Josquin anyway...--Jubilee♫clipman 00:27, 4 December 2009 (UTC)
I would also recommend to use the canonical spelling of all composers mentioned in the article, e.g. Béla Bartók instead of Bela Bartok, Josquin des Prez instead of Josquin Des Prez, Johann Fux instead of Johann Joseph Fux, etc., or piped links for cases like Orlando Lasso. -- Michael Bednarek (talk) 03:35, 3 December 2009 (UTC)
YesY Done the ones I've found so far. --Jubilee♫clipman 00:27, 4 December 2009 (UTC)
You should use the "music" template for accidentals so that the sharps and flats render on all browsers. ({{music|sharp}}) and ({{music|flat}}) instead of ♯ and ♭.DavidRF (talk) 04:52, 3 December 2009 (UTC)
YesY Done all sharps and flats; and added the natural to avoid ambiguity in certain places (possibly more to find). --Jubilee♫clipman 00:41, 4 December 2009 (UTC)
Thanks guys! Those are critical - and often subtly hidden - sylistic and technical aspects that certainly need cleanup! (BTW, there is also {{music|natural}}, which needs to be used, too. instead of ♮ - I wondered why some people used those...) I'll sort all those points out and resubmit. Any more? Also, is my text closer to the actual subject, having been purged of the melodic uses - or should that stuff be put back in? Does "quartal harmony" really cover melody, in other words? What about all that stuff about "a Procrustean bed" and so on? Is that not a bit OR, or at least POV? How can that section be rewritten? Any thing else in the content that needs to be redone? Thanks for the input! --Jubilee♫clipman 23:11, 3 December 2009 (UTC)

Dumping my text over[edit]

4 days and no further comments, so it is time to be bold. I will try to explain the basic rationale in the edit summary. I will also add inline wiki-comments to highlight remaining deficiences in the text. OK, here goes.... --Jubilee♫clipman 00:39, 7 December 2009 (UTC)

All done. I'll go through and add the tags later, but I've added a couple of general ones ("more footnotes" and "original research") already. I've also decided to remove all the stuff about chord symbols (they are not used enough for the massive blurb and the main article on chord notation explains anyway if anyone really wants to know), and I've removed my gloss about "notes" and "tones" (most people know about this). The inversion stuff is explained far better in its main article and there is an inline wiki pointing there. I've added all the removed stuff to this talk page, below. --Jubilee♫clipman 01:27, 7 December 2009 (UTC)

PS, please comment below at Comments on edited page. Thanks. --Jubilee♫clipman 03:27, 7 December 2009 (UTC)

Removed material[edit]

Removed from introduction as explained above[edit]

As the text appeared prior to my edit:

The interval concept refers to the pitch-distance between two successively or simultaneously sounding tones. Under inversion one finds those intervals which together make up an octave; a third inverts to a sixth. The term descending fourth (or descending fifth, third, etc.) is used for intervals displaced into the octave below. A rising fifth C - G, for example, inverts to the descending fourth G - C.

In this article, Chord symbols will have a capital letter for the Fundamental or Tonic, which indicates a major third and fifth above forming a Major Triad. The addition of m stands for Minor, in which a minor instead of a major third sounds against the tonic. Also, with the addition add, extra tones at a specified distance from the tonic sound. In C6 or C(add6) appear the tones C - E - G - A. C7 refers to a C-major chord with an additional Minor seventh, having the tones C - E - G - B♭. This chord functions in classical tonality as the Dominant seventh chord.

The addition maj7 (an abbreviation of major seventh) extends the triad with an additional Major seventh. Both seventh chords can be even further extended with a major Ninth, written as C9 or Cmaj9, respectively. The abbreviation sus4 (suspended fourth, a Suspended chord) indicates that the expected third in a stable major or minor triad is replaced by a fourth instead. In modern music this chord is often used in a distinct way so it can also stand for itself and not function as an altered triad.

As the text appeared after my edit (removed after I dumped the text):

When "inverting" intervals, one finds those intervals which together make up an octave: for example, a major third inverts to a minor sixth because the two combine to make an octave (Conversely, the minor third inverts to a major sixth: see the article on musical inversion for a detailed explanation.) Note that in effect, the second note of the rising perfect fifth C-G, can be put into the lower octave to describe a descending perfect fourth; because the note G is not exactly at the center of the octave C-C, the distance from the lower C to the G is not the same distance as that going from the higher C to the same G. The thirds and sixths invert this way too, as do the seconds and sevenths. This is another way of looking at inversion and explains the usage of the word (upward inverts to downward).

