1000/999: Difference between revisions
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{{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''' | '''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 == | ||
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]]. | |||
== | == 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 == | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
Latest revision as of 13:34, 15 February 2026
| Interval information |
thisutriyo negative 2nd
reduced
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.