1000/999: Difference between revisions

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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 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 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
Ratio 1000/999
Subgroup monzo 2.3.5.37 [3 -3 3 -1
Size in cents 1.7321¢
Name Millenisma (proposed name)
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 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.

See also