In this article, where tertian harmony is discussed, chord symbols utilise a simple capital letter for the root of a major triad, which has a major third and perfect fifth above the root. The addition of m to the capital letter stands for minor, which has a minor third and perfect fifth above the root. Also, the addition of numbers (with or without maj, add or sus) indicates extra notes at specified distances from the root. A particular case in point is the abbreviation sus4 (suspended fourth, a Suspended chord) which indicates that the expected third in a stable major or minor triad is replaced by a fourth. In modern music, however, this chord is often used in a distinct way, standing for itself and not functioning as an "altered" triad.

Note and tone

It should be mentioned that the words "note" and "tone" are used in different countries to refer to the same concept: a unique and identified pitch. However, because the word "tone" also means "two semitones", the word "note" is preferred in this article for the specific meaning defined in the previous sentence. Hence the expression "five-note chord" is used rather than the more ambiguous "five-tone chord". The word "tone" is always used in the other sense; hence we have "wholetone scale", "tritone" and "meantone temperament"

Not sure how to deal with these next few[edit]

This has no real relevence as it stands[edit]

For instance, in this Alleluia (Loudspeaker.svgListen) by Pérotin, the fourth is favoured. This example from the score shows that the interval of a fourth constitutes over fifteen percent of the interval relationships.

Use of fourths in Pérotin's Alleluia

I agree. To look at lines in this style, which is not really harmonic music, for this context is a reach and kind of muddies the waters. J Civil 04:27, 2 February 2013 (UTC) — Preceding unsigned comment added by Jan civil (talkcontribs)

POV and relates to melody anyway[edit]

In Josquin Des Prez's 1515 Mass Missa Pange Lingua Loudspeaker.svgListen) or the two-part Domine, dominus noster it [ie the harmony] still feels sparse. Ascending and descending lines in the individual parts of the following example outline a fourth interval with their range.

Extract from Benedictus from Missa Pange Lingua by Josquin Des Prez

This one is too general to include anywhere and would probably be unwelcome at "JS Bach" (also, the translation of the quote is wrong: spiel means play not mirror)[edit]

This older style of counterpoint was often overlaid with a fully formed tonality in the works of the High Baroque. In the Cruxifixus of Johann Sebastian Bach's Mass in B Minor the intervals of the ascending fourth and descending fifth are thoroughly emphasized. His keyboard works, such as the Fugue No.22 in the first book of the Well-Tempered Clavier or the Sinfonia no.9 (Loudspeaker.svgListen) there is an extreme density of imitation (very often at the interval of a fourth) with such great care taken to maintain coherent harmony that Paul Hindemith would refer to Bach's counterpoint as a "harmony preserving carnival-mirror" („wahres harmonische Vexierspiel“) in his teachings.

Opening measures of J.S.Bachs Sinfonia in F-minor, BWV 795

This one is actually wrong (the chords are simple octaves with a fourth added not "quartal triads")[edit]

In the fourth piece from the first book of Debussy's Préludes, Les sons et les parfums tournent dans l'air du soir (Fr: Sounds and Perfumes Stir in the Evening Air), triadic fourth chords in the right hand over "normal" four-note chords in the left hand (Loudspeaker.svgListen).

Measures 28 und 29 from Claude Debussy's Préludes Book 1, No. 4, Les sons et les parfums tournent dans l`air du soir

(UTC)

Melody again[edit]

The Freiburg musicologist Christian Berger pointed out in his writing Atonality and Tradition - Webern's Four Pieces for Violin and Piano op. 7 („Atonalität und Tradition – Anton Weberns Vier Stücke für Geige und Klavier op. 7“) a connection between Wagner's so-called Liebestod-Melody (Love-Death) from the second act of the opera Tristan und Isolde and Webern's work. Both works set in the leap of a fourth (E - A) two semitones downwards (A - G - G). The target of this descending line becomes a starting point for the next upward fourth (G - C), and this procedure is repeated many times. In Webern's use of this device, Berger found eight consecutive fourths set in this way.

