Pandiatonicism 1; Is It a Thing?

The term "pandiatonicism" was coined by Nicolas Slonimsky in the second edition of Music Since 1900 (1938) to describe harmonic language that uses the notes of any diatonic scale in a non-tonal manner.

It is a somewhat problematic term for two reasons:

1. It is partly defined by what it is not: It is not tonal, despite being based primarily on the diatonic notes of any key or scale.
2. There appears to be no widely-accepted understanding of the term beyond acceptance of the idea that it involves almost exclusively diatonic notes; it is defined differently by different writers.

Regarding the first issue, let's explore how a composition can be based on the diatonic notes of a key or scale but not be tonal. I will suggest that the following conditions should apply:

• It does not use functional harmony progressions, such as ii - V - I, IV - I, V - vi, etc., because these are the harmonic building blocks that establish a key in tonal music.
• It does not follow the voice-leading conventions of tonality that apply to the resolution of tendency tones, which include:
• Chord extensions: 7ths, 9ths, 11ths, and 13ths,
• The leading tone in dominant harmony,
• Suspensions and retardations,
• The 5th of diminished chords.
  
• The next two voice-leading practices are common in tonal music, but I don't think they apply to pandiatonicism:
• The 6 & 4 of the cadential 6/4 (I don't see how pandiatonic music can have a cad. 6/4, since it is part of a progression that typically establishes a key),
• Most chromatically-altered notes (this is irrelevant if only diatonic notes are used). 
• Can pandiatonic music have a tonic chord or tonic note? As you can see in the discussion below there is disagreement on this. My feeling is that it can, as long as it is not established by the means used in tonal music. Establishing a tonic note or chord through non-tonal means can be challenging, but it is not impossible

Another problematic aspect is that it is defined differently by different people. For example:

• The Wikipedia article on Pandiatonicism states that "all seven degrees of the diatonic scale [are] used freely in democratic equality."
• I believe that this idea came from Slonminsky (1938). I take this to mean that there is no hierarchy of diatonic notes and triads, unlike tonal music, in which different notes and triads often have specific roles to play, such as dominant-function chords (V, vii°), predominant-function chords (IV, ii), and tonic chords.
• The composer in me finds this to be an interesting idea. The problem with this description, however, is that I don't think that many of the works cited as examples of pandiatonicism have this quality (democratic equality of all diatonic notes).
• Richard Kostelanetz, in A Dictionary of the Avant-Gardes (2013, 465) writes: "The functional importance of the primary triads...remains undiminished in pandiatonic harmony." (Wikipedia says that this "appears to be quoting Slonminsky," FWIW.)
• I find this an odd statement. How is music in which primary triads have undiminished functional importance any different from tonality?
• On the other hand, Bryan R. Simms argues that "pandiatonicism does not project a clear and stable tonic" (Music of the Twentieth Century: Style and Structure (1986, 63-64). 
• This is closer to my understanding of pandiatonicism.
• Also from Wikipedia: "Pandiatonic music typically uses the diatonic notes freely in dissonant combinations without conventional resolutions and/or without standard chord progressions, but always with a strong sense of tonality due to the absence of chromatics."
• I agree with the everything in the above statement until the last part: "always with a strong sense of tonality due to the absence of chromatics.
• Wait… what? There are two problems with this statement:
1. Tonality isn't defined by an "absence of chromatics." Almost all tonal music uses chromaticism, such as modulation, applied dominants, mode mixture, augmented sixth chords, etc., at least in classical and jazz music. "Chromaticism" comes from the Greek word for "colour," which conveys the implication that music without it is colourless.
2. If you play a random series of pointillistic white notes or white note clusters on piano, will it necessarily result in music with a "strong sense of tonality?" Tonality isn't just about the notes used in a passage of music; it's about the way those notes are used. The only way for music to have a "strong sense of tonality" is for it to be tonal, which usually includes chromaticism.
• In Slonminky's 1947 edition of his Music Since 1900 he suggested that pandiatonicism can be considered to be "a diatonic counterpart of Arnold Schoenberg's twelve-tone technique, whereby melodies may be made up of seven different notes of the diatonic scale, and then be inverted, retrograded, or both. According to this system, "strict pandiatonic counterpoint" may use progressions of seven different notes in each voice, with no vertical duplication" ("Pandiatonicism," in Wikipedia, the Free Encyclopedia. Retrieved 21 Jan, 2024).  
• This is an interesting compositional idea that might be fun to try, but I would suggest that almost no works that get cited as examples of pandiatonicism have this quality.
• I will also suggest that Slonminsky was writing as an advocate for the concept of pantdiatonicism here, not as an impartial scholar making observations on existing musical practices. I'm not sure that he included any examples of diatonic serialism. This is not to suggest that such examples don't exist – Aaron Copland tried this, and possibly Stravinsky as well (I'll try to do some more research to find out more about this).

