Revision of Terhardt's Psychoacoustical Model of the Root(s) of a Musical Chord

1988 ◽  
Vol 6 (1) ◽  
pp. 65-93 ◽  
Author(s):  
Richard Parncutt
Keyword(s):  
Music Theory ◽  
Generalized Model ◽  
New Model ◽  
Pitch Class ◽  
Absolute Value ◽  
Class C

The predictions of Terhardt's octave-generalized model of the root of a musical chord occasionally disagree with music theory (notably, in the case of the minor triad). The model is improved by assigning appropriate weights to the intervals used in the model's "subharmonic matching" routine. These intervals, called "root-supports," include the P8 (unison), P5, M3, m7, M9 (M2), and m3. The new model calculates the salience of each pitch class (C, C#/Db..B) as an absolute value. The most likely candidate for the root of a chord corresponds to the most salient pitch class in all cases where the root is unambiguously defined in music theory. The model also calculates a "root ambiguity" value for each chord, a measure of its dissonance. Effects of voicing (inversion, spacing, and doubling) and context on the root are considered.

Some new pitch paradoxes and their implications

1992 ◽  
Vol 336 (1278) ◽  
pp. 391-397 ◽  
Keyword(s):  
Speech Production ◽  
Spectral Envelope ◽  
Pitch Class ◽  
Speech Characteristics ◽  
Class C ◽  
Tritone Paradox ◽  
Sound Patterns ◽  
The Way

This paper explores two new paradoxical sound patterns. The tones used to produce these patterns consist of six octave-related harmonics, whose amplitudes are scaled by a bell-shaped spectral envelope; these tones are clearly defined in terms of pitch class (C, C#, D, and so on) but are poorly defined in term s of height. One pattern consists of two tones that are separated by a half-octave. It is heard as ascending when played in one key, yet as descending when played in a different key. Further, when the pattern is played in any one key it is heard as ascending by some listeners but as descending by others (the tritone paradox). Another pattern that consists of simultaneous pairs of tones displays related properties (the semitone paradox). It is shown that the way the tritone paradox is perceived correlates with the speech characteristics of the listener, including his or her linguistic dialect. The findings suggest that the same, culturally acquired representation of pitch classes influences both speech production and also perception of this musical pattern.

scholarly journals Effects of Chord Inversion and Bass Patterns on Harmonic Expectancy in Musicians

2021 ◽  
Vol 39 (1) ◽  
pp. 41-62
Author(s):  
Emily Schwitzgebel ◽  
Christopher Wm. White
Keyword(s):  
Music Theory ◽  
Computational Experiment ◽  
Behavioral Responses ◽  
Computational Experiments ◽  
Pitch Class ◽  
Frequency Measurements ◽  
Transition Models ◽  
N Gram

This study tests the respective roles of pitch-class content and bass patterns within harmonic expectation using a mix of behavioral and computational experiments. In our first two experiments, participants heard a paradigmatic chord progression derived from music theory textbooks and were asked to rate how well different target endings completed that progression. The completion included the progression’s paradigmatic target, different inversions of that chord (i.e., different members of the harmony were heard in the lowest voice), and a “mismatched” target, a triad that shared its lowest pitch with the paradigmatic ending but altered other pitch-class content. Participants generally rated the paradigmatic target most highly, followed by other inversions of that chord, with lowest ratings generally elicited by the mismatched target. This suggests that listeners’ harmonic expectations are sensitive to both bass patterns and pitch-class content. However, these results did not hold in all cases. A final computational experiment was run to determine whether variations in behavioral responses could be explained by corpus statistics. To this end, n-gram chord-transition models and frequency measurements were compiled for each progression. Our findings suggest that listeners rate highly and have stronger expectations about chord progressions that occur frequently and behave consistently within tonal corpora.

