Spiral chart - Revision history

Fredg999: Fredg999 moved page Kite's thoughts on spiral charts to Spiral chart over a redirect without leaving a redirect: Undo move by User:TallKite (topic is broader than a single approach)

2025-08-20T21:35:04Z

Fredg999 moved page Kite's thoughts on spiral charts to Spiral chart over a redirect without leaving a redirect: Undo move by User:TallKite (topic is broader than a single approach)

← Older revision	Revision as of 21:35, 20 August 2025
(No difference)

Fredg999: Rework lead section

2025-08-20T21:34:27Z

Rework lead section

← Older revision		Revision as of 21:34, 20 August 2025
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	A '''spiral chart''' is ~~an illustration which converts~~ a ~~circle~~ of ~~repeats~~ of an interval in ~~one~~ [[~~edo~~]] (~~or simply~~ a ~~temperament~~-~~agnostic~~ chain of that interval~~) into~~ a ~~self~~-~~similar~~ spiral ~~shape, so~~ that ~~it may be compared with~~ a ~~circle~~ of the ~~same~~ interval in a ~~smaller coprime edo~~.		[[File:41-edo spiral with notes.png\|thumb\|A 12-spoke spiral chart showing the [[chain of fifths]] of [[41edo]], with note names in [[Kite's ups and downs notation]].]]
			{{Wikipedia\|Circle of fifths#Enharmonic equivalents, theoretical keys, and the spiral of fifths}}
			A '''spiral chart''' is a {{w\|spiral}}-shaped visualization of an [[interval chain]], generated by [[stacking]] the same [[interval]] repeatedly above or below itself. A series of points along the spiral show the intervals, usually [[octave-reduced]] (i.e. [[interval class]]es), or alternatively the note names (i.e. [[pitch class]]es), that make up the interval chain.

			Spiral charts can be used to visualize open interval chains, which never return to the starting interval class exactly, notably in [[just intonation]]. They can also be used to visualize closed interval chains, especially when they contain an interval class that is very close in [[pitch]] to the starting interval class (i.e. a [[comma]]). Using a spiral chart for closed chains emphasizes the parts of the chain which are slightly pitch-shifted copies of another part of the chain, although as a side effect, equivalent pitches can be found at multiple points along the spiral. In both cases (open and closed chains), the spacing of notes around the spiral can be adjusted so that comma-separated interval classes are aligned on the same ''spoke'', a straight or slightly curved line radiating from the center. By extension, spiral charts can be used to compare an [[edo]] to a smaller [[coprime]] edo by choosing the number of spokes accordingly.

			For example, whereas the [[circle of fifths]] of [[12edo]] closes after 12 fifths, as it comes back exactly to the starting interval class, the corresponding 12-spoke spiral of fifths instead starts a new loop at that point. If the spiral of fifths is used to represent a chain of pure fifths ([[3/2]]), then the first interval class on the second loop is a [[Pythagorean comma]] away from the starting interval class, and so on.

	Spiral charts were first known to be used by Jeff Jensen in 2004,<ref>https://jjensen.org/spiral5ths/Spiral5ths.html</ref> to describe the chain of fifths as it relates to 12edo. Much of the theory on this page, however, comes from [[Kite Giedraitis]], no later than April 2014		Spiral charts were first known to be used by Jeff Jensen in 2004,<ref>https://jjensen.org/spiral5ths/Spiral5ths.html</ref> to describe the chain of fifths as it relates to 12edo. Much of the theory on this page, however, comes from [[Kite Giedraitis]], no later than April 2014
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	File:31-edo spiral.png\|31edo spiral chart		File:31-edo spiral.png\|31edo spiral chart
	File:41-edo spiral.png\|41edo spiral chart		File:41-edo spiral.png\|41edo spiral chart
	~~File:41-edo spiral with notes.png\|41edo spiral chart (notation)~~
	File:53-edo spiral.png\|53edo spiral chart		File:53-edo spiral.png\|53edo spiral chart
	</gallery>The same information can be presented as a table. To follow the circle of 5ths, read the columns left to right, and within each column read top to bottom.		</gallery>The same information can be presented as a table. To follow the circle of 5ths, read the columns left to right, and within each column read top to bottom.

TallKite: TallKite moved page Spiral chart to Kite's thoughts on spiral charts: Editor VectorGraphics has repeatedly edited pages I've written about my own research and inserted misinformation. On discord he is openly hostile to me. This move is necessary to avoid a toxic work environment for me.

2025-08-20T00:43:34Z

TallKite moved page Spiral chart to Kite's thoughts on spiral charts: Editor VectorGraphics has repeatedly edited pages I've written about my own research and inserted misinformation. On discord he is openly hostile to me. This move is necessary to avoid a toxic work environment for me.

