alina abraham - Academia.edu (original) (raw)
Papers by alina abraham
⦁ Abraham [aka: Novac, L. A.], & Charalambides, S. (2003). A New Model of Perception in (Music) Acoustics: The Equiangular Spiral Pathway, in P. Slezak (Ed.), Proceedings of the Joint International Conference on Cognitive Science with the Australasian Society for Cognitive Science. Sydney: Uni..., 2003
Argument: The harmonic series of a fundamental sound (fig. 1) follows the pathway of the equiangu... more Argument: The harmonic series of a fundamental sound (fig. 1) follows the pathway of the equiangular spiral (fig. 2). In (physics) acoustics the harmonic series of a fundamental sound analysis is made only from the perspective of a linear approach 1 only and the same approach carries over to the Theory of Music 2 . In Physics Fourier analysis brings representations of different sinusoidal wave sum models, which may not necessarily be linear. This however does not convey the inherent properties of the harmonics series which is the point the we will try illustrate by making use of the logarithmic spiral. (When Descartes discovered the spiral in the 17th century, music was leaving "the Quadrivium", the arena of sciences (Coelho, 1969)) until the recovery with the scientific aesthetics started in the middle of the 19th century with Hanslick and continued into the next century with Ghyka. 1 Fourier analysis does not refer to the relation between harmonics but to the "representation of sound's frequencies as sum of pure sinusoidal waves" 2 Pythagoras explained the perfect intervals as consonances resulting from the perfect mathematical relations of the first triangular numbers 1,2,3 and 4 ("perfect" these proportions in the sense that they will not change with any reference point, e.g. fig.1: following the harmonic (pitch/frequency) series for the other intervals the proportions will be multiple instead (imperfect): 5/4 and 9/7 and 11/9 for the major third; 6/5 and 7/6 for the minor third, etc) Continuing the Pythagorean tradition (where the perfect intervals were the expression of the universal harmony in terms of proportions _ lengths: 1/2 for the perfect octave, 2/3 for the perfect fifth and 3/4 for the perfect forth and 1/length = pitch_ together with philosophical & mathematical models ("circle of fifths", Apel, 1976), in the same tradition Boethius and Zarlino explained further intervals (Apel, 1976) relating to those to same arithmetical, and geometrical models (Boethius: the major/minor third as arithmetic/harmonic mean of the octave; Zarlino the major/minor chord)
Argument: The harmonic series of a fundamental sound (fig. 1) follows the pathway of the equiangu... more Argument: The harmonic series of a fundamental sound (fig. 1) follows the pathway of the equiangular spiral (fig. 2).
Argument: The harmonic series of a fundamental sound (fig. 1) follows the pathway of the equiangu... more Argument: The harmonic series of a fundamental sound (fig. 1) follows the pathway of the equiangular spiral (fig. 2). In (physics) acoustics the harmonic series of a fundamental sound analysis is made only from the perspective of a linear approach 1 only and the same approach carries over to the Theory of Music 2 . In Physics Fourier analysis brings representations of different sinusoidal wave sum models, which may not necessarily be linear. This however does not convey the inherent properties of the harmonics series which is the point the we will try illustrate by making use of the logarithmic spiral. (When Descartes discovered the spiral in the 17th century, music was leaving "the Quadrivium", the arena of sciences (Coelho, 1969)) until the recovery with the scientific aesthetics started in the middle of the 19th century with Hanslick and continued into the next century with Ghyka. 1 Fourier analysis does not refer to the relation between harmonics but to the "repre...
as per page 2 of the poster here on ResearchGate website; Authors: Abraham (aka: Novac) & Charala... more as per page 2 of the poster here on ResearchGate website; Authors: Abraham (aka: Novac) & Charalambides, “A New Model of Perception in (Music) Acoustics: The Equiangular Spiral Pathway,” in P. Slezak (Ed.), Proceedings of the Joint International Conference on Cognitive Science with the Australasian Society for Cognitive Science. Sidney: University of New South Wales, Vol. 2, pp. 496–500, 2003.
