Towards a Music Algebra: Fundamental Harmonic Substitutions in Jazz

Cataldo, Carmine

doi:10.22161/ijaers.5.1.9

Cited by 13 publications

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“…SCALES AS VECTORS If we denote with X a generic note belonging to the Chromatic scale, and with t a whole tone interval [1] …”

Section: IImentioning

confidence: 99%

A Simplified Introduction to Music Algebra: from the Scale Vectors to the Modal Tensor

Cataldo¹

2018

IJAERS

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Abstract-In I. BRIEF INTRODUCTIONWe start by defining the Ionian scale a vector whose components are nothing but the degrees of the scale. The same procedure is applied to all the scales that derive from the above-mentioned. Subsequently, we define the Ionian Modal Tensor and, by resorting to the concepts of standard basis and dot product, we deduce the seventh chords vector. A reasonable mastery of the fundamental notions concerning vectors and matrices is required. II. SCALES AS VECTORSFor example, by setting X = C, from (1) we banally obtain:Obviously, whatever scale can be represented as a vector. In this regard, let's consider all the modes (or scales) that can be deduced from the Ionian one (Dorian, Phrygian, Lydian, Mixolydian, Aeolian, Locrian) [3] [4]. Bearing in mind the Ionian harmonization, and denoting with s Ion,n the scale vector derived from the n-th degree of the Ionian scale (n is a positive integer that runs from 1 to 7), we can write, with obvious meaning of the notation, the following:,6 ( ) = ( ) = + 9 2 (8)Clearly, the opposite procedure can be easily followed: in other terms, we can choose any mode (among those to date considered) and determine the Ionian scale from which it derives (if we select a mode and set Y, we can determine X). If we set X = C, from (3), (4), (5), (6), (7), (8) and (9) we obtain, respectively:,2 ( ) = ( ) = ( , , , , , , ),3 ( ) = ℎ ( ) = ( , , , , , , ),4 ( ) = ( ) = ( , , , , , , ),5 ( ) = ( ) = ( , , , , , , ),6 ( ) = ( ) = ( , , , , , , ),7 ( ) = ( ) = ( , , , , , , )

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“…SCALES AS VECTORS If we denote with X a generic note belonging to the Chromatic scale, and with t a whole tone interval [1] …”

Section: IImentioning

confidence: 99%

A Simplified Introduction to Music Algebra: from the Scale Vectors to the Modal Tensor

Cataldo¹

2018

IJAERS

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“…We can write: In order to clarify the last transformations, let's suppose we are dealing with a song in the key of C. The abovementioned transformation simply requires that the chord F7, if preceded by G7 or D b 7, must be regarded as deriving from a Tritone Substitution applied to B7 (that, in turn, will be regarded, at a later time, as deriving from a Secondary Dominant Substitution [6] [7] applied to Bm7b5).…”

Section: Similitude Inverse Substitutionsmentioning

confidence: 99%

Music Algebra: Harmonic Progressions Analysis and CAT (Cataldo Advanced Transformations)

Cataldo¹

2018

IJAERS

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“…Se indichiamo X una generica nota appartenente alla scala Cromatica, e con t un intervallo pari ad un tono intero [1] [2], possiamo rappresentare la scala Ionica in forma vettoriale:…”

Section: Scale In Forma DI Vettoriunclassified

Towards a Music Algebra: Fundamental Harmonic Substitutions in Jazz

Abstract: Abstract-In

Cited by 13 publications

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A Simplified Introduction to Music Algebra: from the Scale Vectors to the Modal Tensor

A Simplified Introduction to Music Algebra: from the Scale Vectors to the Modal Tensor

Music Algebra: Harmonic Progressions Analysis and CAT (Cataldo Advanced Transformations)

Algebra Musicale: dai Vettori Scala al Tensore Modale - Music Algebra: from the Scale Vectors to the Modal Tensor

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