BudjarnLambeth: Uncategorised page

2025-12-28T00:10:50Z

Uncategorised page

← Older revision		Revision as of 00:10, 28 December 2025
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			[[Category:31edo]]

TallKite at 06:44, 10 November 2025

2025-11-10T06:44:53Z

← Older revision		Revision as of 06:44, 10 November 2025
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TallKite at 06:44, 10 November 2025

2025-11-10T06:44:21Z

@@ Line 78: / Line 78: @@
 |-
+!
-! colspan="6" |
-! colspan="7" |
 |-
 !2
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 |-
+!
-! colspan="6" |
-| colspan="7" |
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 !16

TallKite: Created page with "See Kite's thoughts on 41edo brass instruments for the reasoning behind these calculations. Approximating 2\31 as 43/41 gives us these valve lengths: {| class="wikitable" |+ !valve !edosteps !ratio !cents !as 31edo |- !1st !2 |43/41 |82.5 |2\31 + 5.0¢ |- !2nd !3 |44/41 |122.3 |3\31 + 6.1¢ |- !3rd !4 |45/41 |161.2 |4\31 + 6.3¢ |- !4th !8 |49/41 |308.6 |8\31 - 1.1¢ |} These valves make the subharmonic series 15-note fragment 58::41, with 57 and 42 missing. In the..."

2025-11-10T06:40:40Z

Created page with "See Kite's thoughts on 41edo brass instruments for the reasoning behind these calculations. Approximating 2\31 as 43/41 gives us these valve lengths: {| class="wikitable" |+ !valve !edosteps !ratio !cents !as 31edo |- !1st !2 |43/41 |82.5 |2\31 + 5.0¢ |- !2nd !3 |44/41 |122.3 |3\31 + 6.1¢ |- !3rd !4 |45/41 |161.2 |4\31 + 6.3¢ |- !4th !8 |49/41 |308.6 |8\31 - 1.1¢ |} These valves make the subharmonic series 15-note fragment 58::41, with 57 and 42 missing. In the..."

New page

See [[Kite's thoughts on 41edo brass instruments]] for the reasoning behind these calculations.

Approximating 2\31 as 43/41 gives us these valve lengths:
{| class="wikitable"
|+
!valve
!edosteps
!ratio
!cents
!as 31edo
|-
!1st
!2
|43/41
|82.5
|2\31 + 5.0¢
|-
!2nd
!3
|44/41
|122.3
|3\31 + 6.1¢
|-
!3rd
!4
|45/41
|161.2
|4\31 + 6.3¢
|-
!4th
!8
|49/41
|308.6
|8\31 - 1.1¢
|}
These valves make the subharmonic series 15-note fragment 58::41, with 57 and 42 missing. In the chart below, ○ is a closed/released valve, and ● is an open/depressed valve. The 3 largest errors are '''bolded'''. Notes are for a Bb trumpet.

The intervals are descending so 82.5¢ means 82.5¢ below the unvalved note. Thus the error is the opposite sign from what one expects. For example, the 1st valve lowers by 82.5¢, 5¢ <u>wider</u> than 2\31, thus the note is 5¢ <u>flat</u> of 31edo.

Note that both 52/41 and 53/41 map to 11\31. Thus 4+8 = 11, 2+3+8 = 12, etc.
{| 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 31
! rowspan="20" |
! colspan="7" |harmonics
|-
!3
!4
!5
!6
!7
!8
!9
|-
!0
!0
!○○○○
!41
!1/1
|0.0
|0.0
|F
|^A# Bb
|D
|F
|G# vAb
|^A# Bb
|C
|-
!
! colspan="6" |
! colspan="7" |
|-
!2
!2
!●○○○
!43
!43/41
|82.5
| -5.0
|^E
|^A
|^C# Db
|^E
|G
|^A
|^B
|-
!3
!3
!○●○○
!44
!44/41
|122.3
| -6.1
|E
|A
|C# vDb
|E
|vG
|A
|B
|-
!4
!4
!○○●○
!45
!45/41
|161.2
| -6.3
|vE
|vA
|^C
|vE
|^F# Gb
|vA
|vB
|-
!5
!2+3
!●●○○
!46
!46/41
|199.2
| -5.7
|^D# Eb
|^G# Ab
|C
|^D# Eb
|F# vGb
|^G# Ab
|^A# Bb
|-
!6
!2+4
!●○●○
!47
!47/41
|236.4
| -4.2
|D# vEb
|G# vAb
|vC
|D# vEb
|^F
|G# vAb
|A# vBb
|-
!7
!3+4
!○●●○
!48
!48/41
|272.9
| -1.9
|^D
|^G
|^B
|^D
|F
|^G
|^A
|-
!8
!8
!○○○●
!49
!49/41
|308.6
|1.1
|D
|G
|B
|D
|vF
|G
|A
|-
!9
!2+3+4
!●●●○
!50
!50/41
|343.6
|4.8
|vD
|vG
|vB
|vD
|^E
|vG
|vA
|-
!10
!2+8
!●○○●
!51
!51/41
|377.8
|9.2
|^C# Db
|^F# Gb
|^A# Bb
|^C# Db
|E
|^F# Gb
|^G# Ab
|-
! rowspan="2" |11
!3+8
!○●○●
!52
!52/41
|411.5
|'''14.3'''
| rowspan="2" |'''C# vDb'''
| rowspan="2" |'''F# vGb'''
| rowspan="2" |'''A# vBb'''
| rowspan="2" |'''C# vDb'''
| rowspan="2" |'''vE'''
| rowspan="2" |'''F# vGb'''
| rowspan="2" |'''G# vAb'''
|-
!4+8
!○○●●
!53
!53/41
|444.4
|'''-18.6'''
|-
!12
!2+3+8
!●●○●
!54
!54/41
|476.8
|'''-12.3'''
|'''^C'''
|'''^F'''
|'''^A'''
|'''^C'''
|'''^D# Eb'''
|'''^F'''
|'''^G'''
|-
!13
!2+4+8
!●○●●
!55
!55/41
|508.6
| -5.3
|C
|F
|A
|C
|D# vEb
|F
|G
|-
!14
!3+4+8
!○●●●
!56
!56/41
|539.8
|2.2
|vC
|vF
|vA
|vC
|^D
|vF
|vG
|-
!
! colspan="6" |
| colspan="7" |
|-
!16
!2+3+4+8
!●●●●
!58
!58/41
|600.5
|'''18.8'''
|'''B'''
|'''E'''
|'''G# vAb'''
|'''B'''
|'''vD'''
|'''E'''
|'''F#'''
|}
Here are the full 2 octaves produced by a Bb trumpet. Note that the bolded notes for the three largest errors often have alternative notes.