Excerpt from the 2nd Act of Richard Wagner's Opera Tristan und Isolde

These have been added to their respective articles (except the strikethrough)[edit]

Added to String Quartet No. 19 (Mozart):

Mozart in his so-called Dissonance Quartet KV 465 (Loudspeaker.svgListen) used Chromatic and Whole tone scales to outline fourths. Arch shaped lines emphasizing fourths in the first Violin (C - F - C) and the Violoncello (G - C - C' - G') are combined with lines emphasizing fifths in the second Violin and Viola. Over the barline between the second and third measures of the example a fourth-suspension can be seen in the second violin's tied C. In another of his String quartets, KV 464, such fourth-suspensions are also very prominent.

Measures 11 to 17 from the first movement of Mozart's String Quartet KV 465

Added to Piano Sonata No. 31 (Beethoven):

Examples of the tonal language are often taken from classical String quartets and Piano music, as in these compositions all of the elements and problems of tonality occur just as in larger works, but the simplicity of instrumentation makes them easier to see. The subject of the fugue of the third movement of Beethoven's Piano sonata op. 110 (Loudspeaker.svgListen) opens with three ascending fourths (A♭ -> D♭ - B♭ -> E♭ - C -> F) and them downwards in gestures outlining fourths (i.e. F - E♭ - D♭ - C). This counterpoint has two themes working together to highlight the fourth.

Opening of the fugue from the third movement of Beethoven's Piano Sonate Op. 110

Added to String Quartet No. 15 (Beethoven):

To begin the second movement of his String Quartet in A Minor op. 132 (Loudspeaker.svgListen) Beethoven exposes the fourth in a three note gesture (G♯ - A - C♯) four times, with all instruments playing in unison. In measure 5 this motive is combined with an inverted variation (outlining a descending fifth) in mixed rhythm.

Opening of the second movement of Beethoven's String Quartet in A-Minor op. 132

--Jubilee♫clipman 01:27, 7 December 2009 (UTC)


Moved to perfect fourth[edit]

I went ahead and moved stuff over to perfect fourth. That is becoming a good article now, coincidently! --Jubilee♫clipman 22:56, 7 December 2009 (UTC)

Moved text[edit]

Short history of the fourth

The use of perfect fourths and fifths to sound in parallel with and to "thicken" the melodic line was prevalent in music prior to the European polyphonic music of the Middle Ages and Renaissance. At this point the perfect fourth was heard as a consonance rather than as a dissonance (see the article Consonance and dissonance). The major and minor thirds were later added and these three interval types (3rd, 4th, 5th)—alongside the major second and minor second—were used freely to add an extra "part" to the texture which was often placed over a droning "tenor" part. This style of writing slowly developed into the triadic polyphony found in the Renaissance. At this stage, the "bare" third (ie no only those two notes are sounding) was felt to be more "pleasing" to the ear than bare seconds, fourths and fifths and the thirds were often use at points of repose; the perfect fourth was used at points of tension and went from being heard as a consonance to being heard as a dissonance. (Seconds have generally always been heard as dissonances because they are so small and occur high up on the harmonic series having complex ratios; the perfect fifth is generally always heard as a consonance because it occurs low down the harmonic series, having a simple ratio of 3-2.) At the beginning of the 20th century, fourths played a strong role in contemporary music-styles, but in quite a different way: "Quartal harmony", the harmonic layering of fourths, imbued modern music with structural commonalities, creating parts more widely separated in space and/or time (because the fourth is a wider interval than the third), and allowing for a very different sound. In a sense, these composers were re-evaluating the fourth as a consonance once again.

The ancient Greeks defined the group of "symphonia", the beautiful intervals, naming the fourth "syllabe" (Greek: fastened together) and later Diatessaron (Greek: by four, from four). This interval became the framework upon which the tetrachords of Greek music theory were built.

In the Middle Ages the fourth was considered to be a consonance, as were the unison, octave, fifth, and later the third. After the 12th century, music theorists sometimes classified the fourth as a dissonance requiring resolution.

In the 13th century, the fourth and fifth together were the concordantiae mediae (middle consonances) after the unison and octave, and before the thirds and sixths. In the 15th century the fourth was considered dissonant, and removed from the group of concords.

Modern acoustic theory supports the medieval interpretation insofar as the intervals of unison, octave, fifth and fourth have particularly simple frequency ratios. The octave has the ratio of 2:1, for example the interval between A' at A440 and A'' at 880 Hz, giving the ratio 880:440, or 2:1. The fifth has a ratio of 3:2, and its complement has the ratio of 3:4. Ancient and medieval music theorists appear to be familiar with these ratios, see for example their experiments on the Monochord.