← Older revision	Revision as of 00:43, 20 August 2025
(No difference)

TallKite: Undo revision 207501 by VectorGraphics (talk)

2025-08-20T00:42:07Z

Undo revision 207501 by VectorGraphics (talk)

← Older revision		Revision as of 00:42, 20 August 2025
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	A '''spiral chart''' is an illustration which converts a circle of repeats of an interval in one [[edo]] (or simply a temperament-agnostic chain of that interval) into a self-similar spiral shape~~. As used by [[Kite Giedraitis]], the concept of spiral charts is applied to edos~~, so that ~~a chain of intervals in one edo~~ may be compared with a circle of the same interval in a smaller coprime edo.		A '''spiral chart''' is an illustration which converts a circle of repeats of an interval in one [[edo]] (or simply a temperament-agnostic chain of that interval) 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 first known to be used by Jeff Jensen in 2004,<ref>https://jjensen.org/spiral5ths/Spiral5ths.html</ref> to describe the chain of fifths as it relates to 12edo. Much of the theory on this page, however, comes from Kite, no later than April 2014		Spiral charts were first known to be used by Jeff Jensen in 2004,<ref>https://jjensen.org/spiral5ths/Spiral5ths.html</ref> to describe the chain of fifths as it relates to 12edo. Much of the theory on this page, however, comes from [[Kite Giedraitis]], no later than April 2014

	== Spirals of twelve fifths ==		== Spirals of twelve fifths ==

TallKite: Undo revision 207502 by VectorGraphics (talk)

2025-08-20T00:41:48Z

Undo revision 207502 by VectorGraphics (talk)

← Older revision		Revision as of 00:41, 20 August 2025
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	A '''spiral chart''' is an illustration which converts a circle of repeats of an interval in an [[edo]] (or simply a temperament-agnostic chain of that interval) into a self-similar spiral shape. As used by [[Kite Giedraitis]], the concept of spiral charts is applied to edos, so that a chain of intervals in one edo may be compared with a circle of the same interval in a smaller coprime edo.		A '''spiral chart''' is an illustration which converts a circle of repeats of an interval in one [[edo]] (or simply a temperament-agnostic chain of that interval) into a self-similar spiral shape. As used by [[Kite Giedraitis]], the concept of spiral charts is applied to edos, so that a chain of intervals in one edo may be compared with a circle of the same interval in a smaller coprime edo.

	Spiral charts were first known to be used by Jeff Jensen in 2004,<ref>https://jjensen.org/spiral5ths/Spiral5ths.html</ref> to describe the chain of fifths as it relates to 12edo. Much of the theory on this page, however, comes from Kite, no later than April 2014		Spiral charts were first known to be used by Jeff Jensen in 2004,<ref>https://jjensen.org/spiral5ths/Spiral5ths.html</ref> to describe the chain of fifths as it relates to 12edo. Much of the theory on this page, however, comes from Kite, no later than April 2014

VectorGraphics at 00:38, 19 August 2025

2025-08-19T00:38:03Z

← Older revision		Revision as of 00:38, 19 August 2025
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	A '''spiral chart''' is an illustration which converts a circle of repeats of an interval in ~~one~~ [[edo]] (or simply a temperament-agnostic chain of that interval) into a self-similar spiral shape. As used by [[Kite Giedraitis]], the concept of spiral charts is applied to edos, so that a chain of intervals in one edo may be compared with a circle of the same interval in a smaller coprime edo.		A '''spiral chart''' is an illustration which converts a circle of repeats of an interval in an [[edo]] (or simply a temperament-agnostic chain of that interval) into a self-similar spiral shape. As used by [[Kite Giedraitis]], the concept of spiral charts is applied to edos, so that a chain of intervals in one edo may be compared with a circle of the same interval in a smaller coprime edo.

	Spiral charts were first known to be used by Jeff Jensen in 2004,<ref>https://jjensen.org/spiral5ths/Spiral5ths.html</ref> to describe the chain of fifths as it relates to 12edo. Much of the theory on this page, however, comes from Kite, no later than April 2014		Spiral charts were first known to be used by Jeff Jensen in 2004,<ref>https://jjensen.org/spiral5ths/Spiral5ths.html</ref> to describe the chain of fifths as it relates to 12edo. Much of the theory on this page, however, comes from Kite, no later than April 2014

VectorGraphics: changed the awkward wording of the first section

2025-08-19T00:37:09Z

changed the awkward wording of the first section

← Older revision		Revision as of 00:37, 19 August 2025
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	A '''spiral chart''' is an illustration which converts a circle of repeats of an interval in one [[edo]] (or simply a temperament-agnostic chain of that interval) into a self-similar spiral shape, so that it may be compared with a circle of the same interval in a smaller coprime edo.		A '''spiral chart''' is an illustration which converts a circle of repeats of an interval in one [[edo]] (or simply a temperament-agnostic chain of that interval) into a self-similar spiral shape. As used by [[Kite Giedraitis]], the concept of spiral charts is applied to edos, so that a chain of intervals in one edo may be compared with a circle of the same interval in a smaller coprime edo.

