Pitch-class prevalence in plainchant, scale-degree consonance, and the origin of the rising leading tone

Parncutt, Richard

doi:10.1080/09298215.2019.1642360

Cited by 4 publications

(2 citation statements)

References 57 publications

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“…The last column in Tables 1-3 is the relative error between the algorithm in this paper and the three-level clipping method. It can be seen from Table 1 that the relative error rate of the two methods is only within 5.1% when the rhythm of the music is slow [14]. This shows that the traditional three-level clipping method is close to the recognition rate of this method.…”

Section: Resultsmentioning

confidence: 80%

The Stability Model of Piano Tone Tuning Based on Ordinary Differential Equations

Guo

2022

Applied Mathematics and Nonlinear Sciences

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Based on the theory of ordinary differential equations, this paper proposes a stable and discriminative method for piano tone tuning. We perform discriminative training on the hidden Markov tone model according to ordinary differential equations' feature extraction parameters and model parameters. The model can improve the recognition rate of piano tones. This paper trains and tests the MAPS universal dataset for musical transcription of automatic piano tones. The model is uniformly trained on the synthetic part and tested on the real recording part. The experimental study found that the proposed model has high recognition stability and accuracy in piano tone recognition.

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Section: Resultsmentioning

confidence: 80%

The Stability Model of Piano Tone Tuning Based on Ordinary Differential Equations

Guo

2022

Applied Mathematics and Nonlinear Sciences

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“…x in order from low to high frequency. Since the low frequency note when the chord is emitted affects people's auditory experience more [27], it will have a greater impact on the overall consonance degree, the two low frequency notes 1…”

Section: Triad Consonance Degreementioning

confidence: 99%

Quantum adaptive approach to chord consonance modeling

HAN,

CHEN,

TIAN

et al. 2023

Proc. Rom. Acad. Ser. A - Math. Phys. Tech. Sci. Inf. Sci.

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In this paper, a chord consonance model is established via complex law analysis to improve the accuracy of music emotion calculation. To address the coupling and the uncertainty of the complex law, quantum adaptive method is applied to the chord consonance calculation. Musical tones, with subjective difference and uncertainty, are constructed into interval consonance quantum state using parameter adaptive method. Quantum logic gates are introduced to describe the coupling between musical tones to establish the chord consonance model. Then, a mixed state density matrix is designed to optimize the calculation of consonance. Experimental results are provided to verify the validity and accuracy of the modelling.

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The Origin of the Dominant: Schoenberg's ‘Strong Progression’ and the Realisation of Implied Virtual Pitches

PARNCUTT

2024

Music Analysis

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In major‐minor tonality, V implies I, and rising fourths, falling thirds and rising seconds between successive chord roots are more common than falling fourths, rising thirds and falling seconds respectively. Possible explanations involve history (in two‐part medieval counterpoint, harmonic major sixths resolved to octaves – maintained in V–I); the rising leading note (V–I includes it, IV–I does not); acoustic speculation (in V–I, the third harmonic of resolves to the second); voice leading (in V7–I, a tritone resolves to a third by contrary step); melodic closure (a rising melodic leap implies subsequent falling steps, and melodies often end with –, harmonised V–I); root newness (chords ‘progress’ if the second chord's root is not part of the first); and tonal stability (V is less stable than IV, giving it a stronger ‘urge’ to resolve). An additional possibility combines the ‘virtual‐pitch’ theory of Ernst Terhardt with the ‘implication‐realisation’ theory of Leonard B. Meyer and Eugene Narmour. Major and minor triads imply subsidiary virtual pitches (missing fundamentals; see Rameau's ‘fundamental bass’) at third and fifth intervals below the root. These weakly perceived pitches are realised in the next chord if the root falls by a third or rises a fourth or major second, creating a feeling of forward progression – while also facilitating intonation for singers and melodic instrumentalists. The theory correctly predicts that successive harmonic complex (but not pure) tones an octave apart sound more similar if rising, and rising octaves are more common than falling in melody. It also explains why Classical modulations are asymmetrical in the opposite direction, major keys tending to modulate to V (not IV) and minor to III (not VI): accidental flats tend to be more perceptually salient or stable than sharps.

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Pitch-class prevalence in plainchant, scale-degree consonance, and the origin of the rising leading tone

Cited by 4 publications

References 57 publications

The Stability Model of Piano Tone Tuning Based on Ordinary Differential Equations

The Stability Model of Piano Tone Tuning Based on Ordinary Differential Equations

Quantum adaptive approach to chord consonance modeling

The Origin of the Dominant: Schoenberg's ‘Strong Progression’ and the Realisation of Implied Virtual Pitches

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