Spiral chart: Difference between revisions

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A '''spiral chart''' is an illustration which converts a circle of repeats of an interval in one [[edo]] into a self-similar spiral shape, so that it may be compared with a circle of the same interval in a smaller coprime edo.

Spiral charts were invented by [[Kite Giedraitis]] ~~no later than~~ 2019.

Spiral charts were invented by [[Kite Giedraitis]] in August 2019.

== Spirals of twelve fifths ==

The spiral charts for [[31edo]], [[41edo]] and [[53edo]] relate each of those edos to [[12edo]]. Each chart has 12 '''wheel-spokes'''.

The larger edo's spiral of fifths is not really a spiral, it's a larger [[circle of fifths]] that ~~you break~~ into a chain ~~and~~ make ~~a bunch of~~ smaller 12-note loops ~~with~~. Then ~~add~~ a few duplicates at each end of the chain, so that ~~you~~ can reconnect the ends mentally ~~and~~ get the original larger circle.

The larger edo's spiral of fifths is not really a spiral, it's a larger [[circle of fifths]] that is broken into a chain to make several smaller 12-note loops. Then a few duplicates are added at each end of the chain, so that one can reconnect the ends mentally to get the original larger circle.

A 12-spoke spiral chart of fifths is only possible if the [[sharpness#dodeca-sharpness|dodeca-sharpness]] (edosteps per [[Pythagorean comma]]) of the larger edo is 1 or -1.

A 12-spoke spiral chart of fifths is only possible if the [[sharpness#dodeca-sharpness|dodeca-sharpness]] (edosteps per [[Pythagorean comma]]) of the larger edo is 1 or -1. A 12-spoke spiral of ''semitones'' is possible for edos of the form 12n+1 or 12n-1, but those spirals are less interesting because they convey very little info that isn't already in the table of edosteps.

=== Gallery ===

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== Spirals of other amounts, other intervals ==

Such a spiral chart can be made for any two edos, as long as they are coprime. It's often a spiral of something other than fifths. In fact, it's a spiral of the nearest miss.

Such a spiral chart can be made for any two edos, as long as they are coprime. It's often a spiral of something other than fifths. In fact, it's a spiral of the [[User:TallKite/The delta method|nearest miss]].

For example, consider [[8edo]] and [[27edo]]. The near misses are 3\8 and 10\27. You get an 8-spoke spiral of 27edo major 3rds. This might be useful for someone researching [[octatonic]] scales in 27edo.

@@ Line 1: / Line 1: @@
 A '''spiral chart''' is an illustration which converts a circle of repeats of an interval in one [[edo]] into a self-similar spiral shape, so that it may be compared with a circle of the same interval in a smaller coprime edo.
-Spiral charts were invented by [[Kite Giedraitis]] no later than 2019.
+Spiral charts were invented by [[Kite Giedraitis]] in August 2019.
 == Spirals of twelve fifths ==
 The spiral charts for [[31edo]], [[41edo]] and [[53edo]] relate each of those edos to [[12edo]]. Each chart has 12 '''wheel-spokes'''.
-The larger edo's spiral of fifths is not really a spiral, it's a larger [[circle of fifths]] that you break into a chain and make a bunch of smaller 12-note loops with. Then add a few duplicates at each end of the chain, so that you can reconnect the ends mentally and get the original larger circle.
+The larger edo's spiral of fifths is not really a spiral, it's a larger [[circle of fifths]] that is broken into a chain to make several smaller 12-note loops. Then a few duplicates are added at each end of the chain, so that one can reconnect the ends mentally to get the original larger circle.
-A 12-spoke spiral chart of fifths is only possible if the [[sharpness#dodeca-sharpness|dodeca-sharpness]] (edosteps per [[Pythagorean comma]]) of the larger edo is 1 or -1.
+A 12-spoke spiral chart of fifths is only possible if the [[sharpness#dodeca-sharpness|dodeca-sharpness]] (edosteps per [[Pythagorean comma]]) of the larger edo is 1 or -1. A 12-spoke spiral of ''semitones'' is possible for edos of the form 12n+1 or 12n-1, but those spirals are less interesting because they convey very little info that isn't already in the table of edosteps.
 === Gallery ===
@@ Line 19: / Line 19: @@
 == Spirals of other amounts, other intervals ==
-Such a spiral chart can be made for any two edos, as long as they are coprime. It's often a spiral of something other than fifths. In fact, it's a spiral of the nearest miss.
+Such a spiral chart can be made for any two edos, as long as they are coprime. It's often a spiral of something other than fifths. In fact, it's a spiral of the [[User:TallKite/The delta method|nearest miss]].
 For example, consider [[8edo]] and [[27edo]]. The near misses are 3\8 and 10\27. You get an 8-spoke spiral of 27edo major 3rds. This might be useful for someone researching [[octatonic]] scales in 27edo.