Kite-valved Brass Instruments: Difference between revisions

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A simple horn without any valves or slides is only capable of playing the harmonic series. A conventional brass instrument (with the exception of the trombone, which is naturally microtonal) has valves that lengthen the tubing and lower the pitch by small amounts, typically a minor 2nd, a major 2nd and a minor 3rd. By selecting the proper combination of valves, the player can "fill the gap" between the various harmonics and play a complete 12-edo scale. The intervals don't add up precisely because they add a fixed length rather than multiply by a fixed ratio. The player must compensate for this.
This page discusses the Kite trumpet, Kite flugelhorn, Kite french horn, Kite tuba, etc., all of which use skip-valves that omit every other step of 41-edo.


A Kite-tuned brass instrument would have 4 valves that lower the pitch by 2\41, 4\41, 8\41 and 16\41. These valves are analogous to the frets of a 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 simple horn without any valves or slides is only capable of playing the harmonic series. A conventional brass instrument (with the exception of the trombone, which is naturally microtonal) has valves that lengthen the tubing and lower the pitch by small amounts, typically a minor 2nd, a major 2nd and a minor 3rd. By selecting the proper combination of valves, the player can fill the gap between the various harmonics and play a complete 12-edo scale. The intervals don't add up precisely because they add a fixed length rather than multiply the length by a fixed ratio. The player must compensate for this.


The individual harmonics in the harmonic series are analogous to the strings of a Kite guitar. The instrument proposed here would have especially long tubing, so that the harmonics 3-9 are easily played, and harmonics 1 and 2 would be unused. The reasoning is that the interval between two harmonics should be an odd number of edosteps, which 3/2 is not. This is so that the harmonic will fill in the gaps of the lower harmonic. Also, each harmonic needs to be at most 16 frets (32 edosteps) from the harmonic above the next harmonic, since that is the range of the valves is 15 frets. Thus the ratio must be at most 12/7 = 32\41. Harmonics 3, 4, 5, 7 and 9 meet these requirements. The 8th harmonic is like an extra string that provides an alternate path to certain notes.  
A skip-valved Kite brass instrument would have 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.)


The fingering chart below assumes the valves run in order 1st = 1 fret, 2nd = 2 frets, 3rd = 4 frets and 4th = 8 frets. It also assumes the lowest note of the instrument is F (with all valves closed, and playing the 1st harmonic). Notes that are duplicated by a higher harmonic are in parentheses.  
The individual harmonics in the harmonic series are analogous to the strings of a Kite guitar. The instrument proposed here would have especially long tubing, so that the harmonics 3-9 are easily played, and harmonics 1 and 2 are not and would be unused. The reasoning is that the interval between two harmonics should be an odd number of edosteps, which 3/2 is not. This is so that the harmonic will fill in the gaps of the lower harmonic. Also, each harmonic needs to be at most 16 frets (32 edosteps) from the harmonic two above it, since that is the range of the valves. Thus the ratio must be at most 12/7 = 32\41. Harmonics 3, 4, 5, 6, 7 and 9 meet these requirements. The 8th harmonic is like an extra string that overlaps the 7th harmonic's notes and provides an alternate path to certain notes. Harmonics 10 and 11 overlap the 9th harmonic, so 9 is a good stopping point.
{| class="wikitable"
 
The fingering chart below assumes the valves run in order with 1st = 1 fret, 2nd = 2 frets, 3rd = 4 frets and 4th = 8 frets. ● = open/depressed, ○ = closed/released. It also assumes the lowest note of the instrument is F (with all valves open, and playing the 1st harmonic). Notes that are duplicated by a higher harmonic are in parentheses. The final column shows the sharpness caused by intervals not adding up precisely.  
{| class="wikitable center-all"
|+
|+
! rowspan="2" |fret
! rowspan="2" |fret
! rowspan="2" |valves
! rowspan="2" |valves
(○ = open,
● = closed)
! colspan="7" |harmonics
! colspan="7" |harmonics
! rowspan="2" |error
|-
|-
!3
!3
Line 32: Line 32:
|F
|F
|G
|G
|0.0¢
|-
|-
!1
!1
Line 42: Line 43:
|^^F/vGb
|^^F/vGb
|^^G/vAb
|^^G/vAb
|0.0¢
|-
|-
!2
!2
Line 52: Line 54:
|F#/^Gb
|F#/^Gb
|G#/^Ab
|G#/^Ab
|0.0¢
|-
|-
!3
!3
Line 62: Line 65:
|vG
|vG
|vA
|vA
|3.8¢
|-
|-
!4
!4
Line 72: Line 76:
|^G
|^G
|^A
|^A
|0.0¢
|-
|-
!5
!5
Line 82: Line 87:
|vG#/Ab
|vG#/Ab
|vA#/Bb
|vA#/Bb
|7.3¢
|-
|-
!6
!6
Line 92: Line 98:
|^G#/vvA
|^G#/vvA
|^A#/vvB
|^A#/vvB
|14.4¢
|-
|-
!7
!7
Line 102: Line 109:
|A
|A
|B
|B
|24.6¢
|-
|-
!8
!8
Line 112: Line 120:
|^^A/vBb
|^^A/vBb
|vC
|vC
|0.0¢
|-
|-
!9
!9
Line 122: Line 131:
|A#/^Bb
|A#/^Bb
|^C
|^C
|13.7¢
|-
|-
!10
!10
Line 132: Line 142:
|vB
|vB
|vC#/Db
|vC#/Db
|27.0¢
|-
|-
!11
!11
Line 142: Line 153:
|^B
|^B
|^C#/vvD
|^C#/vvD
|43.0¢
|-
|-
!12
!12
Line 152: Line 164:
|C
|C
|D
|D
|52.7¢
|-
|-
!13
!13
Line 162: Line 175:
|^^C
|^^C
|^^D/vEb
|^^D/vEb
|70.8¢
|-
|-
!14
!14
Line 172: Line 186:
|C#/^Db
|C#/^Db
|D#/^Eb
|D#/^Eb
|88.5¢
|-
|-
!15
!15
Line 182: Line 197:
|vD
|vD
|vE
|vE
|108.4¢
|}
|}
The next chart shows each harmonic's 16 notes plotted against the full 41edo gamut of notes. There is over 2 octaves total range. Note the 7 missing notes in the lowest part of the range, and the 3 missing notes in the highest part. The next two harmonics, 10 and 11, mostly duplicate the pitches in harmonic 9.
One way to correct the cents errors might be to have a 5th valve, a trombone-style one, that moves a tiny amount depending on which of the other 4 valves are open. It could be done with a microchip, 4 sensors and a very accurate stepper motor. It would run off a battery, or perhaps solar power.
{| class="wikitable"
 
