1000/999: Difference between revisions
Added the name proposed by francium |
27/25 and 40/37 aren't necessarily commas |
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|Name=Millenisma (proposed name)}} | |Name=Millenisma (proposed name)}} | ||
'''1000/999''' is a [[37-limit]] [[superparticular interval|superparticular comma]] of about 1.7 [[cent]]s. It is the difference between the | '''1000/999''' is a [[37-limit]] [[superparticular interval|superparticular comma]] of about 1.7 [[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 [[5-limit]] triptolemaic augmented second ([[125/108]]) is approximately 253{{c}}. The difference between these intervals equals 1000/999. | 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. | ||
Revision as of 22:26, 14 February 2026
| 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 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 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.