1000/999: Difference between revisions
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'''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 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]]. | ||
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 [[5-limit]] triptolemaic augmented second ([[125/108]]) 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 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]]. | ||
Revision as of 13:10, 11 May 2025
| Interval information |
thisutriyo negative 2nd
reduced
1000/999, is a 37-limit superparticular comma of about 1.7 cents. It is the difference between the commas 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 5-limit triptolemaic augmented second (125/108) 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.
Proposed names
Francium proposed the name millenisma in 2025, referring to the Latin word for thousand.