	Spiral charts were first known to be used by Jeff Jensen in 2004,<ref>https://jjensen.org/spiral5ths/Spiral5ths.html</ref> to describe the chain of fifths as it relates to 12edo. Much of the theory on this page, however, comes from [[Kite ~~Giedraitis]]~~, no later than April 2014		Spiral charts were first known to be used by Jeff Jensen in 2004,<ref>https://jjensen.org/spiral5ths/Spiral5ths.html</ref> to describe the chain of fifths as it relates to 12edo. Much of the theory on this page, however, comes from Kite, no later than April 2014

	== Spirals of twelve fifths ==		== Spirals of twelve fifths ==

TallKite: Undo revision 207425 by VectorGraphics (talk) Spiral charts are not just about arranging the chain of fifths into a spiral. They are a tool to compare two different edos, which Jensen did not do.

2025-08-18T13:28:47Z

Undo revision 207425 by VectorGraphics (talk) Spiral charts are not just about arranging the chain of fifths into a spiral. They are a tool to compare two different edos, which Jensen did not do.

← Older revision		Revision as of 13:28, 18 August 2025
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	A '''spiral chart''' is an illustration which converts a circle of repeats of an interval in one [[edo]] (or simply a temperament-agnostic chain of that interval) into a self-similar spiral shape, so that it may be compared with a circle of the same interval in a (smaller) coprime edo.		A '''spiral chart''' is an illustration which converts a circle of repeats of an interval in one [[edo]] (or simply a temperament-agnostic chain of that interval) 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 first known to be used by Jeff Jensen in 2004,<ref>https://jjensen.org/spiral5ths/Spiral5ths.html</ref> to describe the chain of fifths as it relates to 12edo. Much of the theory on this page, however, comes from [[Kite Giedraitis]], no later than April 2014		Spiral charts were first known to be used by Jeff Jensen in 2004,<ref>https://jjensen.org/spiral5ths/Spiral5ths.html</ref> to describe the chain of fifths as it relates to 12edo. Much of the theory on this page, however, comes from [[Kite Giedraitis]], no later than April 2014

TallKite: Undo revision 207452 by VectorGraphics (talk)

2025-08-18T13:28:09Z

Undo revision 207452 by VectorGraphics (talk)

← Older revision		Revision as of 13:28, 18 August 2025
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	A '''spiral chart''' is an illustration which converts a circle of repeats of an interval in one [[edo]] (or simply a temperament-agnostic chain of that interval) into a self-similar spiral shape, so that it may be compared with a circle of the same interval in a ~~related~~ edo.		A '''spiral chart''' is an illustration which converts a circle of repeats of an interval in one [[edo]] (or simply a temperament-agnostic chain of that interval) 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 first known to be used by Jeff Jensen in 2004,<ref>https://jjensen.org/spiral5ths/Spiral5ths.html</ref> to describe the chain of fifths as it relates to 12edo. Much of the theory on this page, however, comes from [[Kite Giedraitis]], no later than April 2014		Spiral charts were first known to be used by Jeff Jensen in 2004,<ref>https://jjensen.org/spiral5ths/Spiral5ths.html</ref> to describe the chain of fifths as it relates to 12edo. Much of the theory on this page, however, comes from [[Kite Giedraitis]], no later than April 2014

VectorGraphics at 09:03, 18 August 2025

2025-08-18T09:03:16Z

← Older revision		Revision as of 09:03, 18 August 2025
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	A '''spiral chart''' is an illustration which converts a circle of repeats of an interval in one [[edo]] (or simply a temperament-agnostic chain of that interval) into a self-similar spiral shape, so that it may be compared with a circle of the same interval in a ~~(smaller) coprime~~ edo.		A '''spiral chart''' is an illustration which converts a circle of repeats of an interval in one [[edo]] (or simply a temperament-agnostic chain of that interval) into a self-similar spiral shape, so that it may be compared with a circle of the same interval in a related edo.

	Spiral charts were first known to be used by Jeff Jensen in 2004,<ref>https://jjensen.org/spiral5ths/Spiral5ths.html</ref> to describe the chain of fifths as it relates to 12edo. Much of the theory on this page, however, comes from [[Kite Giedraitis]], no later than April 2014		Spiral charts were first known to be used by Jeff Jensen in 2004,<ref>https://jjensen.org/spiral5ths/Spiral5ths.html</ref> to describe the chain of fifths as it relates to 12edo. Much of the theory on this page, however, comes from [[Kite Giedraitis]], no later than April 2014