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Kite's thoughts on 41edo brass instruments: Difference between revisions

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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.
This page discusses the Kite trumpet, Kite flugelhorn, Kite french horn, Kite tuba, etc.,  
 
== Full 41edo instruments ==
The intervals don't add up precisely because they add a fixed length rather than multiply the length by a fixed ratio. But the ratios do add up in a sense.
 
The 4 valves can lower the pitch by various JI ratios:
{| class="wikitable"
|+
!valve
!edosteps
!ratio
!over-54
!cents
!41edo
|-
!1st
!2
|28/27
|56/54
|63
|2\41 + 4¢
|-
!2nd
!3
|19/18
|57/54
|94
|3\41 + 6¢
|-
!3rd
!4
|29/27
|58/54
|124
|4\41 + 7¢
|-
!4th
!8
|31/27
|62/54
|239
|8\41 + 5¢
|}
Consider a trumpet of 54 units of length (54 cm, 54 inches, whatever). Each valve adds 2, 3, 4 or 8 cm of length. When two valves are opened, these additions are summed. For example the first two valves add 2+3 = 5 cm of length. Thus 56/54 "plus" 57/54 equals 59/54. Subharmonic series 69::54
 
{| class="wikitable center-all"
|+
! colspan="2" rowspan="2" |edosteps
to lower by
! rowspan="2" |valves
! rowspan="2" |subhar-
monics
! rowspan="2" |as a
ratio
! rowspan="2" |cents
! rowspan="2" |error
from 41
! rowspan="18" |
! colspan="7" |harmonics
|-
!3
!4
!5
!6
!7
!8
!9
|-
!0
!0
!○○○○
!54
!1/1
|0.0
|0.0
|F
|Bb
|vD
|F
|vAb
|Bb
|C
|-
!2
!2
!●○○○
!56
!28/27
|63.0
|4.4
|^E
|^A
|C# ^Db
|^E
|G
|^A
|^B
|-
!3
!3
!○●○○
!57
!19/18
|93.6
|5.8
|E
|A
|vC# Db
|E
|vG
|A
|B
|-
!4
!4
!○○●○
!58
!29/27
|123.7
|6.6
|vE
|vA
|^^C vDb
|vE
|^F# vvG
|vA
|vB
|-
!5
!2+3
!●●○○
!59
!59/54
|153.3
|7.0
|^D# vvE
|^G# vvA
|^C
|^D# vvE
|F# ^Gb
|^G# vvA
|^A# vvB
|-
!6
!2+4
!●○●○
!60
!10/9
|182.4
|6.8
|D# ^Eb
|G# ^Ab
|C
|D# ^Eb
|vF# Gb
|G# ^Ab
|A# ^Bb
|-
!7
!3+4
!○●●○
!61
!61/54
|211.0
|6.1
|vD# Eb
|vG# Ab
|vC
|vD# Eb
|^^F vGb
|vG# Ab
|vA# Bb
|-
!8
!8
!○○○●
!62
!31/27
|239.2
|5.0
|^^D vEb
|^^G vAb
|^B
|^^D vEb
|^F
|^^G vAb
|^^A vBb
|-
!9
!2+3+4
!●●●○
!63
!7/6
|266.9
|3.5
|^D
|^G
|B
|^D
|F
|^G
|^A
|-
!10
!2+8
!●○○●
!64
!32/27
|294.1
|1.5
|D
|G
|vB
|D
|vF
|G
|A
|-
!11
!3+8
!○●○●
!65
!65/54
|321.0
| -1.0
|vD
|vG
|^A# vvB
|vD
|^E
|vG
|vA
|-
!12
!4+8
!○○●●
!66
!11/9
|347.4
| -3.8
|^C# vvD
|^F# vvG
|A# ^Bb
|^C# vvD
|E
|^F# vvG
|^G# vvA
|-
!13
!2+3+8
!●●○●
!67
!67/54
|373.4
| -7.0
|C# ^Db
|F# ^Gb
|vA# Bb
|C# ^Db
|vE
|F# ^Gb
|G# ^Ab
|-
!14
!2+4+8
!●○●●
!68
!34/27
|399.1
| -10.7
|vC# Db
|vF# Gb
|^^A vBb
|vC# Db
|^D# vvE
|vF# Gb
|vG# Ab
|-
!15
!3+4+8
!○●●●
!69
!23/18
|424.4
| -14.7
|^^C vDb
|^^F vGb
|^A
|^^C vDb
|D# ^Eb
|^^F vGb
|^^G vAb
|-
!16
!2+3+4+8
!●●●●
!70
!35/27
|449.3
| -19.0
|^C
|^F
|A
|^C
|vD# Eb
|^F
|^G
|}
 
 
 
{| class="wikitable mw-collapsible mw-collapsed center-all"
|+
Full 2 octave range (low note C)
! rowspan="2" |41-edo
gamut
! colspan="7" |harmonics
|-
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!4
!5
!6
!7
!8
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== Skip-valved instruments ==
Skip-valves 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 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.
Retrieved from "https://en.xen.wiki/w/Kite%27s_thoughts_on_41edo_brass_instruments"