Not published - needing feedback/improvement , 2024
This article addresses the subject of prime numbers in the discipline of mathematicsnumber theory... more This article addresses the subject of prime numbers in the discipline of mathematicsnumber theory, from a music acoustics perspective, as discussed by a researcher musician from New Zealand. The study draws on lateral thinking, positivism, historical research, and autobiography. My aim was to look for patterns in prime numbers. I selected N = [1... 280] from the Natural Numbers Series (NNS) and organised it in base 10 and 20. I highlighted the primes. No pattern was seen. I shifted the examination towards a Pitched Sound Harmonic Series (PSHS)-that is analogue to NNS except that its partials (frequencies range) are intrinsically organised in base 2, 4, 8, etc. along the octaves. I examined a PSHS on 'C' = [1... 20]. Zooming into the sound-pitches analogue to primes, a sense of hidden patterning drifting along the octaves, emerged. I re-organised N = [1... 280] in base 8. Patterns deriving from the pair-primes 5 and 7 ocurred between numbers with a vectorial-trajectory spiralling from the top-right corner of the diagram to the opposite down-left corner, with a constant addition of 6 units, occasionally pausing there where multiples of previous units were sitting. Gaps between primes proved to always be odd numbers.
2012 Seventh International Conference on Knowledge, Information and Creativity Support Systems, 2012
For any pitched sound in nature, there is an inner structure of that sound displaying a series of... more For any pitched sound in nature, there is an inner structure of that sound displaying a series of harmonics, or partials, that vibrate with different frequencies. Due to the mathematical underpinnings of those frequencies, the pitched sound may be visualized with a Cartesian (logarithmic) spiral design . The language of mathematics and music can therefore be pictorial, and so the elements of music -e.g., intervals, rhythmic and harmonic structures; these originate in the harmonic series (THS), and can be matched against spiral and circle designs. This paper discusses such visualizations suggesting from preliminary findings that pictorial representations of music are beneficial to: I. Explain the form in a musical piece; II. Facilitate students' understanding of compositional processes in music; III. Enhance memorization in music performance; IV. Develop such visualizations into a method of teaching in music and coaching for music performance. Narrative enquiry is the framework for an envisaged qualitative study , which engages creativity and visualization in music performance, teaching, learning, coaching, music composition and analysis.
ABSTRACT For any pitched sound in nature, there is an inner structure of that sound displaying a ... more ABSTRACT For any pitched sound in nature, there is an inner structure of that sound displaying a series of harmonics, or partials, that vibrate with different frequencies. Due to the mathematical underpinnings of those frequencies, the pitched sound may be visualized with a Cartesian (logarithmic) spiral design [16]. The language of mathematics and music can therefore be pictorial, and so the elements of music - e.g., intervals, rhythmic and harmonic structures; these originate in the harmonic series (THS), and can be matched against spiral and circle designs. This paper discusses such visualizations suggesting from preliminary findings that pictorial representations of music are beneficial to: 1. Explain the form in a musical piece; 2. Facilitate students' understanding of compositional processes in music; 3. Enhance memorization in music performance; 4. Develop such visualizations into a method of teaching in music and coaching for music performance. Phenomenology and narrative enquiry is the framework for the current practice lead research [5], [23] which engages creativity and visualization in music performance, teaching, learning, coaching, music composition and analysis
as per page 2 of the poster here on ResearchGate website; Authors: Abraham (aka: Novac) & Charala... more as per page 2 of the poster here on ResearchGate website; Authors: Abraham (aka: Novac) & Charalambides, “A New Model of Perception in (Music) Acoustics: The Equiangular Spiral Pathway,” in P. Slezak (Ed.), Proceedings of the Joint International Conference on Cognitive Science with the Australasian Society for Cognitive Science. Sidney: University of New South Wales, Vol. 2, pp. 496–500, 2003.
For any pitched sound in nature, there is an inner structure of that sound displaying a series of... more For any pitched sound in nature, there is an inner structure of that sound displaying a series of harmonics, or partials, that vibrate with different frequencies. Due to the mathematical underpinnings of those frequencies, the pitched sound may be visualized with a Cartesian (logarithmic) spiral design [16]. The language of mathematics and music can therefore be pictorial, and so the elements of music - e.g., intervals, rhythmic and harmonic structures; these originate in the harmonic series (THS), and can be matched against spiral and circle designs. This paper discusses such visualizations suggesting from preliminary findings that pictorial representations of music are beneficial to: 1. Explain the form in a musical piece; 2. Facilitate students' understanding of compositional processes in music; 3. Enhance memorization in music performance; 4. Develop such visualizations into a method of teaching in music and coaching for music performance. Phenomenology and narrative enquiry...
