Geometric Construction of Pythagorean and Just Musical Scales and Commas
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Springer
2023
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| Truy cập trực tuyến: | https://link.springer.com/article/10.1007/s00283-022-10260-4 https://dlib.phenikaa-uni.edu.vn/handle/PNK/7641 |
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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 |
| _version_ |
1762456094294147072 |
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8.893527 |