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Geometric Construction of Pythagorean and Just Musical Scales and Commas

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Bibliographic Details
Main Authors: Børre, Nyhoff, Alv I., Aarskog, Sverre, Holm
Format: Book
Language:English
Published: Springer 2023
Subjects:
G-sharp and A-flat
Pythagorean comma
Online Access:https://link.springer.com/article/10.1007/s00283-022-10260-4
https://dlib.phenikaa-uni.edu.vn/handle/PNK/7641
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spelling oai:localhost:PNK-76412023-04-06T07:17:10Z Geometric Construction of Pythagorean and Just Musical Scales and Commas Børre, Nyhoff Alv I., Aarskog Sverre, Holm G-sharp and A-flat Pythagorean comma CC BY To your average pianist, G-sharp and A-flat are the same. They are located at the same black key between the white G and A keys, but with different names. For other musicians, however, for example violinists, they are different notes. They would claim that the piano represents a compromise, since it is often tuned to the equal-tempered scale, while other musical scales, based on simple harmonic ratios, often appear more harmonious to the ear. This article explains and illustrates this dilemma geometrically. In these scales, G-sharp and A-flat will no longer be the same. The difference between them is called the Pythagorean comma, and the name hints at the long history of music theory. 2023-04-06T07:17:10Z 2023-04-06T07:17:10Z 2023 Book https://link.springer.com/article/10.1007/s00283-022-10260-4 https://dlib.phenikaa-uni.edu.vn/handle/PNK/7641 en application/pdf Springer
institution Digital Phenikaa
collection Digital Phenikaa
language English
topic G-sharp and A-flat
Pythagorean comma
spellingShingle G-sharp and A-flat
Pythagorean comma
Børre, Nyhoff
Alv I., Aarskog
Sverre, Holm
Geometric Construction of Pythagorean and Just Musical Scales and Commas
description CC BY
format Book
author Børre, Nyhoff
Alv I., Aarskog
Sverre, Holm
author_facet Børre, Nyhoff
Alv I., Aarskog
Sverre, Holm
author_sort Børre, Nyhoff
title Geometric Construction of Pythagorean and Just Musical Scales and Commas
title_short Geometric Construction of Pythagorean and Just Musical Scales and Commas
title_full Geometric Construction of Pythagorean and Just Musical Scales and Commas
title_fullStr Geometric Construction of Pythagorean and Just Musical Scales and Commas
title_full_unstemmed Geometric Construction of Pythagorean and Just Musical Scales and Commas
title_sort geometric construction of pythagorean and just musical scales and commas
publisher Springer
publishDate 2023
url https://link.springer.com/article/10.1007/s00283-022-10260-4
https://dlib.phenikaa-uni.edu.vn/handle/PNK/7641
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score 8.887836

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