Argument: The harmonic series of a fundamental sound (fig. 1) follows the pathway of the equiangu... more Argument: The harmonic series of a fundamental sound (fig. 1) follows the pathway of the equiangular spiral (fig. 2). In (physics) acoustics the harmonic series of a fundamental sound analysis is made only from the perspective of a linear approach 1 only and the same approach carries over to the Theory of Music 2 . In Physics Fourier analysis brings representations of different sinusoidal wave sum models, which may not necessarily be linear. This however does not convey the inherent properties of the harmonics series which is the point the we will try illustrate by making use of the logarithmic spiral. (When Descartes discovered the spiral in the 17th century, music was leaving "the Quadrivium", the arena of sciences (Coelho, 1969)) until the recovery with the scientific aesthetics started in the middle of the 19th century with Hanslick and continued into the next century with Ghyka. 1 Fourier analysis does not refer to the relation between harmonics but to the "repre...
In the process of language acquisition infants may throw tantrums parents may not be prepared for... more In the process of language acquisition infants may throw tantrums parents may not be prepared for. 'Baby Signs' language - which represents a collection of 100 universal signs common in infants, offers a solution, not to mention that research says this solution it increases all participants' IQ for the first three years of practice.
Teaching Documents by alina abraham
This thesis is a qualitative study employing autoethnography, critical autoethnography, thematic ... more This thesis is a qualitative study employing autoethnography, critical autoethnography, thematic analysis and art-based research, to explore 21 st century piano pedagogy. The study involved interviews with 10 internationally established pedagogues with studio piano practices in New Zealand, USA, and Europe-Switzerland, Germany, Hungary, Romania. In this study I argue that 21 st century piano pedagogy draws on the piano pedagogy traditions of the previous three centuries with a trend towards an increasing degree of variety, creativity,
⦁ Abraham [aka: Novac, L. A.], & Charalambides, S. (2003). A New Model of Perception in (Music) Acoustics: The Equiangular Spiral Pathway, in P. Slezak (Ed.), Proceedings of the Joint International Conference on Cognitive Science with the Australasian Society for Cognitive Science. Sydney: Uni..., 2003
Argument: The harmonic series of a fundamental sound (fig. 1) follows the pathway of the equiangu... more Argument: The harmonic series of a fundamental sound (fig. 1) follows the pathway of the equiangular spiral (fig. 2). In (physics) acoustics the harmonic series of a fundamental sound analysis is made only from the perspective of a linear approach 1 only and the same approach carries over to the Theory of Music 2 . In Physics Fourier analysis brings representations of different sinusoidal wave sum models, which may not necessarily be linear. This however does not convey the inherent properties of the harmonics series which is the point the we will try illustrate by making use of the logarithmic spiral. (When Descartes discovered the spiral in the 17th century, music was leaving "the Quadrivium", the arena of sciences (Coelho, 1969)) until the recovery with the scientific aesthetics started in the middle of the 19th century with Hanslick and continued into the next century with Ghyka. 1 Fourier analysis does not refer to the relation between harmonics but to the "representation of sound's frequencies as sum of pure sinusoidal waves" 2 Pythagoras explained the perfect intervals as consonances resulting from the perfect mathematical relations of the first triangular numbers 1,2,3 and 4 ("perfect" these proportions in the sense that they will not change with any reference point, e.g. fig.1: following the harmonic (pitch/frequency) series for the other intervals the proportions will be multiple instead (imperfect): 5/4 and 9/7 and 11/9 for the major third; 6/5 and 7/6 for the minor third, etc) Continuing the Pythagorean tradition (where the perfect intervals were the expression of the universal harmony in terms of proportions _ lengths: 1/2 for the perfect octave, 2/3 for the perfect fifth and 3/4 for the perfect forth and 1/length = pitch_ together with philosophical & mathematical models ("circle of fifths", Apel, 1976), in the same tradition Boethius and Zarlino explained further intervals (Apel, 1976) relating to those to same arithmetical, and geometrical models (Boethius: the major/minor third as arithmetic/harmonic mean of the octave; Zarlino the major/minor chord)
Argument: The harmonic series of a fundamental sound (fig. 1) follows the pathway of the equiangu... more Argument: The harmonic series of a fundamental sound (fig. 1) follows the pathway of the equiangular spiral (fig. 2).
