41edo - Revision history

Vector at 14:37, 4 April 2026

2026-04-04T14:37:39Z

← Older revision		Revision as of 14:37, 4 April 2026
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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.

Inthar: /* JI approximation */

2026-03-01T04:29:37Z

JI approximation

← Older revision		Revision as of 04:29, 1 March 2026
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	!Quality		!Quality
	\|Subminor		\|Subminor
	\|'''~~Novaminor~~'''		\|'''Farminor'''
	\|~~Pentaminor~~		\|Nearminor
	\|Neutral		\|Neutral
	\|~~Pentamajor~~		\|Nearmajor
	\|'''~~Novamajor~~'''		\|'''Farmajor'''
	\|Supermajor		\|Supermajor
	\|-		\|-

Inthar: /* Chords */

2026-03-01T04:28:50Z

Chords

← Older revision		Revision as of 04:28, 1 March 2026
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	=== Chords ===		=== Chords ===
	41edo has three different flavors of minor and major intervals as well as neutral intervals. Its subminor and supermajor intervals approximate simpler septimal ratios such as 7/4 and 9/7, while its supraminor ("~~pentaminor~~") and submajor ("~~pentamajor~~") intervals approximate classical 5-limit harmony which includes ratios like 5/4 and 9/5, and its plain major and plain minor intervals approximate classic 3-limit ratios. As a result, 41edo has nine qualities of tertian, fifth-bounded triad: tendo, supermajor, novamajor, ~~pentamajor~~, neutral, ~~pentaminor~~, novaminor, subminor. However, 41edo lacks true interordinal intervals (to reach a tuning with both neutrals and interordinals, 58edo must be used), so as for latal fourth-bounded triads, there are only four qualities.		41edo has three different flavors of minor and major intervals as well as neutral intervals. Its subminor and supermajor intervals approximate simpler septimal ratios such as 7/4 and 9/7, while its supraminor ("nearminor") and submajor ("nearmajor") intervals approximate classical 5-limit harmony which includes ratios like 5/4 and 9/5, and its plain major and plain minor intervals approximate classic 3-limit ratios. As a result, 41edo has nine qualities of tertian, fifth-bounded triad: tendo, supermajor, novamajor, nearmajor, neutral, nearminor, novaminor, subminor. However, 41edo lacks true interordinal intervals (to reach a tuning with both neutrals and interordinals, 58edo must be used), so as for latal fourth-bounded triads, there are only four qualities.

	=== Scales ===		=== Scales ===

Inthar: /* Practice */

2026-02-23T04:55:13Z

Practice

← Older revision		Revision as of 04:55, 23 February 2026
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	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.		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.

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

Inthar: /* Chords */

2026-02-12T18:22:12Z

Chords

← Older revision		Revision as of 18:22, 12 February 2026
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	=== Chords ===		=== Chords ===
	41edo has three different flavors of minor and major intervals as well as neutral intervals. Its subminor and supermajor intervals approximate simpler septimal ratios such as 7/4 and 9/7, while its supraminor ("pentaminor") and submajor ("pentamajor") intervals approximate classical 5-limit harmony which includes ratios like 5/4 and 9/5, and its plain major and plain minor intervals approximate classic 3-limit ratios. As a result, 41edo has nine qualities of tertian, fifth-bounded triad: tendo, supermajor, novamajor, pentamajor, neutral, pentaminor, novaminor, subminor. However, 41edo lacks true ~~interseptimal~~ intervals (to reach a tuning with both neutrals and ~~interseptimals~~, 58edo must be used), so as for latal fourth-bounded triads, there are only four qualities.		41edo has three different flavors of minor and major intervals as well as neutral intervals. Its subminor and supermajor intervals approximate simpler septimal ratios such as 7/4 and 9/7, while its supraminor ("pentaminor") and submajor ("pentamajor") intervals approximate classical 5-limit harmony which includes ratios like 5/4 and 9/5, and its plain major and plain minor intervals approximate classic 3-limit ratios. As a result, 41edo has nine qualities of tertian, fifth-bounded triad: tendo, supermajor, novamajor, pentamajor, neutral, pentaminor, novaminor, subminor. However, 41edo lacks true interordinal intervals (to reach a tuning with both neutrals and interordinals, 58edo must be used), so as for latal fourth-bounded triads, there are only four qualities.