The next chart shows each harmonic's 16 notes plotted against the full 41edo gamut of notes. There is over 2 octaves total range. Note the 8 missing notes in the lowest part of the range, and the 3 missing notes in the highest part, all marked with asterisks. The next two harmonics, 10 and 11, merely extend the pitches of harmonic 9 without supplying any missing notes. Likewise the previous harmonic, 2, merely extends the pitches of harmonic 3 downwards.
{| class="wikitable mw-collapsible mw-collapsed center-all"
|+
|+
Full 2 octave range (low note C)
! rowspan="2" |41-edo
! rowspan="2" |41-edo
gamut
gamut
Line 207: Line 226:
|
|
|-
|-
!
!*
|
|
|
|
Line 225: Line 244:
|
|
|-
|-
!
!*
|
|
|
|
Line 243: Line 262:
|
|
|-
|-
!
! *
|
|
|
|
Line 252: Line 271:
|
|
|-
|-
!
!  
|vD
|vD
|
|
Line 261: Line 280:
|
|
|-
|-
!D
!D *
|
|
|
|
Line 279: Line 298:
|
|
|-
|-
!
!*
|
|
|
|
Line 297: Line 316:
|
|
|-
|-
!
!*
|
|
|
|
Line 315: Line 334:
|
|
|-
|-
!
!*
|
|
|
|
Line 333: Line 352:
|
|
|-
|-
!
!*
|
|
|
|
Line 1,008: Line 1,027:
|D
|D
|-
|-
!
!*
|
|
|
|
Line 1,026: Line 1,045:
|^^D/vEb
|^^D/vEb
|-
|-
!
!*
|
|
|
|
Line 1,044: Line 1,063:
|D#/^Eb
|D#/^Eb
|-
|-
!
! *
|
|  
|
|
|
|
Line 1,062: Line 1,081:
|vE
|vE
|}
|}
[[Category:Kite Guitar]]
[[Category:41edo]]

Latest revision as of 20:42, 22 August 2021

This page discusses the Kite trumpet, Kite flugelhorn, Kite french horn, Kite tuba, etc., all of which use skip-valves that omit every other step of 41-edo.

A simple horn without any valves or slides is only capable of playing the harmonic series. A conventional brass instrument (with the exception of the trombone, which is naturally microtonal) has valves that lengthen the tubing and lower the pitch by small amounts, typically a minor 2nd, a major 2nd and a minor 3rd. By selecting the proper combination of valves, the player can fill the gap between the various harmonics and play a complete 12-edo scale. The intervals don't add up precisely because they add a fixed length rather than multiply the length by a fixed ratio. The player must compensate for this.

A skip-valved Kite brass instrument would have 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. 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.)

The individual harmonics in the harmonic series are analogous to the strings of a Kite guitar. The instrument proposed here would have especially long tubing, so that the harmonics 3-9 are easily played, and harmonics 1 and 2 are not and would be unused. The reasoning is that the interval between two harmonics should be an odd number of edosteps, which 3/2 is not. This is so that the harmonic will fill in the gaps of the lower harmonic. Also, each harmonic needs to be at most 16 frets (32 edosteps) from the harmonic two above it, since that is the range of the valves. Thus the ratio must be at most 12/7 = 32\41. Harmonics 3, 4, 5, 6, 7 and 9 meet these requirements. The 8th harmonic is like an extra string that overlaps the 7th harmonic's notes and provides an alternate path to certain notes. Harmonics 10 and 11 overlap the 9th harmonic, so 9 is a good stopping point.