Argument: The harmonic series of a fundamental sound (fig. 1) follows the pathway of the equiangu... more Argument: The harmonic series of a fundamental sound (fig. 1) follows the pathway of the equiangular spiral (fig. 2). In (physics) acoustics the harmonic series of a fundamental sound analysis is made only from the perspective of a linear approach 1 only and the same approach carries over to the Theory of Music 2 . In Physics Fourier analysis brings representations of different sinusoidal wave sum models, which may not necessarily be linear. This however does not convey the inherent properties of the harmonics series which is the point the we will try illustrate by making use of the logarithmic spiral. (When Descartes discovered the spiral in the 17th century, music was leaving "the Quadrivium", the arena of sciences (Coelho, 1969)) until the recovery with the scientific aesthetics started in the middle of the 19th century with Hanslick and continued into the next century with Ghyka. 1 Fourier analysis does not refer to the relation between harmonics but to the "repre...
as per page 2 of the poster here on ResearchGate website; Authors: Abraham (aka: Novac) & Charala... more as per page 2 of the poster here on ResearchGate website; Authors: Abraham (aka: Novac) & Charalambides, “A New Model of Perception in (Music) Acoustics: The Equiangular Spiral Pathway,” in P. Slezak (Ed.), Proceedings of the Joint International Conference on Cognitive Science with the Australasian Society for Cognitive Science. Sidney: University of New South Wales, Vol. 2, pp. 496–500, 2003.
Not published - needing feedback/improvement , 2024
This article addresses the subject of prime numbers in the discipline of mathematicsnumber theory... more This article addresses the subject of prime numbers in the discipline of mathematicsnumber theory, from a music acoustics perspective, as discussed by a researcher musician from New Zealand. The study draws on lateral thinking, positivism, historical research, and autobiography. My aim was to look for patterns in prime numbers. I selected N = [1... 280] from the Natural Numbers Series (NNS) and organised it in base 10 and 20. I highlighted the primes. No pattern was seen. I shifted the examination towards a Pitched Sound Harmonic Series (PSHS)-that is analogue to NNS except that its partials (frequencies range) are intrinsically organised in base 2, 4, 8, etc. along the octaves. I examined a PSHS on 'C' = [1... 20]. Zooming into the sound-pitches analogue to primes, a sense of hidden patterning drifting along the octaves, emerged. I re-organised N = [1... 280] in base 8. Patterns deriving from the pair-primes 5 and 7 ocurred between numbers with a vectorial-trajectory spiralling from the top-right corner of the diagram to the opposite down-left corner, with a constant addition of 6 units, occasionally pausing there where multiples of previous units were sitting. Gaps between primes proved to always be odd numbers.
2012 Seventh International Conference on Knowledge, Information and Creativity Support Systems, 2012
For any pitched sound in nature, there is an inner structure of that sound displaying a series of... more For any pitched sound in nature, there is an inner structure of that sound displaying a series of harmonics, or partials, that vibrate with different frequencies. Due to the mathematical underpinnings of those frequencies, the pitched sound may be visualized with a Cartesian (logarithmic) spiral design . The language of mathematics and music can therefore be pictorial, and so the elements of music -e.g., intervals, rhythmic and harmonic structures; these originate in the harmonic series (THS), and can be matched against spiral and circle designs. This paper discusses such visualizations suggesting from preliminary findings that pictorial representations of music are beneficial to: I. Explain the form in a musical piece; II. Facilitate students' understanding of compositional processes in music; III. Enhance memorization in music performance; IV. Develop such visualizations into a method of teaching in music and coaching for music performance. Narrative enquiry is the framework for an envisaged qualitative study , which engages creativity and visualization in music performance, teaching, learning, coaching, music composition and analysis.
