Kite's thoughts on 41edo brass instruments: Difference between revisions
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| Line 37: | Line 37: | ||
!1st | !1st | ||
!2 | !2 | ||
|28/27 | |[[28/27]] | ||
|56/54 | |56/54 | ||
|63.0 | |63.0 | ||
| Line 44: | Line 44: | ||
!2nd | !2nd | ||
!3 | !3 | ||
|19/18 | |[[19/18]] | ||
|57/54 | |57/54 | ||
|93.6 | |93.6 | ||
| Line 51: | Line 51: | ||
!3rd | !3rd | ||
!4 | !4 | ||
|29/27 | |[[29/27]] | ||
|58/54 | |58/54 | ||
|123.7 | |123.7 | ||
| Line 58: | Line 58: | ||
!4th | !4th | ||
!8 | !8 | ||
|31/27 | |[[31/27]] | ||
|62/54 | |62/54 | ||
|239.2 | |239.2 | ||
|8\41 + 5.0¢ | |8\41 + 5.0¢ | ||
|} | |} | ||
These valves make the subharmonic series 15-note fragment 71::54, with 70 and 55 missing. | These valves make the subharmonic series 15-note fragment 71::54, with 70 and 55 missing. Slightly adjusting the cents of each valve may slightly improve the intonation. | ||
In the chart below, ○ is a closed/released valve and ● is an open/depressed valve. The fingering chart assumes the valves run in order with 1st = 2\41, 2nd = 3\41, 3rd = 4\41 and 4th = 8\41. The largest errors are '''bolded'''. Notes are for a Bb trumpet. Many notes have alternate fingerings. Notes in parentheses have an alternate fingering with markedly better intonation. | In the chart below, ○ is a closed/released valve and ● is an open/depressed valve. The fingering chart assumes the valves run in order with 1st = 2\41, 2nd = 3\41, 3rd = 4\41 and 4th = 8\41. The largest errors are '''bolded'''. Notes are for a Bb trumpet. Many notes have alternate fingerings. Notes in parentheses have an alternate fingering with markedly better intonation. | ||
| Line 71: | Line 71: | ||
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 is actually 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 is actually 16! This is fortuitous because 4/3 is 17\41 and 16 edosteps neatly fills the gap between the 3rd and 4th harmonics. | ||
The error from 41edo is the sum of the valve ratio's error and the harmonic's error. For example, 28/27 is 4.4¢ flat of 2\41 and the 5th harmonic is 5.8¢ sharp of 13\41, so the error for C# is 1.4¢. | The error from 41edo is the sum of the valve ratio's error and the harmonic's error. For example, 28/27 is 4.4¢ flat of 2\41 and the 5th harmonic is 5.8¢ sharp of 13\41, so the error for the 5th harmonic's C# is 1.4¢. | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
| Line 425: | Line 425: | ||
Here are the full 2 octaves produced by a Bb trumpet. The low vF and the high vC are missing. | |||
{| class="wikitable mw-collapsible mw-collapsed center-all" | {| class="wikitable mw-collapsible mw-collapsed center-all" | ||