(Loudspeaker.svgListen) with perfect (a), augmented (b) and diminished (c) fourths

In the years that followed, the frequency ratios of these intervals would change slightly as different systems of tuning, such as meantone temperament, well temperament, and equal temperament were developed.

In early western polyphony, these simpler intervals (unison, octave, fifth and fourth) were generally preferred. However, in its development between the 12th and 16th centuries:

  1. In the earliest stages, these simple intervals occur so frequently that they appear to be the favourite sound of composers.
  2. Later, the more "complex" intervals (thirds, sixths, and tritones) move gradually from the margins to the centre of musical interest.
  3. By the end of the Middle Ages, new rules for voice leading had been laid, re-evaluating the importance of unison, octave, fifth and fourth and handling them in a more restricted fashion (for instance, the later forbidding of parallel octaves and fifths).

The music of the 20th century for the most part discards the rules of "classical" western tonality. For instance, composers such as Erik Satie borrowed stylistic elements from the Middle Ages, but some composers found more innovative uses for these intervals. It became very common in the 20th century for the fourth to be used as a structural element.

[Definition left in]

Middle Ages

In medieval music, the tonality of the common practice period had not yet developed, and many examples may be found with harmonic structures that are built on fourths and fifths. The Musica enchiriadis of the mid 10th century, a guidebook for musical practice of the time, described singing in parallel fourths, fifth and octaves. This development continued, and the music of the Notre Dame school may be considered the apex of a coherent harmony in this style.

Fourths in Guillaume Du Fay's Antiphon Ave Maris Stella

For instance, in one Alleluia (Loudspeaker.svgListen) by Pérotin, the fourth is favoured. Elsewhere, in parallel organum at the fourth, the upper line would be accompanied a fourth below. Also important was the practice of Fauxbourdon, which is a three voice technique (not infrequently improvisatory) in which the two lower voices proceed parallel to the upper voice at a fourth and sixth below. Fauxbourdon, while making extensive use of fourths, is also an important step towards the later triadic harmony of tonality, as it may be seen as a first inversion (or 6/3) triad.

This parallel 6/3 triad was incorporated into the contrapuntal style at the time, in which parallel fourths were sometimes considered problematic, and written around with ornaments or other modifications to the Fauxbourdon style. An example of this is the start of the Marian-Antiphon Ave Maris Stella (Loudspeaker.svgListen) by Guillaume Dufay, a master of Fauxbourdon.

In medieval thought, contemplation of the musical intervals was frequently expressed from theological perspectives. Pope John XXII issued a bull in 1324 forbidding most contrapuntal practice, but permitting on solemn occasions an enrichment of the plainchant by the concord of the octave which he described as a symbol for the perfect beauty and holiness of God, sounding out over earthly imperfection and infertility, along with the fifth and fourth which have a similar purity.

Renaissance and Baroque

The development of tonality continued through the Renaissance until it was fully realized at last by composers of the Baroque era.

Conventional closing cadences

As time progressed through the late Renaissance and early Baroque, the fourth became more understood as an interval that needed resolution. Increasingly the harmonies of fifths and fourths yielded to uses of thirds and sixths. In the example, cadence forms from works by Orlando di Lasso and Palestrina show the fourth being resolved as a suspension. (Loudspeaker.svgListen)

In the early Baroque music of Claudio Monteverdi and Girolamo Frescobaldi triadic harmony was thoroughly utilized. Diatonic and chromatic passages strongly outlining the interval of a fourth appear in the Lamento genre, and often in Passus duriusculus passages of chromatic descent. In the madrigals of Claudio Monteverdi and Carlo Gesualdo the intensive interpretation of the text (Word painting) frequently highlights the shape of a fourth as an extremely delayed resolution of a fourth suspension. Also, in Frescobaldi's Chromatic Toccata of 1635 the outlined fourths overlap, bisecting various church modes.

In the first third of the 18th century, ground-laying theoretical treatises on composition and harmony were written. Jean-Philippe Rameau completed his treatise Le Traité de l'harmonie réduite à ses principes naturels (French: the theory of harmony reduced to its natural principles) in 1722 which supplemented his work of four years earlier, Nouveau Système de musique theoretique (French: new system of music theory); these together may be considered the cornerstone of modern Music theory relating to consonance and harmony. The Austrian composer Johann Fux published in 1725 his powerful treatise on the composition of Counterpoint in the style of Palestrina under the title Gradus ad Parnassum (Latin: The Steps to Parnassus). He outlined various types of counterpoint (e.g. Note against note), and suggested a careful application of the fourth so as to avoid dissonance.