Here is my suggestion for composition students: I encourage you to try writing something that can be considered pandiatonic if the idea interests you.

However, given the fact that a universally agreed-upon definition of pandiatonicism does not exist, I would to suggest the following guidelines:

1. Avoid anything in melodic lines or harmonic progressions that suggests tonality.
2. Avoid establishing a tonic. Or if this is too disturbing, establish a tonic, but not by any method associated with tonality; for example, Ti-Do and So-Do, if supported by dominant-to-tonic (or dominant to sub-mediant) harmony, are overtly tonal and should therefore be avoided.
   → On the other hand, if Ti-Do is supported by non-tonic-to-dominant harmony, such as iii to ii⁷, or I⁷ to IV, it is available.
3. Aim to use all pitches of whatever scale you use equitably and democratically.
4. Triads may be used only if they do not progress as they do in tonal music.
   → See the Kostka & Payne chord progression chart below for a summary of how diatonic chords usually progress in tonal music.
5. Try to use non-triadic constructions as well, such as quartal and quintal harmony.
   → One challenge in using these types of harmonies is that, depending on what note you start on, you might end up with accidentals if trying to maintain a vertical structure of perfect fourths, such as C - F - Bb - Eb - Ab, etc. While occasional accidentals are fine in pandiatonicism, for the most part the objective is to avoid them. They are fine if required for modulations, however.
   → If you want to write quartal harmony using only perfect fourths and white notes (i.e., no accidentals), for example, you could build up from B: B - E - A - D - G - C - F.
   → If you want to try this with quintal harmony, build up from the last note above (F): F - C - G - D - A - E - B.
6. Give Slonminsky's serialist diatonicism a try if you wish.

You may find it challenging to write music you enjoy without borrowing common practices from tonal music; therein lies the reason tonal music is so widely embraced: Its practices have evolved over centuries to sound good to Western ears. We talk about Ti "wanting" to rise to Do in a V-I progression, or of a chord seventh "wanting" to resolve down by step to a consonance in the next chord, or a 4 "wanting" to resolve down to 3 in a 4-3 suspension, because these practices sound good or "right" to our ears, so writing tonal music in which these practices are not followed can feel very "wrong" to us.

(On a side note, I am curious to know if the tonal music practices that sound "right" to our ears have corollaries in music of other cultures, such as South-Indian classical music, or traditional Chinese music. Do they use anything like dominant-tonic harmony?)

For this reason, you may find it easier to write pandiatonic music that avoids triadic progressions, such as Slonminsky's serialist approach to diatonicism, or pointillistic music in which widely-spaced notes are distributed in unpredictable ways.

I'll stop here for now; I will post some links to pandiatonic music in my next blog post.

Please let me know your thoughts below in the comments section!

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How diatonic chords in classical music usually progress: Chord-Flow Chart (from Kostka, Stefan M., and Dorothy Payne. Tonal harmony: With an introduction to twentieth-Century music. New York etc.: McGraw-Hill, 2009. P. 111):

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Check out the next post, Pandiatonicism 2, to listen to various works that some have claimed to be pandiatonic.

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You may also like these posts on Post-Tonal Harmony Ideas:

Post-Tonal Harmony Ideas (1)

Post-Tonal Harmony Ideas (2)

Post-Tonal Harmony Ideas (3)

Ostinatos; making a lot from a little (2. Rite of Spring)

Further to my previous blog entry…

If the 339 consecutive repetitions of a 2-bar rhythmic ostinato pattern in Ravel's Boléro (1928) don't constitute overuse of an idea, then what does?

