Scale of the Day: B Dorian diminished 4 mapped to the Square-root-of-2

The B Dorian diminished 4 mapped to the Square-root-of-2 Scale.

Melody Study: Melody #1 - Just Transposition and Retrograde Melody

Proceeding forward with a study of melodic transformative theory let's return to the initial hymn melody:


Example 1: Hymn Melody

Just Transposition

Here is the 5-limit tuning worked out in a previous post:


Example 2: Hymn Melody in 5-limit Just Intonation

Transposition involves moving each pitch in a melodic line by a fixed interval. In just transposition we simply use a fixed just interval. To calculate the correct frequency ratio one only needs to multiply by the fixed interval ratio. For example, if we were to transpose this 5-limit hymn melody up by an 8/7 major second we would have the following:


Example 3: Hymn Melody transposed by 8/7.

Now this 5-limit melodic line is shifted into a 7-limit space, even though the melodic line itself adheres to a 5-limit sound. It is only 7-limit relative to the E Flat 1/1 pitch.

Retrograde Melody

Another relatively straight forward function for melodic transformation is retrograde melody. For example, this hymn melody played in reverse would look like this:


Example 4: Hymn Melody - Retrograde.

A couple of variations on the retrograde function to consider involve separating the pitch sequence and rhythm and reversing them independently.


Example 5: Hymn Melody - Pitch order Retrograde.


Example 6: Hymn Melody - Rhythmic Retrograde.

These are relatively simple operations that could be combined with transposition functions (or any other functions) to form counterpoint lines with the original melodic line for a unified polyphonic texture or used sequentially for melodic variation. Next time we return to this melody we'll take a look at some possible inversion strategies.

Scale of the Day: E Flat Dorian

Synthesized audio sample of an E Flat Dorian Scale.

See also:
E Flat Dorian Scale notated.
E Flat Dorian Interval Analysis.

Happily Ever After

I find Happily Ever After by Randy Hostetler in my ears as I periodically approach this outstanding work from time to time to experience this epic text piece that transcends the limitations and frustrations of spoken language to reveal the rich potential of text-sound. This piece uses a great idea realized with talent and an ear for detail.

Happily Ever After is a 43-minute work consisting of manipulated recordings of Randy Hostetler and 64 of his friends and families telling stories. Each story begins with "Once upon a time..." and ends with "... happily ever after." Everything in between is up to the story teller as a loose improvisation in narration. These performances are manipulated largely by temporal and thematic placement and the actual language is never obscured beyond some careful overlaps between storytellers (and even these are panned comfortably within the stereo field so that one can pick out a story line at any moment).

This work accomplishes something extremely rare in text-music compositions. Less than 20 minutes into this work it eliminates my resistance to text-sound and the pervasive consciousness of tangling sound with literal meanings vanishes and a carefully woven texture reveals something beautiful and human. One becomes emerged within the attractive din of a family gathering in a warm home. For a work limited to the sound of recorded voices there's a rich texture that emerges from the range of age, gender and varying degrees of enthusiasm, humor, melancholy, remorse, regret, irony, sarcasm, seriousness and comfort level with being recorded. The piece opens with a brilliant overdub of multiple "Once upon a time" along with another massive wave of "okay, is this thing on?" before opening up into a wide polyphony of human experience. There's a surprising dynamic range that keeps the experience vibrant as one strains to hear a lone, quiet story telling before being swept up in a wave of activity.

What emerges from this texture, and this experience, is a pervasive sense of a meta-story of the multiple components of human mortality. No single story slides into focus. Some episodes slide into the foreground but the overall "story" is more impression than narration. This is an unusual, fantastic work that illuminates an unpretentious vulnerability that works on so many different levels.

Scale of the Day: G Dorian diminished 4

The intervallic content of the G Dorian diminished 4 Scale.

Scale of the Day: B Pythagorean Dorian

The B Pythagorean Dorian Scale. Note the symmetry between the +3.91 cent 9/8 major second with the -3.91 cent 16/9 minor seventh. Or the -5.87 cent 32/27 minor third to the +5.87 16/9 major sixth. The sound of the Dorian scale owes much to the perfect symmetry of inverse interval classes contained within the octave.

Scale of the Day: F Sharp Aeolian mapped to the Square-root-of-2

The F Sharp Aeolian mapped to the Square-root-of-2 Scale.