Kite's thoughts on 41edo brass instruments: Difference between revisions
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|8\41 + 5.0¢ | |8\41 + 5.0¢ | ||
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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. 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 | 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 | ||
|vD | |vD | ||
|vG | |vG | ||
| Line 259: | Line 259: | ||
!11/9 | !11/9 | ||
|347.4 | |347.4 | ||
| | | 3.8 | ||
|^C# vvD | |^C# vvD | ||
|^F# vvG | |^F# vvG | ||
| Line 274: | Line 274: | ||
!67/54 | !67/54 | ||
|373.4 | |373.4 | ||
| | | 7.0 | ||
|C# ^Db | |C# ^Db | ||
|F# ^Gb | |F# ^Gb | ||
| Line 289: | Line 289: | ||
!34/27 | !34/27 | ||
|399.1 | |399.1 | ||
| ''' | | '''10.7''' | ||
|'''vC# Db''' | |'''vC# Db''' | ||
|'''vF# Gb''' | |'''vF# Gb''' | ||
| Line 304: | Line 304: | ||
!23/18 | !23/18 | ||
|424.4 | |424.4 | ||
| '''-14. | | '''-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 | ||