User:CritDeathX/Sam's Musings: Difference between revisions

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== Christopher Temperament ==

Christopher temperament is the name I give to the 2.3.7.11.13-limit temperament with a generator of a sharp [[7/6]] that tempers out [[99/98]], 44/43, 17496/16807, etc. It would be a generator of [[Orwell]] if it wasn't for the fact that its too sharp. Two generators give an 8c sharp [[11/8]], three of them make a 0.7c flat [[13/8]], and five make a 4c ~~sharp~~ [[9/8]].

Christopher temperament is the name I give to the 2.3.7.11.13-limit temperament with a generator of a sharp [[7/6]] that tempers out [[99/98]], 44/43, 17496/16807, etc. It would be a generator of [[Orwell]] if it wasn't for the fact that its too sharp. Two generators give an 8c sharp [[11/8]], three of them make a 0.7c flat [[13/8]], and five make a 4c flat [[9/8]].

Using a [http://www.microtonalsoftware.com/scale-tree.html?left=13&right=17&rr=1200&ioi=279.944474 scale tree], you can find the EDOs that approximate the generator, starting with [[13edo|13]] & [[17edo|17EDO]]; you could also find a zigzag series of EDOs that approximate the generator, starting with 13 & [[30edo|30]].

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!199.72

|-

|16/9

|16/9 +4c

|22/21

|16/13

|16/11

|16/11 -8c

|12/7

|12/7 -12c

|1/1

|7/6

|7/6 +12c

|11/8

|11/8 +8c

|13/8

|21/11

|9/8

|9/8 -4c

|}

=== MOS ~~Scales~~ ===

=== MOS Scale ===

(charts inspired from [[Andrew Heathwaite's MOS Investigations]])

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c = 39.28 (13x)

The interesting pattern while writing this was that you had a pretty simple procedure to find sizes of this temperament; your L will usually be s generators away, and visa versa. In order to find the next MOS (and incidentally the size of L in the next MOS), just find the chroma (L-s) in generator steps.

For example, in 4L1s, the L is 1 generator up; s is 4 generators down. The chroma is 9 generators down, and is also the L of 4L5s.

@@ Line 23: / Line 23: @@
 == Christopher Temperament ==
-Christopher temperament is the name I give to the 2.3.7.11.13-limit temperament with a generator of a sharp [[7/6]] that tempers out [[99/98]], 44/43, 17496/16807, etc. It would be a generator of [[Orwell]] if it wasn't for the fact that its too sharp. Two generators give an 8c sharp [[11/8]], three of them make a 0.7c flat [[13/8]], and five make a 4c sharp [[9/8]].
+Christopher temperament is the name I give to the 2.3.7.11.13-limit temperament with a generator of a sharp [[7/6]] that tempers out [[99/98]], 44/43, 17496/16807, etc. It would be a generator of [[Orwell]] if it wasn't for the fact that its too sharp. Two generators give an 8c sharp [[11/8]], three of them make a 0.7c flat [[13/8]], and five make a 4c flat [[9/8]].
 Using a [http://www.microtonalsoftware.com/scale-tree.html?left=13&right=17&rr=1200&ioi=279.944474 scale tree], you can find the EDOs that approximate the generator, starting with [[13edo|13]] & [[17edo|17EDO]]; you could also find a zigzag series of EDOs that approximate the generator, starting with 13 & [[30edo|30]].
@@ Line 41: / Line 41: @@
 !199.72
 |-
-|16/9
+|16/9 +4c
 |22/21
 |16/13
-|16/11
+|16/11 -8c
-|12/7
+|12/7 -12c
 |1/1
-|7/6
+|7/6 +12c
-|11/8
+|11/8 +8c
 |13/8
 |21/11
-|9/8
+|9/8 -4c
 |}
-=== MOS Scales ===
+=== MOS Scale ===
 (charts inspired from [[Andrew Heathwaite's MOS Investigations]])
@@ Line 412: / Line 412: @@
 c = 39.28 (13x)
+The interesting pattern while writing this was that you had a pretty simple procedure to find sizes of this temperament; your L will usually be s generators away, and visa versa. In order to find the next MOS (and incidentally the size of L in the next MOS), just find the chroma (L-s) in generator steps.
+For example, in 4L1s, the L is 1 generator up; s is 4 generators down. The chroma is 9 generators down, and is also the L of 4L5s.