The Micro- and Macrostructural Design of Improvised Music

1987 ◽  
Vol 5 (2) ◽  
pp. 133-172 ◽  
Author(s):  
Jeff Pressing
Keyword(s):  
Music Theory ◽  
Time Scale ◽  
Distribution Patterns ◽  
Traditional Music ◽  
Pitch Class ◽  
Microstructural Parameters ◽  
Performance Effects ◽  
Improvised Music ◽  
Automatic Transcription ◽  
Pitch Class Sets

Two short pieces of freely improvised music by the same performer were recorded in microstructural detail by the use of a specially constructed automatic transcription apparatus. The apparatus consists of a modified DX7 synthesizer and 2650 microprocessor which interfaces with other computers for data processing. The resultant music is transcribed into a modified form of traditional notation and subjected to both micro- and macrostructural analysis. Microanalysis includes the areas of timing (interonset and duration distributions, displacement, chordal spreads, etc.), dynamics ( key velocity, quantization, chordal patterns, etc.), and legatoness (relative, absolute, pedaling). Macroanalysis uses the full panoply of devices from traditional music theory (tonal procedures, rhythmic and motivic design, pitch class sets, etc.). Correlations between microstructural parameters, and with macrostructure, were found to be highly significant in Improvisation A, which had a supplied external pulse, but largely absent in Improvisation B, which had no such pulse. Where pulse was present, rhythmic design was found to be based largely on pulse subdivision and shifting. Some performance effects (e.g., chordal spreads) operated over a time scale of 10 msec or less. Others (e.g., synchronization to an external pulse) showed less resolution. Differences in the distribution patterns of interonset times, durations, and legatoness suggest three independent underlying temporal mechanisms that may sometimes link together in coordination with macrostructure. Quantization ("categorical production") of some variables (interonset times, key velocities) was clearly established. The results were also interpreted in relation to an earlier model of improvisation (Pressing, 1987).

Introducing a New Model of Sweet Taste Receptor, a Class C G-protein Coupled Receptor (C GPCR)

2019 ◽  
Vol 77 (3) ◽  
pp. 227-243 ◽  
Author(s):  
Elaheh Kashani-Amin ◽  
Amirhossein Sakhteman ◽  
Bagher Larijani ◽  
Azadeh Ebrahim-Habibi
Keyword(s):  
G Protein ◽  
Taste Receptor ◽  
Sweet Taste ◽  
G Protein Coupled Receptor ◽  
New Model ◽  
Sweet Taste Receptor ◽  
Class C ◽  
G Protein Coupled

scholarly journals Why Are There Twenty-Nine Tetrachords? A Tutorial on Combinatorics and Enumeration in Music Theory

2007 ◽  
Vol 13 (4) ◽  
Author(s):  
Julian Hook
Keyword(s):  
Eighteenth Century ◽  
Music Theory ◽  
Equivalence Classes ◽  
Equivalence Relations ◽  
Pitch Class ◽  
Musical Structures ◽  
Pitch Class Sets ◽  
Combinatorial Methods ◽  
Pólya’S Enumeration Theorem

Many techniques in combinatorial mathematics have applications in music theory. Standard formulas for permutations and combinations may be used to enumerate melodies, rhythms, rows, pitch-class sets, and other familiar musical entities subject to various constraints on their structure. Some music scholars in the eighteenth century advocated elementary combinatorial methods, including dice games, as aids in composition. Problems involving the enumeration of set classes, row classes, and other types of equivalence classes are more difficult and require advanced techniques for their solution, notably Pólya’s Enumeration Theorem. Such techniques are applicable in a wide variety of situations, enabling the enumeration of diverse musical structures in scales of various cardinalities and under various definitions of equivalence relations.

The Hitachi Model HS-8 Electron Microscope

1967 ◽  
Vol 25 ◽  
pp. 238-239
Author(s):  
H. Akabori ◽  
K. Nishiwaki ◽  
K. Yoneta
Keyword(s):  
Electron Microscope ◽  
New Model ◽  
Predecessor Model

By improving the predecessor Model HS- 7 electron microscope for the purpose of easier operation, we have recently completed new Model HS-8 electron microscope featuring higher performance and ease of operation.

516: A Simplified Method to Estimate the Absolute Renal Uptake of 99MTC-DMSA: Evaluation with a New Model using the Radioactivity of Nephrectomy Specimens as Reference

2005 ◽  
Vol 173 (4S) ◽  
pp. 140-141
Author(s):  
Mariana Lima ◽  
Celso D. Ramos ◽  
Sérgio Q. Brunetto ◽  
Marcelo Lopes de Lima ◽  
Carla R.M. Sansana ◽  
...  
Keyword(s):  
New Model ◽  
Renal Uptake ◽  
Simplified Method ◽  
The Absolute
Sign in / Sign up

Export Citation Format

Share Document