Or, to rephrase the question in a less acerbic way, Ravel's Boléro is his most popular work (according to Wikipedia), yet from start to finish it repeats a 2-bar rhythmic pattern without change or interruption; how does Boléro maintain our interest? Why are most listeners not bored, troubled, or driven mad by the 339 incessant repetitions of this ostinato rhythm?

The explanation is that there are other musical aspects that change and evolve continuously throughout the work, and these are what sustain our interest, such as: 

1. It begins almost inaudibly (so quietly that, when I worked as a record department sales clerk as a student, many people who purchased the album tried to return it, thinking there was something wrong with the audio), and grows steadily and inexorably over its 15-16 minute length to become as loud as possible at the end; it is a study in how to write an extraordinarily-long crescendo for orchestra; 
2. As such, it is a masterpiece of orchestration, filled from start to finish with colour and texture changes that reflect Ravel's brilliance as an orchestrator. The two-part theme is repeated many times, but each presentation uses a different orchestration (and hence a different colour), and the orchestration also changes within thematic presentations as well.
3. Its form is essentially a theme and variations, and just as in the best examples of this form, our interest is sustained by hearing many permutations of the main theme, instead of becoming annoyed that a given theme is played over and over again. The unusual aspect in Boléro is that the pitch content of the theme is never varied (except for a modulation in the final 40 seconds), just the colour (orchestration and texture) and dynamics. 

• This idea is not original to Ravel, however; another mono-thematic work that begins quietly and, over the course of multiple thematic repetitions, eventually becomes very loud, is Grieg's "In the Hall of the Mountain King," from Peer Gynt (1875), composed 53 years earlier.

If Boléro consisted only of 339 repetitions of a short idea, and nothing else, I'll go out on a limb and speculate that the composition would be less popular.  😄

Or perhaps it would have become celebrated as the grand-daddy of minimalism… 😴

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Igor Stravinsky: The Rite of Spring

Igor Stravinsky's The Rite of Spring (1913) makes extensive use of ostinati, and, more generally, repetitive elements, so today we will look at some of the ways Stravinsky used one particular ostinato, the repeated four-16^th-note idea in the excerpt below.

It is introduced at the end of the first section (Introduction) of Part 1, played by pizzicato violins, while a clarinet sustains a lengthy trill (this is at about the 3-minute mark in the YouTube video at the end of this post; all other timings indicated below refer to this video):

It is a pretty simple idea by itself, but its simplicity makes it useful, because it works well with many other ideas. Therein lies one of the keys to writing a good, multi-purpose, ostinato: While good music can be written with longer and more complex ostinati, a short, simple idea is probably more flexible, because it can support a variety of other ideas.

The above excerpt introduces the ostinato somewhat hesitantly, instead of introducing the idea and immediately continuing with almost incessant repetitions, as we found (see previous post) in Boléro. Stravinsky is saving more regular repetitions of this idea for the next section. He is "planting a seed," giving us a taste of an idea that will become increasingly prominent and repetitive.

Sure enough, about 10 seconds later, he gives us a somewhat longer version of the ostinato, which leads to the strongly-rhythmic bitonal (E (enh.) in the lower strings, Eb7 in the upper strings) chord repetitions that are one of this work's most memorable features, which mark the start of the next section, Augers of Spring/Dances of the Young Girls. This starts at 3:20 in the video below:

Incidentally, for those interested in "golden mean" ratios, note that in its first three presentations, the ostinato is heard twice, once, (thus three times so far), and Five times, adding up to eight times, all of which are numbers in the Fibonacci series (1, 2, 3, 5, 8…). Sadly, the next time we hear the idea (see excerpt below) it is only presented four times, which is not a Fibonacci number. 😢 It is used eighteen times consecutively the time after that (part of which is two excerpts below), and this too is not a Fibonacci number. 😭 This is a work clearly in need of a revision! 😎 [Okay, I promise to insert no more emoticons in today's post. The are very useful, though…]