The fingering chart below assumes the valves run in order with 1st = 1 fret, 2nd = 2 frets, 3rd = 4 frets and 4th = 8 frets. ● = open/depressed, ○ = closed/released. It also assumes the lowest note of the instrument is F (with all valves open, and playing the 1st harmonic). Notes that are duplicated by a higher harmonic are in parentheses. The final column shows the sharpness caused by intervals not adding up precisely.

fret valves harmonics error
3 4 5 6 7 8 9
0 ●●●● C F vA C ^^D/vEb F G 0.0¢
1 ○●●● ^^C ^^F/vGb ^A ^^C D#/^Eb ^^F/vGb ^^G/vAb 0.0¢
2 ●○●● C#/^Db F#/^Gb vA#/Bb C#/^Db vE F#/^Gb G#/^Ab 0.0¢
3 ○○●● vD vG ^A#/vvB vD ^E vG vA 3.8¢
4 ●●○● ^D ^G B ^D (F) ^G ^A 0.0¢
5 ○●○● vD#/Eb vG#/Ab vC vD#/Eb (^^F/vGb) vG#/Ab vA#/Bb 7.3¢
6 ●○○● ^D#/vvE ^G#/vvA ^C ^D#/vvE (F#/^Gb) ^G#/vvA ^A#/vvB 14.4¢
7 ○○○● E A vC#/Db E (vG) A B 24.6¢
8 ●●●○ vF ^^A/vBb ^C#/vvD vF (^G) ^^A/vBb vC 0.0¢
9 ○●●○ ^F A#/^Bb D ^F (vG#/Ab) A#/^Bb ^C 13.7¢
10 ●○●○ vF#/Gb vB (^^D/vEb) vF#/Gb (^G#/vvA) vB vC#/Db 27.0¢
11 ○○●○ ^F#/vvG ^B (D#/^Eb) ^F#/vvG (A) ^B ^C#/vvD 43.0¢
12 ●●○○ G (C) (vE) (G) (^^A/vBb) C D 52.7¢
13 ○●○○ ^^G/vAb (^^C) (^E) (^^G/vAb) (A#/^Bb) ^^C ^^D/vEb 70.8¢
14 ●○○○ G#/^Ab (C#/^Db) (F) (G#/^Ab) (vB) C#/^Db D#/^Eb 88.5¢
15 ○○○○ (vA) (vD) (^^F/vGb) (vA) (^B) vD vE 108.4¢

One way to correct the cents errors might be to have a 5th valve, a trombone-style one, that moves a tiny amount depending on which of the other 4 valves are open. It could be done with a microchip, 4 sensors and a very accurate stepper motor. It would run off a battery, or perhaps solar power.

The next chart shows each harmonic's 16 notes plotted against the full 41edo gamut of notes. There is over 2 octaves total range. Note the 8 missing notes in the lowest part of the range, and the 3 missing notes in the highest part, all marked with asterisks. The next two harmonics, 10 and 11, merely extend the pitches of harmonic 9 without supplying any missing notes. Likewise the previous harmonic, 2, merely extends the pitches of harmonic 3 downwards.

Full 2 octave range (low note C)
41-edo

gamut

harmonics
3 4 5 6 7 8 9
C C
*
^^C
*
C#/^Db
*
vD
D *
^D
*
vD#/Eb
*
^D#/vvE
*
E E
*
vF
F F
^F
^^F/vGb
vF#/Gb
F#/^Gb
^F#/vvG
vG
G G
^G
^^G/vAb
vG#/Ab
G#/^Ab
^G#/vvA
(vA) vA
A A
^A
^^A/vBb
vA#/Bb
A#/^Bb
^A#/vvB
vB
B B
^B
vC
C (C) C
^C
(^^C) ^^C
vC#/Db
(C#/^Db) C#/^Db
^C#/vvD
(vD) vD
D D
^D
(^^D/vEb) ^^D/vEb
vD#/Eb
(D#/^Eb) D#/^Eb
^D#/vvE
(vE) vE
E E
(^E) ^E
vF
F (F) (F) F
^F
(^^F/vGb) (^^F/vGb) ^^F/vGb
vF#/Gb
(F#/^Gb) F#/^Gb
^F#/vvG
(vG) vG
G (G) G
(^G) ^G
(^^G/vAb) ^^G/vAb
(vG#/Ab) vG#/Ab
(G#/^Ab) G#/^Ab
(^G#/vvA) ^G#/vvA
(vA) vA
A (A) A
^A
(^^A/vBb) ^^A/vBb
vA#/Bb
(A#/^Bb) A#/^Bb
^A#/vvB
(vB) vB
B B
(^B) ^B
vC
C C
^C
^^C
vC#/Db
C#/^Db
^C#/vvD
vD
D D
*
^^D/vEb
*
D#/^Eb
*
vE
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