1000/999: Difference between revisions

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{{Infobox Interval

| Ratio = 1000/999

| Name = millenisma

| Color name = 37uy<sup>3</sup>-2 <br> thisutriyo negative 2nd

| 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 ==

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 ~~also~~ 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.

== See also ==

* [[Unnoticeable comma]]

* [[List of superparticular intervals]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
 | Ratio = 1000/999
+| Name = millenisma
 | Color name = 37uy<sup>3</sup>-2 <br> thisutriyo negative 2nd
 | 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 ==
-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]].
+/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]].
-/999 is also 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.
 == See also ==
-* [[Unnoticeable comma]]
 * [[List of superparticular intervals]]