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.

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.

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.

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 ==

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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.
+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.
-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.
-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 ==