Very soon after the previous excerpt, at about 3:35 in the video below, the heavily-accented repeated chords are interrupted, and we hear the first presentation of the ostinato figure with counterpoint, consisting of an arpeggiated chord in the bassoons, which is itself repeated. Notice that the bitonality continues, this time between the ostinato (Eb7) and the counterpoint below it (E enh.):

This next excerpt, which starts at about 3:45 of the video, gives us another melody, once again with repetitive elements, this time above the ostinato. Note the frequent colour changes in Stravinsky's orchestration of the melody; the reduction below does not accurately reflect this, but there are 6 colour changes to the melody in 6 bars. When you listen to the full orchestra version (in the video below), note as well that the ostinato at this point is buried in the texture, almost inaudible within the heavily accented chord repetitions (not shown in this example, but the chords are the same as in the last 2 bars of the previous example):

New melodic fragments are superimposed on the 4-note ostinato over the two minutes that follow the previous excerpt, one of which is this one, which is again repetitive, and occurs at about 5:25 of the video:

Please suggest other works that make prominent use of ostinati – one such piece is Stravinsky's, L'Histoire du Soldat – and I will possibly (see explanation at the end of this post) discuss them in future blogs… At the very least, I can compile a list with your suggestions. If you can, try to be specific about where the ostinati occur within the work you are citing. In the mean-time, I already have an idea for a third post in this series.

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Below is a recording of The Rite of Spring on a video that shows the score. Try to find other uses of the ostinato discussed above. As well, try to listen to it more than once, in order to find other ostinati, and the degree to which repetition of musical ideas is used. If you don't have enough time to hear the entire piece, listen to at least the first 6 minutes; all of the above examples occur within that time.

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Explanation of my use of the word "possibly" with regards to doing more blogs on this topic:

My only hesitation is that the amount of time involved doing a post such as this one is daunting. It involved making score reductions in Finale of the sections I wanted to use as examples, saving them as GIFs and importing them into this blog, recording the musical examples, importing them into Audacity and splicing them into sections that corresponded with the notated examples, saving them in two different audio formats (MP3 and OGG) because not all web browsers read MP3s, uploading the audio files to my website, and then inserting the code that lets the Blogger website read and play audio files on all major web browsers. Plus the time spent fixing things that didn't work along the way. Not complaining, mind you! I enjoy doing this, but it is time consuming.

That said, and to repeat what I wrote above, I do have another post in the works on this topic, so there will be at least three in the series, and possibly more if people make suggestions regarding other works with prominent use of ostinati.

Post-Tonal Harmony Ideas (3)

I wrote a short piece for today's post, based on the arpeggiated chords presented in section 8 of my Post-Tonal Harmony Ideas (1) post. You may wish to listen to those chords again before listening to today's composition , but it's fine to skip this and just listen to the piece below.

The chords in section 8 of Post-Tonal Harmony Ideas (1) were constructed by superimposing different harmonic structures found in tonal music, such as an F# major triad and C major triad, a combination used by Stravinsky in Petroushka, in order to create post-tonal sonorities.

There are no particular "rules" to follow in combining chords in this way, but I would suggest that the resulting sonority should not sound overtly tonal; if you start with a G chord and superimpose an F chord, for example, it would result in a G¹¹ chord, which is overtly tonal.

That said, however, it is really the context in which such chords are used that determines whether they are tonal or post-tonal. If you play the chord in bar 3 below, for example, and resolve it to an Eb chord, it will sound like an altered V⁷ resolving to I in Eb major, because bar 3 starts with a Bb⁷ chord. If you play the same chord (bar 3) but move to a different sonority that in no way suggests an Eb chord, then you've placed it in a post-tonal context.

Another suggestion, if you try this approach, is to use chord combinations in which the two triad-based chords have no notes in common with each other, although that is by no means an essential condition.

The approach I find that works best is to work these out at a piano, exploring the possibilities by playing different chords in each hand until you find combinations you like, and then immediately write them down. Frequently, the experimentation may involve just altering one note at a time until you find a sonority that you'd like to keep.

Once you have a collection of chord combinations that you like, you can use them however you wish in a composition; you can transpose them, add further notes to them or otherwise modify them, invert them, re-use them, etc.

