49/48: Difference between revisions

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== Temperaments ==

49/48 is [[tempered out]] in [[15edo]] and [[19edo]], where the two intervals are equated, and the fourth is split in a perfect half. In the 2.3.7 [[subgroup]], this is known as the [[semaphore]] temperament, and the comma is thus known as the '''semaphore comma''' or '''semaphoresma'''. It cannot be tempered out if all of the consonances of the 7-odd-limit are [[distinct]], but it ''can'' be equated with other commas; for example (49/48)/([[81/80]]) = [[245/243]], (49/48)/([[64/63]]) = [[1029/1024]], (49/48)/([[3125/3072]]) = [[3136/3125]], (49/48)/([[50/49]]) = [[2401/2400]], ([[128/125]])/(49/48) = [[6144/6125]], ([[36/35]])/(49/48) = [[1728/1715]].

49/48 is [[tempered out]] in [[15edo]] and [[19edo]], where the two intervals are equated, and the fourth is split in a perfect half. In the 2.3.7 [[subgroup]], this is known as the [[semaphore]] temperament, and the comma is thus known as the '''semaphore comma''' or '''semaphoresma'''.

See [[Semaphoresmic family]] for the rank-3 family where it is tempered out. See [[Semaphoresmic clan]] for the rank-2 clan where it is tempered out.

It cannot be tempered out if all of the consonances of the 7-odd-limit are [[distinct]], but it ''can'' be equated with other commas; for example:

* (49/48)/([[81/80]]) = [[245/243]]

* (49/48)/([[64/63]]) = [[1029/1024]]

* (49/48)/([[3125/3072]]) = [[3136/3125]]

* (49/48)/([[50/49]]) = [[2401/2400]]

* ([[128/125]])/(49/48) = [[6144/6125]]

* ([[36/35]])/(49/48) = [[1728/1715]]

See [[Semaphoresmic family]] for the rank-3 family where it is tempered out. See [[Semaphoresmic clan]] for the rank-2 clan where it is tempered out.

== See also ==

@@ Line 15: / Line 15: @@
 == Temperaments ==
-/48 is [[tempered out]] in [[15edo]] and [[19edo]], where the two intervals are equated, and the fourth is split in a perfect half. In the 2.3.7 [[subgroup]], this is known as the [[semaphore]] temperament, and the comma is thus known as the '''semaphore comma''' or '''semaphoresma'''. It cannot be tempered out if all of the consonances of the 7-odd-limit are [[distinct]], but it ''can'' be equated with other commas; for example (49/48)/([[81/80]]) = [[245/243]], (49/48)/([[64/63]]) = [[1029/1024]], (49/48)/([[3125/3072]]) = [[3136/3125]], (49/48)/([[50/49]]) = [[2401/2400]], ([[128/125]])/(49/48) = [[6144/6125]], ([[36/35]])/(49/48) = [[1728/1715]].
+/48 is [[tempered out]] in [[15edo]] and [[19edo]], where the two intervals are equated, and the fourth is split in a perfect half. In the 2.3.7 [[subgroup]], this is known as the [[semaphore]] temperament, and the comma is thus known as the '''semaphore comma''' or '''semaphoresma'''.
-See [[Semaphoresmic family]] for the rank-3 family where it is tempered out. See [[Semaphoresmic clan]] for the rank-2 clan where it is tempered out.
+It cannot be tempered out if all of the consonances of the 7-odd-limit are [[distinct]], but it ''can'' be equated with other commas; for example:
+* (49/48)/([[81/80]]) = [[245/243]]
+* (49/48)/([[64/63]]) = [[1029/1024]]
+* (49/48)/([[3125/3072]]) = [[3136/3125]]
+* (49/48)/([[50/49]]) = [[2401/2400]]
+* ([[128/125]])/(49/48) = [[6144/6125]]
+* ([[36/35]])/(49/48) = [[1728/1715]]
+See [[Semaphoresmic family]] for the rank-3 family where it is tempered out. See [[Semaphoresmic clan]] for the rank-2 clan where it is tempered out.
 == See also ==