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]].

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 ==

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 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]].

@@ Line 6: / Line 6: @@
 '''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 ==
-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 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]].