Here is the piece; you can hear it with the audio player below the score:

 

More Details on this Composition:

• I began with the first three arpeggiated post-tonal chords presented in my Post-Tonal Harmony Ideas (1) post (they are in section 8, numbers 1, 2, and 3). 
• I transposed the second arpeggio, and subsequently re-used and transposed the other arpeggios as well. 
• In bar 7, I introduced a new chord (i.e., one that wasn't in the original blog post), which consisted of a Db Maj.7th chord plus an Eb Maj.7th with augmented fifth. I also reused transpositions of this chord.
• One way to vary these chords, aside from changing notes within them, is to add notes on top of them that are not part of the original sonority; I did this a few times in this piece, especially in my choice of flute notes.
• As you can hear, I took time in the score to move from one sonority to another, because the harmonic complexity of these chords is, to me, inherently captivating, and it takes time for the ear (well, the brain, actually) to absorb them. 
• Harmonic progressions using these chords can proceed as quickly as you want, however.
• This is "colour-based" composition; each chord has its own colour. The process is something like an artist creating an abstract painting using only splashes of colour here and there, with the result being pleasing to the eye (well, the brain, actually).
• "Mystery" and "Wonder" were the names of two of our cats that passed away several years ago.

Final Thought: Practicality

• One very practical advantage of this approach to composition is that the chords should fit naturally into the pianist's hands, provided you started by experimenting at the piano with chords that fit your hands. A skilled pianist has spent years training their hands to instantly form the correct shape in playing tonal chord structures, like triads and 7th chords, so if you use those same chord shapes, but combine them in untraditional ways, the pianist is likely to find the music easier to play than a lot of contemporary music.

How Important is Originality in Art?

I think many people would suggest that originality is an essential ingredient in art. As an example, an excellent copy of the Mona Lisa, virtually indistinguishable from the original, might be valued at a few hundred (or a few thousand) dollars, whereas if the actual Mona Lisa is as close to priceless as is possible for a painting. Two identical works of art; one original and iconic, the other a reproduction, but the first is much more highly-valued than the second by virtue of its originality.

This looks like the Mona Lisa; the actual painting, however, is in the Louvre behind bullet-proof glass.

But there are cases where a lack of originality seems less crucial to the value ascribed to a work of art. Many artists have created numerous variants of the same, or similar, things — consider Monet's approximately 250 paintings of water lilies (as well as his series of paintings of Poplars, Haystacks, Rouen Cathedral, Mornings on the Seine, and the London Houses of Parliament), Degas' extraordinary penchant for dancers as a subject (more than half of his vast output of paintings, drawings, and sculptures is devoted to the activities of the ballet dancers and dance students), or Georgia O'Keefe's paintings of flowers — all highly regarded, but, thematically, not particularly original.

Two of the 19 paintings from Monet's "The Houses of Parliament" series. All are the same size, and from the same perspective, but show changes in lighting and hue at different times of day, and in different weather conditions.

If you enjoy visiting art museums, there is a reasonable chance you may have seen Rodin's "The Thinker," his most famous work, and one of the most-recognized (and most-satirized) sculptures ever. The original was 27.5 inches high, but there are over 20 additional casts of the work in various sizes, most of which were executed by his apprentices, as I understand it. Their lack of originality does not prevent them from being prominently displayed (and hence valued) in museums around the world.

"The Thinker," Rodin. At least 20 casts were made of this sculpture.

The paintings in Monet’s Houses of Parliament series are similar – each is of the same subject, viewed from the same vantage point, and on the same size canvas -- and dissimilar – each view represents a different time of day (which alters the lighting), and different atmospheric conditions (hazy, foggy (or smoggy), and different cloud formations). The point, as it relates to originality, is that Monet did not attempt to paint a series of completely different (and therefore highly original) paintings; he wanted to paint the same thing repeatedly in slightly different ways, and we value each individual painting highly nonetheless.

These examples, and many others, suggest that the role of originality in evaluating art may sometimes be relatively minor.

Stravinsky is supposed to have said “good composers borrow, great composers steal,” ^{[ 1 ]} which is itself an adaptation (or theft?!) of T. S. Elliott’s “Immature poets imitate; mature poets steal,” from Elliott's essay on English dramatist Phillip Massinger (1920). It is a clever line, the merits of which are of course debatable, but for me the point is that artists frequently influence one another; part of the way many artists discover their own voices is by emulating, or appropriating, to varying degrees, aspects of the work of others.

