41edo - Revision history

Inthar at 15:03, 6 June 2026

2026-06-06T15:03:56Z

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	=== Regular temperaments ===		=== Regular temperaments ===
	41edo shares Schismic (and its extension Garibaldi, and thus Marvel and ~~Hemifamity~~) with 29edo, Slendric (and its extension Miracle) with 31edo, Tetracot with 34edo, and Magic with 22edo. Magic is especially important here as it forms the fret layout and main string tuning for the Kite guitar.		41edo shares Schismic (and its extension Garibaldi, and thus Marvel and Aberschismic) with 29edo, Slendric (and its extension Miracle) with 31edo, Tetracot with 34edo, and Magic with 22edo. Magic is especially important here as it forms the fret layout and main string tuning for the Kite guitar.

	It also contains a slightly-stretched version of equal Bohlen-Pierce tuning (where the perfect twelfth of 3/1 is split into 13 equal parts) via every fifth step. If used in a linear temperament as the generator, this temperament is called Bohpier.		It also contains a slightly-stretched version of equal Bohlen-Pierce tuning (where the perfect twelfth of 3/1 is split into 13 equal parts) via every fifth step. If used in a linear temperament as the generator, this temperament is called Bohpier.

Vector at 01:42, 29 May 2026

2026-05-29T01:42:16Z

← Older revision		Revision as of 01:42, 29 May 2026
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	== Notation ==		== Notation ==
	Since 41edo has a perfect fifth which is split exactly in half, semisharps and semiflats (as in [[Diatonic notation\|neutral diatonic notation]]) can be used to notate it. A useful addition is ups and downs, which naturally reflect 41edo's structure, as 5/4 is downmajor, 81/64 is major, and 9/7 is upmajor. (In fact, "up" can be declared equivalent to "super"/"supra" and "down" equivalent to "sub".)		Since 41edo has a perfect fifth which is split exactly in half, semisharps and semiflats (as in [[Diatonic notation\|neutral diatonic notation]]) can be used to notate it. A useful addition is ups and downs, which naturally reflect 41edo's structure, as 5/4 is downmajor, 81/64 is major, and 9/7 is upmajor. (In fact, "up" can be declared equivalent to "super"/"supra" and "down" equivalent to "sub"; preferable to Unque and also indicative of the flat tuning of 5/4 in the temperament.)

	== Practice ==		== Practice ==

Vector at 01:41, 29 May 2026

2026-05-29T01:41:11Z

← Older revision		Revision as of 01:41, 29 May 2026
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	Most notably, the Kite Guitar itself uses 41edo, and is advertised as a general-purpose just-intonation-esque instrument, notably treating 41edo implicitly as the solution to compromising high-accuracy JI with equal temperament. The Kite Guitar manages the high density of notes by only having frets for every other note of 41edo, and tuning the strings in a way that allows one string to fill in the gaps of an adjacent string.		Most notably, the Kite Guitar itself uses 41edo, and is advertised as a general-purpose just-intonation-esque instrument, notably treating 41edo implicitly as the solution to compromising high-accuracy JI with equal temperament. The Kite Guitar manages the high density of notes by only having frets for every other note of 41edo, and tuning the strings in a way that allows one string to fill in the gaps of an adjacent string.

	On another note, the ''color notation'' system seems specifically well-designed for 41edo, as a tuning of tetracot with high accuracy in the 2.3.5.7.11 subgroup. Colors can unambiguously be assigned to 41edo interval qualities without any of the extra overhead that comes with managing color notation for just intonation or larger edos, but while feeling like it uses the notation to its full potential. The qualities in order, from subminor to supermajor, are ''zo'' (7/), minor ''wa'' (/3), ''gu'' (/5), ''(i)la'' (11)'', yo'' (5/), major ''wa'' (3/), and ''ru'' (/7). This also serves to explain the unusual nature of "la" as "lavender", with the 11/ and /11 colors conflated due to the fact that in 41edo, rastmic tempering is assumed.		On another note, the ''color notation'' system seems specifically well-designed for 41edo, as a tuning of tetracot with high accuracy in the 2.3.5.7.11 subgroup. Colors can unambiguously be assigned to 41edo interval qualities without any of the extra overhead that comes with managing color notation for just intonation or larger edos, but while feeling like it uses the notation to its full potential. The qualities in order, from subminor to supermajor, are ''zo'' (7/), minor ''wa'' (3), ''gu'' (/5), ''(i)la'' (11)'', yo'' (5/), major ''wa'' (3), and ''ru'' (/7). This also serves to explain the unusual nature of "la" as "lavender", with the 11/ and /11 colors conflated due to the fact that in 41edo, rastmic tempering is assumed.

	Additionally, ups and downs seems to work particularly well for the combination of undecimal garibaldi, slendric, and rastmic tempering, which is a characteristic of specifically 41edo, due to allowing the arrow to refer to a large number of different structural commas that are in the size range.		Additionally, ups and downs seems to work particularly well for the combination of undecimal garibaldi, slendric, and rastmic tempering, which is a characteristic of specifically 41edo, due to allowing the arrow to refer to a large number of different structural commas that are in the size range.

Vector at 01:40, 29 May 2026

2026-05-29T01:40:47Z

← Older revision		Revision as of 01:40, 29 May 2026
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	41edo is used by the musician and conlanger Lamplight as a standard tuning for their ''Shasavic'' theory of music.		41edo is used by the musician and conlanger Lamplight as a standard tuning for their ''Shasavic'' theory of music.

