Kite's thoughts on fifthspans: Difference between revisions

Line 261:

After finding F, there are two ways to proceed. The first way is easier if using a spreadsheet or other software. Multiply F by X and reduce it modulo N. If the number is greater than N/2, further reduce it by subtracting N. For example, the fifthspan of 8\17 is (-5 ⋅ 8) mod 17 = 11, which reduces to -6.

The second way is easier to calculate in one's head, especially for larger edos. It uses the name of the interval in [[Ups and ~~Downs Notation~~|ups and downs notation]]. One up has a fifthspan of F. The fifthspans of any ups or downs are added onto the fifthspan of the un-upped/downed interval. Again, If the number is greater than N/2, subtract N. For example, 8\17 is an up-4th. The fifthspan of a 4th is -1, and the fifthspan of ^1 is -5, and -1 + -5 = -6. Thus in any single-ring edo, the fifthspan of vM2 is 2-F, and the fifthspan of ^^4 is 2F-1.

The second way is easier to calculate in one's head, especially for larger edos. It uses the name of the interval in [[Ups and downs notation|ups and downs notation]]. One up has a fifthspan of F. The fifthspans of any ups or downs are added onto the fifthspan of the un-upped/downed interval. Again, If the number is greater than N/2, subtract N. For example, 8\17 is an up-4th. The fifthspan of a 4th is -1, and the fifthspan of ^1 is -5, and -1 + -5 = -6. Thus in any single-ring edo, the fifthspan of vM2 is 2-F, and the fifthspan of ^^4 is 2F-1.

== The fifthspan mapping ==

@@ Line 261: / Line 261: @@
 After finding F, there are two ways to proceed. The first way is easier if using a spreadsheet or other software. Multiply F by X and reduce it modulo N. If the number is greater than N/2, further reduce it by subtracting N. For example, the fifthspan of 8\17 is (-5 ⋅ 8) mod 17 = 11, which reduces to -6.
-The second way is easier to calculate in one's head, especially for larger edos. It uses the name of the interval in [[Ups and Downs Notation|ups and downs notation]]. One up has a fifthspan of F. The fifthspans of any ups or downs are added onto the fifthspan of the un-upped/downed interval. Again, If the number is greater than N/2, subtract N. For example, 8\17 is an up-4th. The fifthspan of a 4th is -1, and the fifthspan of ^1 is -5, and -1 + -5 = -6. Thus in any single-ring edo, the fifthspan of vM2 is 2-F, and the fifthspan of ^^4 is 2F-1.
+The second way is easier to calculate in one's head, especially for larger edos. It uses the name of the interval in [[Ups and downs notation|ups and downs notation]]. One up has a fifthspan of F. The fifthspans of any ups or downs are added onto the fifthspan of the un-upped/downed interval. Again, If the number is greater than N/2, subtract N. For example, 8\17 is an up-4th. The fifthspan of a 4th is -1, and the fifthspan of ^1 is -5, and -1 + -5 = -6. Thus in any single-ring edo, the fifthspan of vM2 is 2-F, and the fifthspan of ^^4 is 2F-1.
 == The fifthspan mapping ==