English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We propose a new way of analyzing musical pieces by using the exceptionalmusical icosahedra where all the major/minor triads are represented by goldentriangles or golden gnomons. First, we introduce a concept of the goldenneighborhood that characterizes golden triangles/gnomons that neighbor a givengolden triangle or gnomon. Then, we investigate a relation between theexceptional musical icosahedra and the neo-Riemannian theory, and find that thegolden neighborhoods and the icosahedron symmetry relate any major/minor triadwith any major/minor triad. Second, we show how the exceptional musicalicosahedra are applied to analyzing harmonies constructed by four or moretones. We introduce two concepts, golden decomposition and golden singular. Thegolden decomposition is a decomposition of a given harmony into the minimumnumber of harmonies constructing the given harmony and represented by thegolden figure (a golden triangle, a golden gnomon, or a golden rectangle). Aharmony is golden singular if and only if the harmony does not have goldendecompositions. We show results of the golden analysis (analysis by the goldendecomposition) of the tertian seventh chords and the mystic chord. While thedominant seventh chord is the only tertian seventh chord that is goldensingular in the type 1[star] and the type 4[star] exceptional musicalicosahedron, the half-diminished seventh chord is the only tertian seventhchord that is golden singular in the type 2 [star] and the type 3[star]exceptional musical icosahedron. Last, we apply the golden analysis to thefamous prelude in C major composed by Johann Sebastian Bach (BWV 846). We found7 combinations of the golden figures on the type 2 [star] or the type 3 [star]exceptional musical icosahedron dually represent all the measures of the BWV846.

General Theory of Music by Icosahedron 2: Analysis of musical pieces by the exceptional musical icosahedra