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 quartertones. | '''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]] | In terms of commas, it is the difference between the following pairs: | ||
* [[289/288]] and [[385/384]] | |||
* [[442/441]] and [[715/714]] | |||
* [[561/560]] and [[1089/1088]] | |||
* [[595/594]] and [[1225/1224]] | |||
* [[936/935]] and [[4914/4913]] | |||
It factors into the following pairs: | |||
* [[2080/2079]] and [[2601/2600]] | |||
* [[1275/1274]] and [[12376/12375]] | |||
== Temperaments == | == Temperaments == | ||
Revision as of 19:09, 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 the following pairs:
- 289/288 and 385/384
- 442/441 and 715/714
- 561/560 and 1089/1088
- 595/594 and 1225/1224
- 936/935 and 4914/4913
It factors into the following pairs:
- 2080/2079 and 2601/2600
- 1275/1274 and 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.