Kite's thoughts on 41edo brass instruments - Revision history

TallKite at 08:02, 11 November 2025

2025-11-11T08:02:02Z

← Older revision		Revision as of 08:02, 11 November 2025
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	!1st		!1st
	!2		!2
	\|28/27		\|[[28/27]]
	\|56/54		\|56/54
	\|63.0		\|63.0
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	!2nd		!2nd
	!3		!3
	\|19/18		\|[[19/18]]
	\|57/54		\|57/54
	\|93.6		\|93.6
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	!3rd		!3rd
	!4		!4
	\|29/27		\|[[29/27]]
	\|58/54		\|58/54
	\|123.7		\|123.7
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	!4th		!4th
	!8		!8
	\|31/27		\|[[31/27]]
	\|62/54		\|62/54
	\|239.2		\|239.2
	\|8\41 + 5.0¢		\|8\41 + 5.0¢
	\|}		\|}
	These valves make the subharmonic series 15-note fragment 71::54, with 70 and 55 missing. ~~Adjusting~~ the cents of each valve slightly ~~will~~ improve the ~~tuning, but not by much~~.		These valves make the subharmonic series 15-note fragment 71::54, with 70 and 55 missing. Slightly adjusting the cents of each valve may slightly improve the intonation.

	In the chart below, ○ is a closed/released valve and ● is an open/depressed valve. The fingering chart assumes the valves run in order with 1st = 2\41, 2nd = 3\41, 3rd = 4\41 and 4th = 8\41. The largest errors are '''bolded'''. Notes are for a Bb trumpet. Many notes have alternate fingerings. Notes in parentheses have an alternate fingering with markedly better intonation.		In the chart below, ○ is a closed/released valve and ● is an open/depressed valve. The fingering chart assumes the valves run in order with 1st = 2\41, 2nd = 3\41, 3rd = 4\41 and 4th = 8\41. The largest errors are '''bolded'''. Notes are for a Bb trumpet. Many notes have alternate fingerings. Notes in parentheses have an alternate fingering with markedly better intonation.
Line 71:		Line 71:
	Note that 69/54 or 23/18 is almost exactly midway between 15\41 and 14\41. And 71/54 is 17\41 - 23.7¢, which is actually 16\41 + 5.5¢. Thus 2+3+4+8 is actually 16! This is fortuitous because 4/3 is 17\41 and 16 edosteps neatly fills the gap between the 3rd and 4th harmonics.		Note that 69/54 or 23/18 is almost exactly midway between 15\41 and 14\41. And 71/54 is 17\41 - 23.7¢, which is actually 16\41 + 5.5¢. Thus 2+3+4+8 is actually 16! This is fortuitous because 4/3 is 17\41 and 16 edosteps neatly fills the gap between the 3rd and 4th harmonics.

	The error from 41edo is the sum of the valve ratio's error and the harmonic's error. For example, 28/27 is 4.4¢ flat of 2\41 and the 5th harmonic is 5.8¢ sharp of 13\41, so the error for C# is 1.4¢.		The error from 41edo is the sum of the valve ratio's error and the harmonic's error. For example, 28/27 is 4.4¢ flat of 2\41 and the 5th harmonic is 5.8¢ sharp of 13\41, so the error for the 5th harmonic's C# is 1.4¢.

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	~~Here are the full 2 octaves produced by a Bb trumpet. Note that the bolded notes for the two largest errors often have alternative fingerings.~~

	*		Here are the full 2 octaves produced by a Bb trumpet. The low vF and the high vC are missing.


	{\| class="wikitable mw-collapsible mw-collapsed center-all"		{\| class="wikitable mw-collapsible mw-collapsed center-all"

TallKite at 04:44, 11 November 2025

2025-11-11T04:44:30Z

← Older revision		Revision as of 04:44, 11 November 2025
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	See also [[Kite's thoughts on 31edo brass instruments]].		See also [[Kite's thoughts on 31edo brass instruments]].