ABSTRACT For any pitched sound in nature, there is an inner structure of that sound displaying a ... more ABSTRACT For any pitched sound in nature, there is an inner structure of that sound displaying a series of harmonics, or partials, that vibrate with different frequencies. Due to the mathematical underpinnings of those frequencies, the pitched sound may be visualized with a Cartesian (logarithmic) spiral design [16]. The language of mathematics and music can therefore be pictorial, and so the elements of music - e.g., intervals, rhythmic and harmonic structures; these originate in the harmonic series (THS), and can be matched against spiral and circle designs. This paper discusses such visualizations suggesting from preliminary findings that pictorial representations of music are beneficial to: 1. Explain the form in a musical piece; 2. Facilitate students' understanding of compositional processes in music; 3. Enhance memorization in music performance; 4. Develop such visualizations into a method of teaching in music and coaching for music performance. Phenomenology and narrative enquiry is the framework for the current practice lead research [5], [23] which engages creativity and visualization in music performance, teaching, learning, coaching, music composition and analysis
as per page 2 of the poster here on ResearchGate website; Authors: Abraham (aka: Novac) & Charala... more as per page 2 of the poster here on ResearchGate website; Authors: Abraham (aka: Novac) & Charalambides, “A New Model of Perception in (Music) Acoustics: The Equiangular Spiral Pathway,” in P. Slezak (Ed.), Proceedings of the Joint International Conference on Cognitive Science with the Australasian Society for Cognitive Science. Sidney: University of New South Wales, Vol. 2, pp. 496–500, 2003.
For any pitched sound in nature, there is an inner structure of that sound displaying a series of... more For any pitched sound in nature, there is an inner structure of that sound displaying a series of harmonics, or partials, that vibrate with different frequencies. Due to the mathematical underpinnings of those frequencies, the pitched sound may be visualized with a Cartesian (logarithmic) spiral design [16]. The language of mathematics and music can therefore be pictorial, and so the elements of music - e.g., intervals, rhythmic and harmonic structures; these originate in the harmonic series (THS), and can be matched against spiral and circle designs. This paper discusses such visualizations suggesting from preliminary findings that pictorial representations of music are beneficial to: 1. Explain the form in a musical piece; 2. Facilitate students' understanding of compositional processes in music; 3. Enhance memorization in music performance; 4. Develop such visualizations into a method of teaching in music and coaching for music performance. Phenomenology and narrative enquiry...
Argument: The harmonic series of a fundamental sound (fig. 1) follows the pathway of the equiangu... more Argument: The harmonic series of a fundamental sound (fig. 1) follows the pathway of the equiangular spiral (fig. 2). In (physics) acoustics the harmonic series of a fundamental sound analysis is made only from the perspective of a linear approach 1 only and the same approach carries over to the Theory of Music 2 . In Physics Fourier analysis brings representations of different sinusoidal wave sum models, which may not necessarily be linear. This however does not convey the inherent properties of the harmonics series which is the point the we will try illustrate by making use of the logarithmic spiral. (When Descartes discovered the spiral in the 17th century, music was leaving "the Quadrivium", the arena of sciences (Coelho, 1969)) until the recovery with the scientific aesthetics started in the middle of the 19th century with Hanslick and continued into the next century with Ghyka. 1 Fourier analysis does not refer to the relation between harmonics but to the "repre...
In the process of language acquisition infants may throw tantrums parents may not be prepared for... more In the process of language acquisition infants may throw tantrums parents may not be prepared for. 'Baby Signs' language - which represents a collection of 100 universal signs common in infants, offers a solution, not to mention that research says this solution it increases all participants' IQ for the first three years of practice.
This thesis is a qualitative study employing autoethnography, critical autoethnography, thematic ... more This thesis is a qualitative study employing autoethnography, critical autoethnography, thematic analysis and art-based research, to explore 21 st century piano pedagogy. The study involved interviews with 10 internationally established pedagogues with studio piano practices in New Zealand, USA, and Europe-Switzerland, Germany, Hungary, Romania. In this study I argue that 21 st century piano pedagogy draws on the piano pedagogy traditions of the previous three centuries with a trend towards an increasing degree of variety, creativity,