2187/2176: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
Created page with "{{Infobox Interval | JI glyph = | Ratio = 2187/2176 | Monzo = -7 7 0 0 0 0 -1 | Cents = 8.7296 | Name = septendecimal schisma | Color name = | FJS name = d-2<sub>17</sub> |..."
 
Xenwolf (talk | contribs)
m size 5 digits
Line 3: Line 3:
| Ratio = 2187/2176
| Ratio = 2187/2176
| Monzo = -7 7 0 0 0 0 -1
| Monzo = -7 7 0 0 0 0 -1
| Cents = 8.7296
| Cents = 8.72960
| Name = septendecimal schisma
| Name = septendecimal schisma
| Color name =  
| Color name =  

Revision as of 14:23, 24 September 2020

Interval information
Ratio 2187/2176
Subgroup monzo 2.3.17 [-7 7 -1
Size in cents 8.729597¢
Name septendecimal schisma
FJS name [math]\displaystyle{ \text{d}{-2}_{17} }[/math]
Special properties reduced
Tenney norm (log2 nd) 22.1822
Weil norm (log2 max(n, d)) 22.1895
Wilson norm (sopfr(nd)) 52
Open this interval in xen-calc

The septendecimal schisma, 2187/2176, is a 17-limit comma measuring about 8.7 cents. Although several times in size, it shares similarities with the schisma – while the schisma is the amount by which 16/15 deviates from 2187/2048, the septendecimal schisma is the amount by which 17/16 deviates from 2187/2048.

Besides the relationship above, it is also the difference between 18/17 and 256/243, between 24/17 and 1024/729, and their respective inverses. Furthermore, it and the septendecimal comma 4131/4096 make a Pythagorean comma.

The septendecimal schisma is significant in Helmholtz-Ellis notation (2020 version) as the 17-limit formal comma which translates a Pythagorean interval to a nearby septendecimal interval. Consequently, 17/16 is represented as an augmented unison. In Functional Just System, however, that role is taken by 4131/4096, so 17/16 is represented as a minor second.

See also