	== ~~Unskipped 41edo~~ instruments ==		== 2-3-4-8 instruments ==
	The best [[Delta-N ratio\|delta-1]]<nowiki/>ratio approximation of 2\41 is 28/27. This gives us these valve lengths:		The best [[Delta-N ratio\|delta-1]]<nowiki/>ratio approximation of 2\41 is 28/27. This gives us these valve lengths:
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	== Skip-valved instruments ==		== Skip-valved instruments ==
	Skip-valves omit every other step of 41-edo. The intonation isn't nearly as good as ~~an unskipped~~ instrument.		Skip-valves omit every other step of 41-edo. The intonation isn't nearly as good as a 2-3-4-8 instrument.

	A skip-valved Kite brass instrument has 4 valves that lower the pitch by 2\41, 4\41, 8\41 and 16\41. Skip-valved is analogous to the skip-fretting of a [[Kite Guitar\|Kite guitar]]. Each fret is 2\41, so these valves are for 1, 2, 4 or 8 frets respectively. Various valve combinations lower the pitch by 1 to 15 frets. (A 1\41 valve is actually physically difficult to make, since the tube length is so short.)		A skip-valved Kite brass instrument has 4 valves that lower the pitch by 2\41, 4\41, 8\41 and 16\41. Skip-valved is analogous to the skip-fretting of a [[Kite Guitar\|Kite guitar]]. Each fret is 2\41, so these valves are for 1, 2, 4 or 8 frets respectively. Various valve combinations lower the pitch by 1 to 15 frets. (A 1\41 valve is actually physically difficult to make, since the tube length is so short.)

TallKite at 04:24, 11 November 2025

2025-11-11T04:24:00Z

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TallKite: corrected the sign of JI errors per harmonic

2025-11-11T00:11:18Z

corrected the sign of JI errors per harmonic

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TallKite: accounted for harmonics 3, 5 and 7 being off in 41edo

2025-11-10T07:48:37Z

accounted for harmonics 3, 5 and 7 being off in 41edo

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TallKite at 06:52, 10 November 2025

2025-11-10T06:52:13Z

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TallKite: TallKite moved page Kite-valved Brass Instruments to Kite's thoughts on 41edo brass instruments

2025-11-10T05:01:14Z

TallKite moved page Kite-valved Brass Instruments to Kite's thoughts on 41edo brass instruments

← Older revision	Revision as of 05:01, 10 November 2025
(No difference)

TallKite at 04:36, 10 November 2025

2025-11-10T04:36:55Z

← Older revision		Revision as of 04:36, 10 November 2025
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	The intervals are descending so 63.0¢ means 63.0¢ below the unvalved note. Thus the error is the opposite sign from what is expected. For example, the 1st valve lowers by 63¢, 4.4¢ more than 2\41, thus the note is 4.4¢ flat of 41edo.		The intervals are descending so 63.0¢ means 63.0¢ below the unvalved note. Thus the error is the opposite sign from what is expected. For example, the 1st valve lowers by 63¢, 4.4¢ more than 2\41, thus the note is 4.4¢ flat of 41edo.

	○ = a closed/released valve, ● = an open/depressed valve. Notes are for a Bb trumpet.		In the chart below, ○ is a closed/released valve, and ● is an open/depressed valve. The 2 largest errors are bolded. Notes are for a Bb trumpet.

	{\| class="wikitable center-all"		{\| class="wikitable center-all"

TallKite at 04:34, 10 November 2025

2025-11-10T04:34:23Z

← Older revision		Revision as of 04:34, 10 November 2025
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	\|8\41 + 5.0¢		\|8\41 + 5.0¢
	\|}		\|}
	These valves make the subharmonic series 15-note fragment 71::54, with 70 and 55 missing. ~~But~~ 71/54 is 17\41 - 23.7¢ which is actually 16\41 + 5.5¢. Thus in the chart below 2+3+4+8 = 16! ~~Note that 69~~/~~54 or 23/18~~ is ~~almost exactly midway between 15~~\41 and ~~14\41~~.		These valves make the subharmonic series 15-note fragment 71::54, with 70 and 55 missing. Note that 69/54 or 23/18 is almost exactly midway between 15\41 and 14\41. And 71/54 is 17\41 - 23.7¢ which is actually 16\41 + 5.5¢. Thus in the chart below 2+3+4+8 = 16! This is fortuitous because 4/3 is 17\41 and 16 edosteps fills the gap between the 3rd and 4th harmonics.