Classical and Romantic

The blossoming of tonality and the establishment of well temperament in Bach's time both had a continuing influence up to the late Romantic period, and the tendencies towards quartal harmony were somewhat suppressed. An increasingly refined cadence, and triadic harmony defined the musical work of this era. Counterpoint was simplified to favour an upper line with a clear accompanying harmony. Still, there are many examples of dense counterpoint utilizing fourths in this style, commonly as part of the background urging the harmonic expression in a passage along to a climax. Mozart in his so-called Dissonance Quartet KV 465 (Loudspeaker.svgListen) used Chromatic and Whole tone scales to outline fourths, and the subject of the fugue in the third movement of Beethoven's Piano sonata op. 110 (Loudspeaker.svgListen) opens with three ascending fourths. These are all melodic examples, however, and the underlying harmony is built on thirds.

[Tristan chord left in but further commented and moved to more relevent place]

[Slavs and Impressionists etc left in as precursors]

--Jubilee♫clipman 23:32, 7 December 2009 (UTC)

Comments on edited page[edit]

Any thoughts? --Jubilee♫clipman 03:29, 7 December 2009 (UTC)

I support what you've done! The page was an idiotic embarrassment before... but it really does need to be cut down much further...! I salute you for doing the work you've done... My own shy suggestion would be to use a proper ('New Grove'?) entry as a model, and just junk the irrelevant and wrong blathercap that makes this page so pitiful... Pfistermeister (talk) 13:02, 7 December 2009 (UTC)
I don't think there is anything shy about calling the efforts of other editors, without whom you would have nothing to criticize, idiotic and embarrassing. Feel free to attempt to make it your ideal, but keep in mind that later other may come along and call your efforts embarrassing and idiotic. Hyacinth (talk) 09:14, 10 December 2009 (UTC)
Thanks! You are right: we need English works to cite from and we need to cut out far more. Actually, much of the "history" stuff would sit better in the article perfect fourth... hm. --Jubilee♫clipman 21:20, 7 December 2009 (UTC)
Other problems: there are still lots of places where the fourths in question are melodic rather than harmonic; the 'Tristan chord' discussion is extremely silly, not least since even an ordinary dominant seventh can be laid out as F - B, D - G; a very good example that's not mentioned is the very opening of 'Daphnis and Chloe', which generates a pile of fifths and then adds a pair of fourth chords above it; and Mahler's Seventh Symphony ought to be shown in an example... Pfistermeister (talk) 22:49, 7 December 2009 (UTC)
I've moved all the history pre-C20th over to the relevent article... (see above). I suspect there may still be a few non-relevent things that need tidying up (and there's still that awful POV thing). The Tristan chord has been changed to a "precursor", if that helps? Scriabin is also a precursor along side the other "Slavs" (as they are called in the article) and the Scandinavians. Daphnis et Chloé and Mahler's 7th need to be here, indeed. --Jubilee♫clipman 23:05, 7 December 2009 (UTC)
Added Ravel's Daphnis et Chloé and Mahler 7th to the mix but we need musical quotes. --Jubilee♫clipman 00:01, 8 December 2009 (UTC)

I've added a smattering of cite, OR, POV and weasel tags to help tidy this up. The shear number makes me realise how far from the ideal this article still is, even after the week or so of work I have ploughed into it... I think I'm going to have to leave it to the rest of the world to tidy up further and cite. Until I get my books from my mother's home that is (no space here). --Jubilee♫clipman 00:04, 10 December 2009 (UTC)

I appreciate the effort made to clean up the article. Sorry I didn't respond earlier; I haven't been very active on Wikipedia the last few years. The large amount of content I added to this page in 2006 was the result of a translation of the German version of this page. For the most part I wasn't trying to filter or edit that version; I was just trying to transfer the information to this English article that was very small at the time. I'm glad that you and others have continued to improve this article, and please continue! - Rainwarrior (talk) 08:02, 30 April 2010 (UTC)
Jeeezus wept! 60% of this page is still fantasy bullshit! If someone else doesn't whittle down this pile of crap, *I will*.
Seriously: what kind of idiot thinks the 'Tristan chord' has something -- anything -- to do with quartal harmony? This page is everything that's wrong with wikipedia: clueless, semi-literate, amateur twaddlings presented as scholarship. Shocking! Pfistermeister (talk) 00:11, 8 January 2011 (UTC)

