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Tonnetz torus Music Theory in 2019 Music Music Theory Geometry

Tonnetz torus Music Theory in 2019 Music Music Theory Geometry

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Are there geometric symmetries in musical harmonics?

The Tonnetz diagram (note that the arrangement here is inverted relative to that used in the text. It appears that there is no rigid standard, ...

John Carlos Baez on Twitter: "The geometry of music revealed! Red lines connect notes that are a major third apart. Green lines connect notes a minor third ...

The Tonnetz in í µí¼' !/!-space. Consonant triads, dyads

The Oettingen/Riemann Tonnetz.

Excerpt of the Tonnetz: trying to match a torus surface to the unit cell.

The tonnetz representation of PRL and vertices transformations with respect to the C major chord.

tonnetz-grid.jpg

The Circle of Fifth.

Tonnetz

Overlap of note sound. Two neighboring notes overlay for duo-chords, three neighboring

For example, the Tonnetz generated by the chords {C,C#,F#}, {C,F,F#} and their transpositions is a circle of 6 tetrahedra. I took some time to draw this ...

C major is three Tonnetz links away from F minor, the same as Eb major

a) P transformation b) R transformation c) L transformation.

J. D. Heinichen's chart of key relationships (1728: 837). Note that in contrast

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Tonnetz-LocalChorts-2

Two ways of chromatically filling a voice-leading whole step are inversionally related, differing

Using C as the base tone class, this circle of fifths (left) demonstrates

Constant-quotient profiles ordered by pitch-class for major-key preludes ( as

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Chew's Spiral Array (adapted from ...

Tonnetz-Torus

Distributions by key and pitch-class compared. Individual plots for the distribution and elapsed

HomTable-4

Chord progression from Pachelbel, Canon in D. Musical ...

Arnold Schoenberg's generic chart of tonal regions in the major mode (1948) is

Tonnetz-NumericalForm

The musical clock. I 0 applied to a C-major triad yields an f-minor triad.

The melody of the contrasting middle section of the Trio creates a chromatic line by juxtaposing

A: Neo-Riemannian Tonnetz. Triangular net with keys as vertices and triads as

Circle-of-Fifths

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Tonnetz-Euler

An overview paper by Herb Klitzner of Quaternion 4D music

Waller's torus from ...

Neo-Riemannian Tonnetz Piano Keys, Music Theory, Jazz, Musicals, Lattices,

Basic Music Theory, Music Visualization, Music Chords, Scale,

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Circle of Fifth's

The musical clock.

Torus and Music Theory Explained

Circle of fifths

(A) Represents the so-called Tonnetz torus on which various pitches can be

Simplices

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Circle of Fifths / Illuminati Eye Original Art by Jen Sorenson. Eric Sorenson · geometry and music

Map of Yale University Campus, overlaid with overlapping Tonnetz nodes.

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iPhone chord progression app review on Practiceapps

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Extra Music Notation: Debussy Arabesque #1 / Infograph

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Category:Tonnetz - Wikimedia Commons Circle Of Fifths, Music Theory, Guitar Chords,

Music; Musician; Score; Composition; Composer; Classical Music; Baroque; Notes

The octatonic system

Transformational Theory in the Undergraduate Curriculum- A Case for Teaching the Neo-Riemannian Approach | Chord (Music) | Harmony

Characterizing A World Music Virtuoso And Potential Remote Teacher: Not So Easy. Music Visualization

Schematic summary of Leman's (2000) periodicity pitch model (Steps 1–3)

HomTable-3

Interval spacing in Isochords' Tonnetz grid between root and nearest tone. Concentric circles denote

HomTable-1

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Lenin, Marxism, Spiral of History. Evocative of the spiral of fifths. Douglas Hope · ACTIVE Music Theory Data Visualizations

+Inversion Symbols +Diatonic Chord +Progressions

(A) Torus as a dynamic model for the recreation (rebirth) of our

Figure 3: Movements and their musical output

Fifteen first chords of Chopin's Prelude 4 Op.28. On the left its simplicial

Part of the calculation of Ritz (ref. M.J. Gander and G. Wanner,

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Chromatic Transformations in Nineteenth Century Music (Kopp 2002) | Chord ( Music) | Harmony

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Example of fundamental bass progression under a chord progression demonstrating the rule of the octave

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Construction of a torus (left) by connecting the two ends of a cylinder that

Various modalities of toroidal geometry: (A) Nested torus structure (B) Torus

Plots of observed and fitted RTs from the stepwise model (Equation 2) across different

rifles: “ Edgard Varèse, Score for Poème électronique ” Music Drawings, Experimental Music

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Polyrhythmic Metronome. Douglas Hope · ACTIVE Music Theory Data Visualizations

Coltrane, John (1926-1967). HANDWRITTEN ALTO SAXOPHONE SOLO ARRANGEMENT FOR “BODY AND SOUL”

Schoenberg, 1936.

An octatonic collection

Topography of tonality sensitivity of rostroventral prefrontal cortex in three listeners across three scanning sessions each

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A: Plot of the local/global CI correlation across time for four melodies from

The nucleous of all music theory - the circle of

Figure 11. A network mapped onto another. One can map musical networks onto visuals

Fig. 3. Complementary WFME scales (a) 7-in-12,

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Early manuscripts in Latin with music notation. Troparium et prosarium Sancti Martialis Lemovicensis 0975-

Folio of the Rossi Codex upon which is written a madrigal. The Codex is one of the earliest sources of Trecento Secular Polyphonic Music.

On the top, the unfolding process is applied to C(3, 4,

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By the way, I'm not introducing anything new here. In fact, Louis Bigo has been working on this simplicial approach in IRCAM. His Ph.D. thesis is available ...