Music is filled with elements common to different composers within an historical period, and sometimes across periods. When we study tonal harmony, we learn that in the "common-practice period" (roughly 1700-1900, in Europe), there were guidelines governing the way in which chords progressed. These guidelines have numerous restrictions as well as some freedoms, but the fact that there are guidelines of any sort means that originality in chord progressions was not highly valued.

Composers in the "common-practice" period made widespread use of a limited selection of musical forms, chief among them sonata form, as well as rondo, binary, ternary, and theme and variations. When we study sonata form, we marvel at the many nuanced differences we find in different compositions, even though the big picture form is the same. Other common elements include the use of Alberti bass accompaniment figures (although it had numerous variants), an extremely-limited selection of cadence types (virtually every composition from that period ended with an 'authentic' (V-I) cadence), common phrase lengths (especially 4-bar phrases) and phrase-structures (although numerous exceptions can be found), and writing for commonly-found ensembles such as the string quartet.

And yet, despite the restrictive nature of these common elements, thousands of wonderful works were written. There is originality to be found in all great (or even good!) works to be sure, but, as with Monet’s parliament paintings, the differences are often fairly nuanced.

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¹ Although there are numerous attributions of this quote to Stravinsky all over the web, I have not come across any that cite a source for it. It seems entirely possible that he said this, but I would like to find out if he actually said or wrote this… If anyone has a citation for this quote, please let me know. Of course, it might also be a sentiment that hacks the world over like to attribute to a famous composer in order to justify theft of intellectual property.^↩

Atonal — Even the word sounds unpleasant!

I find above all that the expression, 'atonal music,' is most unfortunate--it is on a par with calling flying 'the art of not falling,' or swimming 'the art of not drowning.' Arnold Schoenberg, Style and Idea, p.210

Do you have an unpleasant connotation with the word, "atonal?"

If you do, you're not alone; many people who have some understanding of what "tonality" means don't seem to feel very warm and fuzzy about the concept of atonality.

But, strictly speaking, all that is meant by the word is that the music in question is not based on tonality. It doesn't really tell us anything about what the music is based on.

A quick primer on tonality, from Wikipedia:

Tonality is a system of music in which specific hierarchical pitch relationships are based on a key "center" or tonic. The term tonalité originated with Alexandre-Étienne Choron (1810) and was borrowed by François-Joseph Fétis in 1840 (Reti, 1958; Simms 1975, 119; Judd, 1998; Dahlhaus 1990). 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-Minor tonality (also called diatonic tonality, common practice tonality, or functional tonality), the system of musical organization of the common practice period, and of Western-influenced popular music throughout much of the world today. [Emphasis mine.]

The "common practice period" is generally understood to refer to the baroque, classical, and romantic periods of European music history, roughly spanning 1600 to 1900. So, using this definition, "atonal" could be applied to medieval plainchant, renaissance masses, most Debussy piano preludes, etc., or it could be referring to a work that involves hitting the keys of a piano with an aluminum (so as not to mar the surface of the bat) baseball bat with reckless abandon. It could be referring to "Le Marteau Sans Maitre" by Pierre Boulez, or to "L'histoire du Soldat" by Igor Stravinsky, or to minimalist works by Steve Reich, Philip Glass, and John Adams, or even parts of "Toontown Follies" by yours truly.

It could refer to music that is as deeply moving and beautiful as any music ever composed, or it could be applied to very harsh, disturbing music.

"Atonal" doesn't necessarily equate with "highly dissonant" any more than "tonal" automatically means "consonant." Dissonance and consonance are essential aspects of tonality, but they are essential aspects of much atonal music as well.

Explore the various sonorities that can be created by the scales and modes that you created for our first project of the semester. There is no ban on the use of major or minor triads; I am hoping that your scales will lead you to discover other sonorities that you like and feel can be used in your compositions, and if some of the sonorities happen to be major or minor, so be it! No problem!

But just try to use them in ways that go beyond their use in the context of tonality.