Rock Music[edit]

Should this section be anything more than a quick note about power chords? Rock music isn't constructed from quartal or quintal haromy; power chords, being strongly tonal but modally ambiguous chords that avoid the harshness you get from 3rds in a distorted timbre, are more a matter of convenience than harmonic intention. BrutishBloodGod (talk) 00:40, 27 December 2009 (UTC)

You are correct, and in fact all of the sections on popular music are misleading as they stand. Much more work is needed to sort this behemoth out... --Jubilee♫clipman 01:23, 28 December 2009 (UTC)
Very right, the articles about jazz and music theory (chords, scales et cetera) also need many corrections. — Preceding unsigned comment added by 87.181.222.215 (talk) 00:48, 30 March 2011
I removed unsourced material. I added sourced material on King Crimson and Robert Fripp. Kiefer.Wolfowitz 20:01, 6 January 2013 (UTC)
It is a moot point, since the Eric Tamm book has now been removed from the list of references, but a "reprint" edition by definition has the same page numbers as the original. It is for this reason that a reprint is not regarded as a separate edition, so that the original should be cited in its stead.—Jerome Kohl (talk) 17:45, 7 January 2013 (UTC)
Thanks for informing me of this defining property of a reprint. My page references come from the MicroSoft Word document at the Tamm's site, and I cannot guarantee that they are identical with reprint edition, which I have never held---for either his Eno or Fripp books. Kiefer.Wolfowitz 21:15, 7 January 2013 (UTC)
BrutishBloodG*d,
Please review the brief discussion (in this article) of Robert Fripp's new standard tuning, which mentions ideas similar to yours. Please help with additional reliable sources, when you have time. Kiefer.Wolfowitz 21:19, 7 January 2013 (UTC)

Sheet music[edit]

Is there a way to make the the sheet music in the Modernism and Postmodernism subsection look better on the page? I tried but couldn't fix it. Right now it is crowding the sides of the articles (esp. [File:Hindemith, Flute Sonata, II quartal harmony.png]), making it hard to read. Plus, some of the music does not line up with text that is talking about it. Squandermania (talk) 00:22, 7 September 2010 (UTC)

Factual inaccuracy[edit]

This preference for fourths in rock stems directly from the chosen "high instrument of rock music", the guitar, on which they are very simple to play because the strings are mainly tuned a fourth apart.[citation needed]

I think the author of this section confuses a few things here. Although it's correct that apart from the B string all strings are tuned a fourth apart, playing two notes together which are a fourth apart does not mean that these notes are examples for the use of quartal harmony. In fact these notes are called double stops and are inverted power chords. If any preference exists in rock music it's the preference for fifths, i.e. power chords. Considering the {{Cn}} tag this looks like original research. — Preceding unsigned comment added by 87.181.222.215 (talk) 00:43, 30 March 2011

Additional citations: History[edit]

Why and where does this article need additional citations for verification? What references does it need and how should they be added? Hyacinth (talk) 04:33, 11 November 2011 (UTC)

Tag removed. Hyacinth (talk) 01:31, 16 February 2012 (UTC)

Removed[edit]

  • In 1912, Leonid Sabaneyev published a work on Scriabin's theoretical ideas about Prometheus: The Poem of Fire in the periodical Der Blaue Reiter,{{Citation needed|date=December 2009}} but his opinions may not have been appropriate. As Hugo Riemann wrote in his Music Lexicon: "Firstly, chords from pure fourths (for example those in Arnold Schoenberg's well cited Chamber Symphony) without extension or mixture are used in the same way as diminished fourths, and secondly, that Scriabin himself looked upon his so-called Mystic Chord not as a quartal structure but as a reflection of the overtone series."<!--- (''„Dabei wurde übersehen, dass erstens Akkorde aus reinen Quarten (wie zum Beispiel in Arnold Schönbergs hierfür mit Recht vielzitierter Kammersinfonie) nicht ohne weiteres mit Mischungen aus übermäßigen, verminderten und reinen Quarten gleichzusetzen ist und zweitens, dass Skrjabin selbst seinen sogenannten ''mystischen Akkord'' keineswegs als Quartenakkord sondern vielmehr als eine Wiederspiegelung der Obertöne ansah.“'')--->{{Cite quote|edition? page? date?|date=December 2009}}

The above was removed as incompletely cited. Hyacinth (talk) 01:04, 2 May 2012 (UTC)