16767/16384: Difference between revisions

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Created page with "{{Infobox Interval | Ratio = 16767/16384 | Name = | Color name = L23o1, latwetho 1sn | Comma = yes }} '''16767/16384''' is a 2.3.23 subgroup comma. It is the amount by which the octave-reduced 23rd harmonic 23/16 exceeds the Pythagorean diminished fifth (1024/729). == Notation == This interval is significant in color notation as the formal comma to translate a Pythagorean interval to a nearby 23-limit (vicesimotertial) interval."
 
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{{Infobox Interval
{{Infobox Interval
| Ratio = 16767/16384
| Ratio = 16767/16384
| Name =  
| Name =23 small diesis
| Color name = L23o1, latwetho 1sn
| Color name = L23o1, latwetho 1sn
| Comma = yes
| Comma = yes
Line 8: Line 8:


== Notation ==
== Notation ==
This interval is significant in [[color notation]] as the formal comma to translate a Pythagorean interval to a nearby 23-limit (vicesimotertial) interval.
This interval is significant in [[color notation]] as the formal comma to translate a Pythagorean interval to a nearby 23-limit (vicesimotertial) interval.
 
It is used in the [[Sagittal notation]] in the [https://en.xen.wiki/w/Sagittal_notation#Promethean Promethean extension], whose name is the 23 small diesis or 23S ( {{sagittal|~|\}} / {{sagittal|~!/}}).

Revision as of 07:32, 25 August 2025

Interval information
Ratio 16767/16384
Subgroup monzo 2.3.23 [-14 6 1
Size in cents 40.00435¢
Name 23 small diesis
Color name L23o1, latwetho 1sn
FJS name [math]\displaystyle{ \text{d}{-2}^{23} }[/math]
Special properties reduced,
reduced harmonic
Tenney norm (log2 nd) 28.0333
Weil norm (log2 max(n, d)) 28.0667
Wilson norm (sopfr(nd)) 69
Comma size medium
Open this interval in xen-calc

16767/16384 is a 2.3.23 subgroup comma. It is the amount by which the octave-reduced 23rd harmonic 23/16 exceeds the Pythagorean diminished fifth (1024/729).

Notation

This interval is significant in color notation as the formal comma to translate a Pythagorean interval to a nearby 23-limit (vicesimotertial) interval.

It is used in the Sagittal notation in the Promethean extension, whose name is the 23 small diesis or 23S ( / ).