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Alternative Music Languages

Air

“Air” is a free composition written with harmonies based upon fifths rather than traditional harmonies based upon thirds.

It can be heard on youtube here.

Being a fifths-based harmony might be thought of as being essentially the same as a fourths-based harmony (being its inversion) which was the structure used in the Minuet in G, Stretched piece, also described on this blog. But the harmonic approaches in these two pieces is quite different.

In the Minuet piece, the fourths-based harmony was mapped from a thirds-based harmony in a more or less direct translation of the patterns of the one into the other. In other words, primary attributes of the traditional thirds-based harmonic relationship structure were used while the underlying intervals were changed—kind of like taking a photograph then stretching one of the dimensions in Photoshop.

In the case of the fifths-based harmony used in Air, there are two major differences. First, the harmonic progressions in Air were not in any way mapped from traditional progressions. The harmonic choices were made solely on the basis of their colors. Second, the harmonic tones were not limited to a traditional scale as they were in the Minuet—meaning, in the Minuet all the tones were taken from a classical minor scale, while in Air there is no such restriction.

Not being constrained to a traditional scale, many of the arpeggiated harmonies in Air veer off into potentially dissonant note groupings. But, with the dissonances placed in higher octaves the effect is not as harsh as if these tones were found among the lower pitches. This effect can be compared to natural harmonics  where the naturally occurring higher harmonics would be quite dissonant if they were in the same octave as the fundamental tone, but as they exist in higher octaves the effect is quite different. Certainly this piece, Air, brings those higher harmonics much closer to the tonic, and relatively louder, than they are within the typical harmonic series; yet the effect, I think, is still quite consonant in feel.

A PDF of the sheet music is found here.

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Atlantic Floor

“Atlantic Floor” is a composition for piano where the melody was determined entirely by the shape of the floor of the Atlantic Ocean along the 33.0205 latitude which runs from South Carolina to Morocco.

The philosophical motivation behind this composition was to use nature in art—not as an inspiration filtered through the artist’s experience and biases, but used directly as much as possible. While a landscape may be photographed, framed, and hung on the wall, in this case the shape of the bed of the ocean was taken to dictate completely the form and melody of the music.

Click here to listen to this piece on youtube.

The topography data for the music—the depth of the ocean along this latitude—was obtained from the website of the National Oceanic and Atmospheric Administration. The data, with depth shown in meters, is shown below. You can imagine, if you will, that this chart is a cutaway of the Atlantic Ocean with South Carolina at the far left, Morocco at the far right, and the heavy solid horizontal line at zero representing sea level. The jagged line is the ocean floor—though note that the width of the chart is not at all on the same scale used to represent the sea depth.

atlantic-floor-topography-data

The 33.0205 latitude intersects the American coastline a bit north of Charleston, South Carolina, specifically at Cape Island near the town of McClellanville. The melodic “trip” begins there, proceeding directly along this latitude and ending on the Moroccan coast a little south of the town of Sidi El Abed. (The choice of this latitude was somewhat but not completely random, as a beginning that included a decent stretch of shallow water was an attribute I was looking for.)

Transforming the shape of the ocean floor into a melody required just a bit of mathematics. From sea level to 120 meters below the surface was mapped to the G an octave and a half above middle C. Every additional 240 meters of depth was taken to indicate a pitch a half step lower. The deeper portions of the ocean, therefore, correspond with lower pitches. The entire depth-to-pitch mapping covered two octaves and is shown below with the pair of numbers next to each letter note representing the depth range in meters corresponding to that pitch.

depth-table

The data series (beginning at the North American coast and ending at the African mainland) was divided into 355 intervals and the depths at those intervals were translated into the pitches that became the melody. Each interval was taken to be the length of one quarter note. The rhythm of repeated melody notes was left to the composer’s discretion (so, for example, three quarter notes of the same pitch could be realized as three quarters, two dotted quarters, or a half followed by a quarter).