	The ~~cents~~ are descending ~~cents, which~~ means ~~positive numbers indicate flatness and negative numbers indicate sharpness~~. For example, the 1st valve lowers by 63¢, 4.4¢ more than 2\41, thus the note is 4.4¢ flat of 41edo.		The intervals are descending so 63.0¢ means 63.0¢ below the unvalved note. Thus the error is the opposite sign from what is expected. For example, the 1st valve lowers by 63¢, 4.4¢ more than 2\41, thus the note is 4.4¢ flat of 41edo.

	○ = a closed/released valve, ● = an open/depressed valve. Notes are for a Bb trumpet.		○ = a closed/released valve, ● = an open/depressed valve. Notes are for a Bb trumpet.
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	!28/27		!28/27
	\|63.0		\|63.0
	\|4.4		\| -4.4
	\|^E		\|^E
	\|^A		\|^A
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	!19/18		!19/18
	\|93.6		\|93.6
	\|5.8		\| -5.8
	\|E		\|E
	\|A		\|A
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	!29/27		!29/27
	\|123.7		\|123.7
	\|6.6		\| -6.6
	\|vE		\|vE
	\|vA		\|vA
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	!59/54		!59/54
	\|153.3		\|153.3
	\|7.0		\| -7.0
	\|^D# vvE		\|^D# vvE
	\|^G# vvA		\|^G# vvA
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	!10/9		!10/9
	\|182.4		\|182.4
	\|6.8		\| -6.8
	\|D# ^Eb		\|D# ^Eb
	\|G# ^Ab		\|G# ^Ab
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	!61/54		!61/54
	\|211.0		\|211.0
	\|6.1		\| -6.1
	\|vD# Eb		\|vD# Eb
	\|vG# Ab		\|vG# Ab
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	!31/27		!31/27
	\|239.2		\|239.2
	\|5.0		\| -5.0
	\|^^D vEb		\|^^D vEb
	\|^^G vAb		\|^^G vAb
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	!7/6		!7/6
	\|266.9		\|266.9
	\|3.5		\| -3.5
	\|^D		\|^D
	\|^G		\|^G
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	!32/27		!32/27
	\|294.1		\|294.1
	\|1.5		\| -1.5
	\|D		\|D
	\|G		\|G
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	!65/54		!65/54
	\|321.0		\|321.0
	\| -1.0		\| 1.0
	\|vD		\|vD
	\|vG		\|vG
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	!11/9		!11/9
	\|347.4		\|347.4
	\| -3.8		\| 3.8
	\|^C# vvD		\|^C# vvD
	\|^F# vvG		\|^F# vvG
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	!67/54		!67/54
	\|373.4		\|373.4
	\| -7.0		\| 7.0
	\|C# ^Db		\|C# ^Db
	\|F# ^Gb		\|F# ^Gb
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	!34/27		!34/27
	\|399.1		\|399.1
	\| '''-10.7'''		\| '''10.7'''
	\|'''vC# Db'''		\|'''vC# Db'''
	\|'''vF# Gb'''		\|'''vF# Gb'''
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	!23/18		!23/18
	\|424.4		\|424.4
	\| '''-14.7'''		\| '''-14.6'''
	\|'''^^C vDb'''		\|'''^^C vDb'''
	\|'''^^F vGb'''		\|'''^^F vGb'''
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	!71/54		!71/54
	\|473.8		\|473.8
	\| 5.5		\| -5.5
	\|^C		\|^C
	\|^F		\|^F

TallKite: done

2025-11-10T04:23:57Z

done

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