*

{| class="wikitable mw-collapsible mw-collapsed center-all"
|+Full 2 octave range (low note B below middle-C)
! rowspan="2" |31-edo
gamut
! colspan="7" |harmonics
|-
!3
!4
!5
!6
!7
!8
!9
|-
!C
|
|
|
|
|
|
|C
|-
!
|
|
|
|
|
|
|(missing)
|-
!
|
|
|
|
|
|
|^B
|-
!B
|
|
|
|
|
|
|B
|-
!
|
|
|
|
|
|
|vB
|-
!
|
|
|
|
|
|^A# Bb
|^A# Bb
|-
!
|
|
|
|
|
|
|A# vBb
|-
!
|
|
|
|
|
|^A
|^A
|-
!A
|
|
|
|
|
|A
|A
|-
!
|
|
|
|
|
|vA
|vA
|-
!
|
|
|
|
|
|^G# Ab
|^G# Ab
|-
!
|
|
|
|
|G# vAb
|G# vAb
|'''G# vAb'''
|-
!
|
|
|
|
|
|^G
|'''^G'''
|-
!G
|
|
|
|
|G
|G
|G
|-
!
|
|
|
|
|vG
|vG
|vG
|-
!
|
|
|
|
|^F# Gb
|^F# Gb
|
|-
!
|
|
|
|
|F# vGb
|'''F# vGb'''
|'''F#'''
|-
!
|
|
|
|
|^F
|'''^F'''
|
|-
!F
|
|
|
|F
|F
|F
|
|-
!
|
|
|
|
|vF
|vF
|
|-
!
|
|
|
|^E
|^E
|
|
|-
!E
|
|
|
|E
|E
|'''E'''
|
|-
!
|
|
|
|vE
|'''vE'''
|
|
|-
!
|
|
|
|^D# Eb
|'''^D# Eb'''
|
|
|-
!
|
|
|
|D# vEb
|D# vEb
|
|
|-
!
|
|
|
|^D
|^D
|
|
|-
!D
|
|
|D
|D
|
|
|
|-
!
|
|
|
|vD
|'''vD'''
|
|
|-
!
|
|
|^C# Db
|^C# Db
|
|
|
|-
!
|
|
|C# vDb
|'''C# vDb'''
|
|
|
|-
!
|
|
|^C
|'''^C'''
|
|
|
|-
!C
|
|
|C
|C
|
|
|
|-
!
|
|
|vC
|vC
|
|
|
|-
!
|
|
|^B
|
|
|
|
|-
!B
|
|
|B
|'''B'''
|
|
|
|-
!
|
|
|vB
|
|
|
|
|-
!
|
|^A# Bb
|^A# Bb
|
|
|
|
|-
!
|
|
|'''A# vBb'''
|
|
|
|
|-
!
|
|^A
|'''^A'''
|
|
|
|
|-
!A
|
|A
|A
|
|
|
|
|-
!
|
|vA
|vA
|
|
|
|
|-
!
|
|^G# Ab
|
|
|
|
|
|-
!
|
|G# vAb
|'''G# vAb'''
|
|
|
|
|-
!
|
|^G
|
|
|
|
|
|-
!G
|
|G
|
|
|
|
|
|-
!
|
|vG
|
|
|
|
|
|-
!
|
|^F# Gb
|
|
|
|
|
|-
!
|
|'''F# vGb'''
|
|
|
|
|
|-
!
|
|'''^F'''
|
|
|
|
|
|-
!F
|F
|F
|
|
|
|
|
|-
!
|
|vF
|
|
|
|
|
|-
!
|^E
|
|
|
|
|
|
|-
!E
|E
|'''E'''
|
|
|
|
|
|-
!
|vE
|
|
|
|
|
|
|-
!
|^D# Eb
|
|
|
|
|
|
|-
!
|D# vEb
|
|
|
|
|
|
|-
!
|^D
|
|
|
|
|
|
|-
!D
|D
|
|
|
|
|
|
|-
!
|vD
|
|
|
|
|
|
|-
!
|^C# Db
|
|
|
|
|
|
|-
!
|'''C# vDb'''
|
|
|
|
|
|
|-
!
|'''^C'''
|
|
|
|
|
|
|-
!C
|C
|
|
|
|
|
|
|-
!
|vC
|
|
|
|
|
|
|-
!
|(missing)
|
|
|
|
|
|
|-
!B
|'''B'''
|
|
|
|
|
|
|}

Kite's thoughts on 31edo brass instruments - Revision history

BudjarnLambeth: Uncategorised page

TallKite at 06:44, 10 November 2025

TallKite at 06:44, 10 November 2025