1000/999: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
Francium (talk | contribs)
Cleanup
 
(4 intermediate revisions by 4 users not shown)
Line 1: Line 1:
{{Infobox Interval
{{Infobox Interval
| Ratio = 1000/999
| Ratio = 1000/999
| Name = millenisma
| Color name = 37uy<sup>3</sup>-2 <br> thisutriyo negative 2nd
| Color name = 37uy<sup>3</sup>-2 <br> thisutriyo negative 2nd
| Comma = yes
| Comma = yes
}}
}}


'''1000/999''', is a [[37-limit]] [[superparticular interval|superparticular comma]] of about 1.7 [[cent]]s. It is the difference between the commas [[27/25]] and [[40/37]].
'''1000/999''' is an [[unnoticeable comma|unnoticeable]] [[37-limit]] [[superparticular interval|superparticular]] [[comma]] of about 1.73 [[cent]]s. It is the difference between the intervals [[27/25]] and [[40/37]].
 
This comma occurs as the difference between certain 5-limit and 37-limit intervals. The octave-reduced 37th harmonic ([[37/32]]) is a [[semifourth]] about 251{{c}}, while the triptolemaic augmented second ([[125/108]]), equal to a stack of three [[5/3]]'s [[octave reduction|octave reduced]], is approximately 253{{c}}. The difference between these intervals equals 1000/999.
 
This relationship demonstrates how this comma may serve as a bridge between the 5-limit and 37-limit systems, allowing for approximations of 37-limit intervals using more common 5-limit intervals. Its small size of 1.7 cents makes it practically imperceptible.


== Temperaments ==
== Temperaments ==
Tempering it out produces the rank-11 '''millenismic''' temperament in the full 37-limit, and the rank-3 '''millenic''' temperament in the 2.3.5.37 [[subgroup]], and enables the [[millenismic chords]].
1000/999 is [[tempering out|tempered out]] in the no-31's 37-limit extension of the [[superlimmal]] temperament. It is also useful for constructing higher-limit extensions of popular temperaments, such as [[kleismic]] and [[amity]].
 
1000/999 is tempered out in the no-31's 37-limit extension of the [[superlimmal]] temperament. It is also useful for constructing higher-limit extensions of popular temperaments, such as [[kleismic]] and [[amity]].


== Proposed names ==
== Etymology ==
[[Francium]] proposed the name '''millenisma''' in 2025, referring to the Latin word for thousand.
[[Francium]] proposed the name '''millenisma''' in 2025, referring to the Latin word for thousand.


== See also ==
== See also ==
* [[Unnoticeable comma]]
* [[List of superparticular intervals]]
* [[List of superparticular intervals]]

Latest revision as of 13:34, 15 February 2026

Interval information
Ratio 1000/999
Subgroup monzo 2.3.5.37 [3 -3 3 -1
Size in cents 1.7321¢
Name millenisma
Color name 37uy3-2
thisutriyo negative 2nd
FJS name [math]\displaystyle{ \text{A1}^{5,5,5}_{37} }[/math]
Special properties superparticular,
reduced
Tenney norm (log2 nd) 19.9301
Weil norm (log2 max(n, d)) 19.9316
Wilson norm (sopfr(nd)) 67
Comma size unnoticeable
Open this interval in xen-calc

1000/999 is an unnoticeable 37-limit superparticular comma of about 1.73 cents. It is the difference between the intervals 27/25 and 40/37.

This comma occurs as the difference between certain 5-limit and 37-limit intervals. The octave-reduced 37th harmonic (37/32) is a semifourth about 251 ¢, while the triptolemaic augmented second (125/108), equal to a stack of three 5/3's octave reduced, is approximately 253 ¢. The difference between these intervals equals 1000/999.

This relationship demonstrates how this comma may serve as a bridge between the 5-limit and 37-limit systems, allowing for approximations of 37-limit intervals using more common 5-limit intervals. Its small size of 1.7 cents makes it practically imperceptible.

Temperaments

1000/999 is tempered out in the no-31's 37-limit extension of the superlimmal temperament. It is also useful for constructing higher-limit extensions of popular temperaments, such as kleismic and amity.

Etymology

Francium proposed the name millenisma in 2025, referring to the Latin word for thousand.

See also