1156/1155: Difference between revisions
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'''1156/1155''' is a [[17-limit]] no-13 [[superparticular]] [[comma]] measuring about 1.41 [[cent]]s. It may be properly described as the ''septendecimal quartertones comma'', since it is the difference between [[34/33]] and [[35/34]], the two 17-limit | '''1156/1155''' is a [[17-limit]] no-13 [[superparticular]] [[comma]] measuring about 1.41 [[cent]]s. It may be properly described as the ''septendecimal quartertones comma'', since it is the difference between [[34/33]] and [[35/34]], the two 17-limit quartertones. | ||
In terms of commas, it is the difference between [[289/288]] and [[385/384]], and between [[936/935]] and [[4914/4913]]. It factors into ([[2080/2079]])([[2601/2600]]), or ([[1275/1274]])([[12376/12375]]). | In terms of commas, it is the difference between [[289/288]] and [[385/384]], and between [[936/935]] and [[4914/4913]]. It factors into ([[2080/2079]])([[2601/2600]]), or ([[1275/1274]])([[12376/12375]]). | ||
Revision as of 18:30, 1 November 2021
| Interval information |
reduced
1156/1155 is a 17-limit no-13 superparticular comma measuring about 1.41 cents. It may be properly described as the septendecimal quartertones comma, since it is the difference between 34/33 and 35/34, the two 17-limit quartertones.
In terms of commas, it is the difference between 289/288 and 385/384, and between 936/935 and 4914/4913. It factors into (2080/2079)(2601/2600), or (1275/1274)(12376/12375).
Temperaments
Tempering out this comma results in 35/33 being split into two equal parts, each representing 34/33~35/34, and enables the related essentially tempered chords. If 9801/9800 is also added to the comma list, the quartertone above becomes literally a quarter of 9/8 and is located right between 33/32, the undecimal quartertone, and 36/35, the septimal quartertone.