	=== Scales ===		=== Scales ===

Hkm: /* JI approximation */

2026-01-28T04:57:30Z

JI approximation

← Older revision		Revision as of 04:57, 28 January 2026
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	==== JI approximation ====		==== JI approximation ====
	41edo is most accurately a 2.3.5.7.11 tuning, though it also has an acceptable if sharp 13th harmonic, notably widening the difference between the [[Collection of chords#Arto triad\|arto]] and [[Collection of chords#Tendo triad\|tendo]] triads such that they become simple [[Slendric]] divisions of the fifth. Because it is not a meantone system, the best diatonic to use for 5-limit harmony is the Zarlino diatonic scale (LMsLMLs), tuned in 41edo as 7-6-4-7-6-7-4. However, it also features a MOS diatonic of 7-7-3-7-7-7-3.		41edo is most accurately a 2.3.5.7.11 tuning, though it also has an acceptable if sharp 13th harmonic, notably widening the difference between the [[Collection of chords#Arto triad\|arto]] (10:13:15) and [[Collection of chords#Tendo triad\|tendo]] (1/10:1/13:1/15) triads such that they become simple [[Slendric]] divisions of the fifth. Because it is not a meantone system, the best diatonic to use for 5-limit harmony is the Zarlino diatonic scale (LMsLMLs), tuned in 41edo as 7-6-4-7-6-7-4. However, it also features a MOS diatonic of 7-7-3-7-7-7-3.

	{{Harmonics in ED\|41\|31\|0}}		{{Harmonics in ED\|41\|31\|0}}
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	\|9/7		\|9/7
	\|}		\|}
	~~Diatonic thirds~~ are bolded.		Thirds available in the diatonic scale generated by stacking the perfect fifth are bolded.

	=== Chords ===		=== Chords ===
	41edo has three different flavors of minor and major intervals as well as neutral intervals. Its subminor and supermajor intervals approximate simpler ~~septal~~ ratios such as 7/4 and 9/7, while its supraminor ("pentaminor") and submajor ("pentamajor") intervals approximate classical 5-limit harmony which includes ratios like 5/4 and 9/5, and its plain major and plain minor intervals approximate classic 3-limit ratios. As a result, 41edo has nine qualities of tertian, fifth-bounded triad: tendo, supermajor, novamajor, pentamajor, neutral, pentaminor, novaminor, subminor. However, 41edo lacks true interseptimal intervals (to reach a tuning with both neutrals and interseptimals, 58edo must be used), so as for latal fourth-bounded triads, there are only four qualities.		41edo has three different flavors of minor and major intervals as well as neutral intervals. Its subminor and supermajor intervals approximate simpler septimal ratios such as 7/4 and 9/7, while its supraminor ("pentaminor") and submajor ("pentamajor") intervals approximate classical 5-limit harmony which includes ratios like 5/4 and 9/5, and its plain major and plain minor intervals approximate classic 3-limit ratios. As a result, 41edo has nine qualities of tertian, fifth-bounded triad: tendo, supermajor, novamajor, pentamajor, neutral, pentaminor, novaminor, subminor. However, 41edo lacks true interseptimal intervals (to reach a tuning with both neutrals and interseptimals, 58edo must be used), so as for latal fourth-bounded triads, there are only four qualities.

	=== Scales ===		=== Scales ===
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	== Practice ==		== Practice ==
	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.

	{{Cat\|Edos}}		{{Cat\|Edos}}

Inthar: /* Regular temperaments */

2026-01-25T07:13:29Z

Regular temperaments

← Older revision		Revision as of 07:13, 25 January 2026
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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, ~~and~~ 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 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.

	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.

Inthar: /* Practice */

2026-01-25T00:30:49Z

Practice

← Older revision		Revision as of 00:30, 25 January 2026
Line 54:		Line 54:
	== Practice ==		== Practice ==
	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.

			{{Cat\|Edos}}