1156/1155

Interval information

Ratio	1156/1155
Factorization	22 × 3-1 × 5-1 × 7-1 × 11-1 × 172
Monzo	[2 -1 -1 -1 -1 0 2⟩
Size in cents	1.498255¢
Name	septendecimal quartertones comma
FJS name	[math]\displaystyle{ \text{d2}^{17,17}_{5,7,11} }[/math]
Special properties	square superparticular, reduced
Tenney height (log2 nd)	20.3486
Weil height (log2 max(n, d))	20.3499
Wilson height (sopfr(nd))	64
Open this interval in xen-calc

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.

See also

• Unnoticeable comma
• List of superparticular intervals