On the Connection between Interval Size Functions and Path Counting

Author(s):  
Evangelos Bampas ◽  
Andreas-Nikolas Göbel ◽  
Aris Pagourtzis ◽  
Aris Tentes
Keyword(s):  
2016 ◽  
Vol 26 (2) ◽  
pp. 421-467 ◽  
Author(s):  
Evangelos Bampas ◽  
Andreas-Nikolas Göbel ◽  
Aris Pagourtzis ◽  
Aris Tentes
Keyword(s):  

2020 ◽  
Author(s):  
Frank Russo ◽  
Dominique T Vuvan ◽  
William Forde Thompson

Note-to-note changes in brightness are able to influence the perception of interval size. Changes that are congruent with pitch tend to expand interval size, whereas changes that are incongruent tend to contract. In the case of singing, brightness of notes can vary as a function of vowel content. In the present study, we investigated whether note-to-note changes in brightness arising from vowel content influence perception of relative pitch. In Experiment 1, three-note sequences were synthesized so that they varied with regard to the brightness of vowels from note to note. As expected, brightness influenced judgments of interval size. Changes in brightness that were congruent with changes in pitch led to an expansion of perceived interval size. A follow-up experiment confirmed that the results of Experiment 1 were not due to pitch distortions. In Experiment 2, the final note of three-note sequences was removed, and participants were asked to make speeded judgments of the pitch contour. An analysis of response times revealed that brightness of vowels influenced contour judgments. Changes in brightness that were congruent with changes in pitch led to faster response times than did incongruent changes. These findings show that the brightness of vowels yields an extra-pitch influence on the perception of relative pitch in song.


2021 ◽  
pp. 2150019
Author(s):  
Takashi Komatsu ◽  
Norio Konno ◽  
Hisashi Morioka ◽  
Etsuo Segawa

We consider the time-independent scattering theory for time evolution operators of one-dimensional two-state quantum walks. The scattering matrix associated with the position-dependent quantum walk naturally appears in the asymptotic behavior at the spatial infinity of generalized eigenfunctions. The asymptotic behavior of generalized eigenfunctions is a consequence of an explicit expression of the Green function associated with the free quantum walk. When the position-dependent quantum walk is a finite rank perturbation of the free quantum walk, we derive a kind of combinatorial construction of the scattering matrix by counting paths of quantum walkers. We also mention some remarks on the tunneling effect.


2020 ◽  
Vol 3 ◽  
pp. 205920432094906
Author(s):  
Aaron Carter-Ényì ◽  
Quintina Carter-Ényì

Smaller corpora and individual pieces are compared to a large corpus of 2,447 hymns using two measures of melodic angularity: mean interval size and pivot frequency. European art music and West African melodies may exhibit extreme angularity. We argue in the latter that angularity is motivated by linguistic features of tone-level languages. We also found the mean interval sizes of African-American Spirituals and Southern Harmony exceed contemporary hymnody of the 19th century, with levels similar to Nigerian traditional music (Yorùbá oríkì and story songs from eastern Nigeria). This is consistent with the account of W. E. B. Du Bois, who argued that African melody was a primary source for the development of American music. The development of the American spiritual coincides with increasing interval size in 19th-century American hymnody at large, surpassing the same measure applied to earlier European hymns. Based on these findings, we recommend techniques of melodic construction taught by music theorists, especially preference rules for step-wise motion and gap-fill after leaps, be tempered with counterexamples that reflect broader musical aesthetics. This may be achieved by introducing popular music, African and African Diaspora music, and other non-Western music that may or may not be consistent with voice leading principles. There are also many examples from the European canon that are highly angular, like Händel’s “Hallelujah” and Schönberg’s Pierrot Lunaire. Although the tendency of textbooks is to reinforce melodic and part-writing prescriptions with conducive examples from the literature, new perspectives will better equip performers and educators for current music practice.


2019 ◽  
Vol 37 (1) ◽  
pp. 57-65 ◽  
Author(s):  
Frank A. Russo ◽  
Dominique T. Vuvan ◽  
William Forde Thompson

Note-to-note changes in brightness are able to influence the perception of interval size. Changes that are congruent with pitch tend to expand interval size, whereas changes that are incongruent tend to contract. In the case of singing, brightness of notes can vary as a function of vowel content. In the present study, we investigated whether note-to-note changes in brightness arising from vowel content influence perception of relative pitch. In Experiment 1, three-note sequences were synthesized so that they varied with regard to the brightness of vowels from note to note. As expected, brightness influenced judgments of interval size. Changes in brightness that were congruent with changes in pitch led to an expansion of perceived interval size. A follow-up experiment confirmed that the results of Experiment 1 were not due to pitch distortions. In Experiment 2, the final note of three-note sequences was removed, and participants were asked to make speeded judgments of the pitch contour. An analysis of response times revealed that brightness of vowels influenced contour judgments. Changes in brightness that were congruent with changes in pitch led to faster response times than did incongruent changes. These findings show that the brightness of vowels yields an extra-pitch influence on the perception of relative pitch in song.


1991 ◽  
Vol 57 (5) ◽  
pp. 417-425 ◽  
Author(s):  
Alan C. Repp ◽  
David Felce ◽  
Lyle E. Barton

2006 ◽  
Vol 35 (1) ◽  
pp. 3-11
Author(s):  
Ananda Sen ◽  
Devadatta Kulkarni

2006 ◽  
Vol 52 (5) ◽  
pp. 880-885 ◽  
Author(s):  
Graham Ross Dallas Jones

Abstract Background: The reporting interval is the bin size used to report numerical pathology results and must be determined for every analyte. The influence of the size of the reporting interval on the critical difference (CD) between two results from the same patient has not been addressed previously. Methods: The effect of changing the reporting-interval size (RIS) on CDs was modeled by use of a spreadsheet application. The findings were applied to data on CDs with analytical precision values from our laboratory. Results: As the RIS increases relative to the combined analytical and within-person biological variation, there is an approximately linear increase in the CD from the value determined by use of published techniques. The revised estimate is as follows: CD = 21/2 × z × (SDa2 + SDi2)1/2 + 1.5 × RIS, where CD, SD, and RIS are all in the same units. This effect is seen for any probability associated with the critical difference and for both uni- and bidirectional changes. Conclusions: The choice of reporting interval should be made in the light of assay requirements. Where there is a clinical need for detection of small changes in analyte concentration, the reporting interval should be kept small relative to the combined variation attributable to assay precision and within-person biological variation.


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