Since the pitches changed at irregular intervals and as the distances between these changes were a critical feature of the topography, I didn’t alter the timing of these distances to fit a regular or constant meter. Instead, the song’s meter varies throughout in order to fit with the rhythm of the pitch changes. The meter is written as measures of 10/8, 8/8, 6/8, and 4/8, with these time signatures helping to organize the driving meter which largely consists of a varying sequence of eighth note triples and duples.

Finally, the song begins and ends with an arpeggiated figure in 10/8 that carries no melody but serves to bookend the rest of the song.

Click here for a PDF of the sheet music.

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Have You Not Known?

Have you not known? Have you not heard?
Has it not been told you from the beginning?
Have you not understood from the foundations of the earth? (Isaiah 40:21, NRSV)

Click here to listen to this piece on youtube.

This composition is encoded text. That is, the music functions not only as a musical composition unto itself, but also as an encoded message of the text from Isaiah shown above.

This encoding was done by first translating the text into phonetic sounds using the International Phonetic Alphabet. Each phonetic vowel sound was assigned a chord type (major, major 7th, and so on…that is, not a specific chord such as C7, but a general chord not assigned to a specific root note) along with a primary melodic note in relation to the chord (the root, third, fifth, or seventh). Each consonant sound was assigned to a melodic phrase to be interpreted relative to the primary melodic note. The root of the chord and the rhythm of the melody was left to be selected by the composer—as well as the manner of the harmonic accompaniment.

Phonetic sounds instead of letters were chosen as the basis for the translation for several reasons. Using phonetic sounds allow the capture of the same sounds in alliteration or rhyming whereas relying on the letters would be less reliable for this. Further, the phonetics approach allowed a better capture of the rhythm of the text which an approach with letters would obscure.

Part of the thinking behind attempting this approach was to add new elements to the music in a pure way, eliminating the bias of the composer. Now certainly the process for this composition outlined above included plenty of input and meddling from the composer. But some of the elements brought in—harmonies, melodic fragments, and form—were out of the hands of the composer.

To some it may sound odd, trying to eliminate the bias of the composer. But the artistic building process—despite it being often called “creation”—is really predominantly regurgitation of the artist’s own aggregated experiences—or, if you will, biases. Thus being able to bring in some new elements to the music, completely unfettered from the composer’s perspective, seemed a worthwhile pursuit, being that it feels to be a rare event.

Click here for a PDF of the sheet music.

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Minuet in G, Stretched

This piece is based on the “Minuet in G,” often attributed to Johann Sebastian Bach and found in “The Notebook for Anna Magdalena Bach.” This version is a recasting of the original into a new language–basically, translating it from its thirds-based harmony into one based on fourths.

Click here to listen to this piece on youtube.

The below illustration can help explain how this conversion was done. The first grouping of eight notes is a series of thirds in C major containing all the natural triads in that key. The first three (C-E-G) form the tonic chord, the group of three starting on the third tone form the dominant (G-B-D) and the final three form the subdominant (F-A-C).

thirds to fourths

Using that same pattern in the next grouping of fourths, we can define the tonic (C-F-Bb), dominant (Bb-Eb-Ab) and subdominant (D-G-C). Once defined, we can then translate a chord sequence written in a traditional thirds-based major key into a key based on fourths.

Now you may notice and ask why the grouping of fourths is based on the natural minor sequence rather than major. The reason for that is simply to keep the minor second intervals (or major sevenths if you prefer) out of the tonic, dominant, and subdominant chords, resulting in a more consonant resulting translation.

So that takes care of translating the harmony, now how about the melody? For that, it was a matter of interpreting the melody either in terms of chord tones or passing tones. Chord tones were then translated into the corresponding chord tones of the new harmony and passing tones in the thirds harmony were converted into passing tones within the fourths harmony.

Now certainly the new melodic realization was not all black and white decisions–translations are never neat and clean. Decisions need to be made to try to maintain the melodic shape of the original as best as possible–certainly someone else performing this same translation would have made some different choices.

But as it is, that is how it was done. I hope you found listening to it and reading about it enjoyable.

This piece was once included in a 60×60 project, the above recording in fact. While I usually would play this song a bit slower, played at the above tempo the piece conveniently clocks in at just one minute.

Click here for a PDF of the sheet music.

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