Fantasy detempers - Revision history

VectorGraphics at 23:38, 29 December 2025

2025-12-29T23:38:35Z

← Older revision		Revision as of 23:38, 29 December 2025
Line 17:		Line 17:
	\|JI otonalities		\|JI otonalities
	\|Size of the odd number in the numerator		\|Size of the odd number in the numerator
			\|-
			\|[[Gnome]]
			\|Temperament which the edo supports
			\|Temperament complexity (Manhattan distance) of temperament intervals
	\|}		\|}

Line 30:		Line 34:
	A dwarf consists of the simplest (by odd-limit) octave-reduced [[JI]] [[Otonality and utonality\|otonal]] intervals that map to each step of the EDO.		A dwarf consists of the simplest (by odd-limit) octave-reduced [[JI]] [[Otonality and utonality\|otonal]] intervals that map to each step of the EDO.

	{{Navbox scale gallery}}		=== Gnome ===
			{{Todo\|inline=1\|text=Complete section}}{{Navbox scale gallery}}

	[[Category:Terms]][[Category:Scales by family]][[Category:Scale naming]][[Category:Edo]]		[[Category:Terms]][[Category:Scales by family]][[Category:Scale naming]][[Category:Edo]]

BudjarnLambeth at 00:39, 28 December 2025

2025-12-28T00:39:08Z

← Older revision		Revision as of 00:39, 28 December 2025
Line 32:		Line 32:
	{{Navbox scale gallery}}		{{Navbox scale gallery}}

	[[Category:Terms]][[Category:Scales by family]][[Category:Scale naming]]		[[Category:Terms]][[Category:Scales by family]][[Category:Scale naming]][[Category:Edo]]

BudjarnLambeth: Navbox

2025-12-28T00:37:16Z

Navbox

← Older revision		Revision as of 00:37, 28 December 2025
Line 29:		Line 29:
	=== Dwarf ===		=== Dwarf ===
	A dwarf consists of the simplest (by odd-limit) octave-reduced [[JI]] [[Otonality and utonality\|otonal]] intervals that map to each step of the EDO.		A dwarf consists of the simplest (by odd-limit) octave-reduced [[JI]] [[Otonality and utonality\|otonal]] intervals that map to each step of the EDO.

			{{Navbox scale gallery}}

	[[Category:Terms]][[Category:Scales by family]][[Category:Scale naming]]		[[Category:Terms]][[Category:Scales by family]][[Category:Scale naming]]

BudjarnLambeth: Uncategorised page

2025-12-28T00:14:56Z

Uncategorised page

← Older revision		Revision as of 00:14, 28 December 2025
Line 29:		Line 29:
	=== Dwarf ===		=== Dwarf ===
	A dwarf consists of the simplest (by odd-limit) octave-reduced [[JI]] [[Otonality and utonality\|otonal]] intervals that map to each step of the EDO.		A dwarf consists of the simplest (by odd-limit) octave-reduced [[JI]] [[Otonality and utonality\|otonal]] intervals that map to each step of the EDO.

			[[Category:Terms]][[Category:Scales by family]][[Category:Scale naming]]

VectorGraphics: Created page with "'''Fantasy detempers''' are a collection of algorithms for forming detemperaments of edos to just intonation, or to a higher-rank regular temperament. They have in common that the simplest interval mapped to each step of the edo is chosen, using some measure of complexity. The name "fantasy detemper" derives from the nomenclature of fantasy races for these methods. {| class="wikitable" |+Summary table !Scale type !Detemperament to !Complexity me..."

2025-11-13T01:02:55Z

Created page with "'''Fantasy detempers''' are a collection of algorithms for forming detemperaments of edos to just intonation, or to a higher-rank regular temperament. They have in common that the simplest interval mapped to each step of the edo is chosen, using some measure of complexity. The name "fantasy detemper" derives from the nomenclature of fantasy races for these methods. {| class="wikitable" |+Summary table !Scale type !Detemperament to !Complexity me..."

New page

'''Fantasy detempers''' are a collection of algorithms for forming [[Detemperament|detemperaments]] of [[Edo|edos]] to just intonation, or to a higher-rank regular temperament. They have in common that the simplest interval mapped to each step of the edo is chosen, using some measure of complexity. The name "fantasy detemper" derives from the nomenclature of fantasy races for these methods.
{| class="wikitable"
|+Summary table
!Scale type
!Detemperament to
!Complexity measure
|-
|[[Hobbit]]
|Temperament which the edo supports
|[[Tenney-Euclidean metrics|Tenney-Euclidean]] octave-equivalent seminorm
|-
|[[Elf]]
|Any temperament, including temperaments which the edo does not support
|Temperament complexity of representative simple JI intervals (chosen by [[Benedetti height]])
|-
|[[Dwarf]]
|JI otonalities
|Size of the odd number in the numerator
|}

== Types ==

=== Hobbit ===
A hobbit consists of the simplest intervals in a temperament which map to the steps of an [[edo]] (or any rank-1 temperament) that supports the temperament. Since a hobbit is octave-equivalent, an octave-equivalent measure of complexity is used. For a rank-2 temperament, the hobbit is the MOS of the EDO's size.

=== Elf ===
An elf consists of the simplest intervals in a temperament which map to the steps of an edo that does NOT support the temperament. In order to do this, a simple JI representative (by Benedetti height) is chosen for each interval of the temperament. Then the simplest of those intervals is chosen for each step of the edo, and then tempered by the temperament to produce the elf.

=== Dwarf ===
A dwarf consists of the simplest (by odd-limit) octave-reduced [[JI]] [[Otonality and utonality|otonal]] intervals that map to each step of the EDO.