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

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autopatrolled, Sysops
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TallKite (talk | contribs)
autopatrolled, Sysops
4,220 edits
accounted for harmonics 3, 5 and 7 being off in 41edo
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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 = 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 = 16! This is fortuitous because 4/3 is 17\41 and 16 edosteps neatly fills the gap between the 3rd and 4th harmonics.
The 5th harmonic is 6


{| class="wikitable center-all"
{| class="wikitable center-all"
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ratio
ratio
! rowspan="2" |cents
! rowspan="2" |cents
! rowspan="2" |error
! colspan="5" |error from 41edo
from 41
! rowspan="19" |
! rowspan="19" |
! colspan="7" |harmonics
! colspan="7" |harmonics
|-
|-
!4, 8
!5
!3, 6
!7
!9
!3
!3
!4
!4
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|0.0
|0.0
|0.0
|0.0
| -5.8
| +0.5
| -3.0
| +1.0
|F
|F
|vA# Bb
|vA# Bb
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!
!
!
!
|
|
|
|
|
|
|
|
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|63.0
|63.0
| -4.4
| -4.4
|'''-10.3'''
| -3.9
| -7.4
| -3.5
|^E
|^E
|^A
|^A
|C# ^Db
|'''C# ^Db'''
|^E
|^E
|G
|G
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|93.6
|93.6
| -5.8
| -5.8
|'''-11.6'''
| -5.3
| -8.8
| -4.8
|E
|E
|A
|A
|vC# Db
|'''vC# Db'''
|E
|E
|vG
|vG
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|123.7
|123.7
| -6.6
| -6.6
|'''-12.5'''
| -6.2
| -9.6
| -5.7
|vE
|vE
|vA
|vA
|^^C vDb
|'''^^C vDb'''
|vE
|vE
|^F# vvG
|^F# vvG
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|153.3
|153.3
| -7.0
| -7.0
|'''-12.8'''
| -6.5
| -9.9
| -6.0
|^D# Eb
|^D# Eb
|^G# vvA
|^G# vvA
|^C
|'''^C'''
|^D# vvE
|^D# vvE
|F# ^Gb
|F# ^Gb
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|182.4
|182.4
| -6.8
| -6.8
|'''-12.6'''
| -6.3
| -9.8
| -5.8
|D# vEb
|D# vEb
|G# ^Ab
|G# ^Ab
|C
|'''C'''
|D# ^Eb
|D# ^Eb
|vF# Gb
|vF# Gb
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|211.0
|211.0
| -6.1
| -6.1
|'''-12.0'''
| -5.7
| -9.1
| -5.2
|vD# Eb
|vD# Eb
|vG# Ab
|vG# Ab
|vC
|'''vC'''
|vD# Eb
|vD# Eb
|^^F vGb
|^^F vGb
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|239.2
|239.2
| -5.0
| -5.0
|'''-10.9'''
| -4.5
| -8.0
| -4.1
|^^D vEb
|^^D vEb
|^^G vAb
|^^G vAb
|^B
|'''^B'''
|^^D vEb
|^^D vEb
|^F
|^F
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|266.9
|266.9
| -3.5
| -3.5
| -9.3
| -3.0
| -6.4
| -2.5
|^D
|^D
|^G
|^G
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|294.1
|294.1
| -1.5
| -1.5
| -7.3
| -1.0
| -4.4
| -0.5
|D
|D
|G
|G
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|321.0
|321.0
| 1.0
| 1.0
| -4.9
|1.5
| -2.0
|1.9
|vD
|vD
|vG
|vG
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|347.4
|347.4
| 3.8
| 3.8
| -2.0
|4.3
|0.8
|4.8
|^C# vvD
|^C# vvD
|^F# vvG
|^F# vvG
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|373.4
|373.4
| 7.0
| 7.0
|1.2
|7.5
|4.1
|8.0
|C# ^Db
|C# ^Db
|F# ^Gb
|F# ^Gb
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|399.1
|399.1
| '''10.7'''
| '''10.7'''
|4.8
|'''11.1'''
|7.7
|'''11.6'''
|'''vC# Db'''
|'''vC# Db'''
|'''vF# Gb'''
|'''vF# Gb'''
|'''^^A vBb'''
|^^A vBb
|'''vC# Db'''
|'''vC# Db'''
|'''^D# vvE'''
|'''^D# vvE'''
|'''vF# Gb'''
|vF# Gb
|'''vG# Ab'''
|'''vG# Ab'''
|-
|-
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|424.4
|424.4
| '''14.7'''
| '''14.7'''
|8.8
|'''15.1'''
|'''11.7'''
|'''15.6'''
|'''^^C vDb'''
|'''^^C vDb'''
|'''^^F vGb'''
|'''^^F vGb'''
|'''^A'''
|^A
|'''^^C vDb'''
|'''^^C vDb'''
|'''D# ^Eb'''
|'''D# ^Eb'''
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|473.8
|473.8
| -5.5
| -5.5
| -11.4
| -5.1
| -8.5
| -4.6
|^C
|^C
|^F
|^F
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|
|
|
|
|C# ^Db
|'''C# ^Db'''
|C# ^Db
|C# ^Db
|
|
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|
|
|
|
|vC# Db
|'''vC# Db'''
|'''vC# Db'''
|'''vC# Db'''
|
|
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|
|
|
|
|^^C vDb
|'''^^C vDb'''
|'''^^C vDb'''
|'''^^C vDb'''
|
|
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|
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|^C
|'''^C'''
|^C
|^C
|
|
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|
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|C
|'''C'''
|
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|
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|vC
|'''vC'''
|
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|
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|^B
|'''^B'''
|
|
|
|
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|
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|
|
|'''^^A vBb'''
|^^A vBb
|
|
|
|
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|
|
|^A
|^A
|'''^A'''
|^A
|
|
|
|
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