A Cheerful Melody Created by Quarter-Tone Clashes

This document introduces a short melodic sketch composed using quarter-tone intervals.
By intentionally incorporating quarter-tone dissonances, the aim was to explore the limits of perceptual tension and how microtonal friction can be used as a compositional tool.
The piece makes active use of close intervals and overlaps of semitone and quarter-tone steps to provoke a distinctive auditory experience.

Reiji's Observations

• This is a piece exploring the sound texture created by clashing quarter tones, discovered while experimenting in 24-tone equal temperament.
• The word "cheerful" in the score title reflects the personal impression felt upon hearing this sequence of tones, though others may perceive it differently.
• A quarter tone in 24-TET is one step; counting from C to just before D gives C, C half-sharp, C♯, and D half-flat as the four tones.
• As a side note, 31-TET approximates 5 divisions, 53-TET about 8, and 41-TET about 7 microtonal steps per whole tone.
• The piece is structured by layering quarter tones a single 24-TET step above each base note.
• The harmonic progression, from the marimba 1 part, goes: C major, F half-sharp major, F♯7, C half-flat major, C7, C half-sharp diminished 7th, D♭ major, D half-flat major.
• In diatonic terms: tonic, tonic half-sharp, subdominant/dominant sharp, tonic half-flat, subdominant/dominant, tonic dim7 half-sharp, tonic sharp, tonic sesquisharp.
• In measure 7, marimba 1 plays E, E♭, D, D♭, while marimba 2 layers a counter-melody of E half-sharp, E half-flat, D half-sharp, and D half-flat for contrast.

Notated Scale Using Subdivided 15/4

Each pitch step approximates a division of the 15/4 interval (major 13th), subdivided into 15, 10, and 5 equal parts. Microtonal deviations are annotated in cents beneath each note.