	~~41edo~~ is ~~used in~~ Kite ~~Giedraitis~~'s Kite Guitar, ~~which~~ manages the high density of notes by only having frets for every other note of 41edo, and tuning the strings in a way that allows one string to fill in the gaps of an adjacent string.		=== Kite's work ===
			There is a large amount of evidence suggesting that Kite's body of work is implicitly designed with 41edo in mind.

			Most notably, the Kite Guitar itself uses 41edo, and is advertised as a general-purpose just-intonation-esque instrument, notably treating 41edo implicitly as the solution to compromising high-accuracy JI with equal temperament. The Kite Guitar manages the high density of notes by only having frets for every other note of 41edo, and tuning the strings in a way that allows one string to fill in the gaps of an adjacent string.

			On another note, the ''color notation'' system seems specifically well-designed for 41edo, as a tuning of tetracot with high accuracy in the 2.3.5.7.11 subgroup. Colors can unambiguously be assigned to 41edo interval qualities without any of the extra overhead that comes with managing color notation for just intonation or larger edos, but while feeling like it uses the notation to its full potential. The qualities in order, from subminor to supermajor, are ''zo'' (7/), minor ''wa'' (/3), ''gu'' (/5), ''(i)la'' (11)'', yo'' (5/), major ''wa'' (3/), and ''ru'' (/7). This also serves to explain the unusual nature of "la" as "lavender", with the 11/ and /11 colors conflated due to the fact that in 41edo, rastmic tempering is assumed.

			Additionally, ups and downs seems to work particularly well for the combination of undecimal garibaldi, slendric, and rastmic tempering, which is a characteristic of specifically 41edo, due to allowing the arrow to refer to a large number of different structural commas that are in the size range.

	{{Navbox EDO}}		{{Navbox EDO}}
	{{Cat\|Edos}}		{{Cat\|Edos}}

Inthar: /* Edostep interpretations */

2026-04-13T04:16:35Z

Edostep interpretations

← Older revision		Revision as of 04:16, 13 April 2026
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	=== Edostep interpretations ===		=== Edostep interpretations ===
	One step of ~~46edo~~ represents the following ratios of 2.3.5.7.11.13.19:		One step of 41edo represents the following ratios of 2.3.5.7.11.13.19:
	* 81/80 (between 5/4 and 81/64)		* 81/80 (between 5/4 and 81/64)
	* 49/48 (between 7/6 and 8/7)		* 49/48 (between 7/6 and 8/7)

Inthar: /* Edostep interpretations */

2026-04-13T04:16:20Z

Edostep interpretations

← Older revision		Revision as of 04:16, 13 April 2026
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	* 55/54 (between 27/20 and 11/8)		* 55/54 (between 27/20 and 11/8)
	* 56/55 (between 5/4 and 14/11)		* 56/55 (between 5/4 and 14/11)
			* 57/56 (between 7/6 and 19/16)
			* 91/90 (between 9/7 and 13/10)
			* 96/95 (between 19/16 and 6/5)
	* 99/98 (between 14/11 and 9/7)		* 99/98 (between 14/11 and 9/7)
	* 121/120 (between 12/11 and 11/10)		* 121/120 (between 12/11 and 11/10)

Inthar: /* Theory */

2026-04-13T04:14:33Z

Theory

@@ Line 46: / Line 46: @@
 |}
 Thirds available in the diatonic scale generated by stacking the perfect fifth are bolded.
 === Derivation ===

Vector at 14:37, 4 April 2026

2026-04-04T14:37:39Z

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	\|}		\|}
	Thirds available in the diatonic scale generated by stacking the perfect fifth are bolded.		Thirds available in the diatonic scale generated by stacking the perfect fifth are bolded.

			=== Derivation ===
			41edo is derived by tempering out neither 81/80 nor 64/63, but rather setting them equal, and using the same step to separate 5/4 from a neutral third and 8/7 from 7/6.

	=== Chords ===		=== Chords ===

Inthar: /* Scales */

2026-04-04T12:14:13Z

Scales

← Older revision		Revision as of 12:14, 4 April 2026
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	=== Scales ===		=== Scales ===
	41edo's 5-limit intervals are not found particularly early on in the chain of fifths, with 6/5 being an augmented second and 5/4 a diminished fourth. Notably, 41edo has a 17-note chromatic scale generated by the perfect fifth, 3-3-3-1-3-3-1-3-3-3-1-3-3-1-3-3-1, in which the classical (~5/4) major and classical (~6/5) minor thirds span the same number of scale steps, giving the scale familiar chord qualities.		41edo's 5-limit intervals are not found particularly early on in the chain of fifths, with 6/5 being an augmented second and 5/4 a diminished fourth. Notably, 41edo has a 17-note chromatic scale generated by the perfect fifth, 3-3-3-1-3-3-1-3-3-3-1-3-3-1-3-3-1, in which the classical (~5/4) major and classical (~6/5) minor thirds span the same number of scale steps, giving the scale familiar chord qualities.

			11-limit [[penslen]] is available in 41edo (because of Slendric and 385/384 tempering): 2-1-5-1-2-5-1-2-5-1-2-1-5-2-1-5.

	=== Regular temperaments ===		=== Regular temperaments ===

Lumithesilly: added steps to the thirds table

2026-03-05T01:59:49Z

added steps to the thirds table

← Older revision		Revision as of 01:59, 5 March 2026
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	\|'''14/11'''		\|'''14/11'''
	\|9/7		\|9/7
			\|-
			!Steps
			\|9
			\|'''10'''
			\|11
			\|12
			\|13
			\|'''14'''
			\|15
	\|}		\|}
	Thirds available in the diatonic scale generated by stacking the perfect fifth are bolded.		Thirds available in the diatonic scale generated by stacking the perfect fifth are bolded.