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

TallKite (talk | contribs)
done
TallKite (talk | contribs)
mNo edit summary
Line 59: Line 59:
|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.
Line 109: Line 109:
!28/27
!28/27
|63.0
|63.0
|4.4
| -4.4
|^E
|^E
|^A
|^A
Line 124: Line 124:
!19/18
!19/18
|93.6
|93.6
|5.8
| -5.8
|E
|E
|A
|A
Line 139: Line 139:
!29/27
!29/27
|123.7
|123.7
|6.6
| -6.6
|vE
|vE
|vA
|vA
Line 154: Line 154:
!59/54
!59/54
|153.3
|153.3
|7.0
| -7.0
|^D# vvE
|^D# vvE
|^G# vvA
|^G# vvA
Line 169: Line 169:
!10/9
!10/9
|182.4
|182.4
|6.8
| -6.8
|D# ^Eb
|D# ^Eb
|G# ^Ab
|G# ^Ab
Line 184: Line 184:
!61/54
!61/54
|211.0
|211.0
|6.1
| -6.1
|vD# Eb
|vD# Eb
|vG# Ab
|vG# Ab
Line 199: Line 199:
!31/27
!31/27
|239.2
|239.2
|5.0
| -5.0
|^^D vEb
|^^D vEb
|^^G vAb
|^^G vAb
Line 214: Line 214:
!7/6
!7/6
|266.9
|266.9
|3.5
| -3.5
|^D
|^D
|^G
|^G
Line 229: Line 229:
!32/27
!32/27
|294.1
|294.1
|1.5
| -1.5
|D
|D
|G
|G
Line 244: Line 244:
!65/54
!65/54
|321.0
|321.0
| -1.0
| 1.0
|vD
|vD
|vG
|vG
Line 259: Line 259:
!11/9
!11/9
|347.4
|347.4
| -3.8
| 3.8
|^C# vvD
|^C# vvD
|^F# vvG
|^F# vvG
Line 274: Line 274:
!67/54
!67/54
|373.4
|373.4
| -7.0
| 7.0
|C# ^Db
|C# ^Db
|F# ^Gb
|F# ^Gb
Line 289: Line 289:
!34/27
!34/27
|399.1
|399.1
| '''-10.7'''
| '''10.7'''
|'''vC# Db'''
|'''vC# Db'''
|'''vF# Gb'''
|'''vF# Gb'''
Line 304: Line 304:
!23/18
!23/18
|424.4
|424.4
| '''-14.7'''
| '''-14.6'''
|'''^^C vDb'''
|'''^^C vDb'''
|'''^^F vGb'''
|'''^^F vGb'''
Line 319: Line 319:
!71/54
!71/54
|473.8
|473.8
| 5.5
| -5.5
|^C
|^C
|^F
|^F