Yer: Difference between revisions
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Yer is an octave-reduced [[wikipedia:Euler–Fokker_genus|Euler-Fokker genus]] of 11, 13, 17, and 19. As such it is a 2.11.13.17.19 limit just intonation tuning (ignoring the 3rd, 5th, and 7th harmonics). | Yer is an octave-reduced [[wikipedia:Euler–Fokker_genus|Euler-Fokker genus]] of 11, 13, 17, and 19. As such it is a 2.11.13.17.19 limit just intonation tuning (ignoring the 3rd, 5th, and 7th harmonics). | ||
{| class="wikitable" | |||
|+ | |||
!name | |||
!frequency multiplier (definition) | |||
!frequency multiplier (decimal) | |||
!pitch (¢) | |||
|- | |||
|1 | |||
|1/1 | |||
|1 | |||
|0 | |||
|- | |||
|13 * 17 * 19 | |||
|4199/4096 | |||
|1.025146484 | |||
|42.9960874 | |||
|- | |||
|17 | |||
|17/16 | |||
|1.0625 | |||
|104.9554095 | |||
|- | |||
|11 * 13 | |||
|143/128 | |||
|1.1171875 | |||
|191.8456041 | |||
|- | |||
|11 * 13 * 17 | |||
|2431/2048 | |||
|1.187011719 | |||
|296.8010136 | |||
|- | |||
|19 | |||
|19/16 | |||
|1.1875 | |||
|297.5130161 | |||
|- | |||
|17 * 19 | |||
|323/256 | |||
|1.26171875 | |||
|402.4684256 | |||
|- | |||
|11 * 13 * 19 | |||
|2717/2048 | |||
|1.326660156 | |||
|489.3586203 | |||
|- | |||
|11 | |||
|11/8 | |||
|1.375 | |||
|551.3179424 | |||
|- | |||
|11 * 13 * 17 * 19 | |||
|46189/32768 | |||
|1.409576416 | |||
|594.3140298 | |||
|- | |||
|11 * 17 | |||
|187/128 | |||
|1.4609375 | |||
|656.2733519 | |||
|- | |||
|13 | |||
|13/8 | |||
|1.625 | |||
|840.5276618 | |||
|- | |||
|11 * 19 | |||
|209/128 | |||
|1.6328125 | |||
|848.8309585 | |||
|- | |||
|13 * 17 | |||
|221/128 | |||
|1.7265625 | |||
|945.4830713 | |||
|- | |||
|11 * 17 * 19 | |||
|3553/2048 | |||
|1.734863281 | |||
|953.786368 | |||
|- | |||
|13 * 19 | |||
|247/128 | |||
|1.9296875 | |||
|1138.040678 | |||
|} | |||
[[File:Yer - cycle view.jpg|thumb| | [[File:Yer - cycle view.jpg|thumb| | ||
Yer - cycle view | Yer - cycle view | ||
Revision as of 20:27, 6 February 2020
Introduction
Yer is an octave-reduced Euler-Fokker genus of 11, 13, 17, and 19. As such it is a 2.11.13.17.19 limit just intonation tuning (ignoring the 3rd, 5th, and 7th harmonics).
| name | frequency multiplier (definition) | frequency multiplier (decimal) | pitch (¢) |
|---|---|---|---|
| 1 | 1/1 | 1 | 0 |
| 13 * 17 * 19 | 4199/4096 | 1.025146484 | 42.9960874 |
| 17 | 17/16 | 1.0625 | 104.9554095 |
| 11 * 13 | 143/128 | 1.1171875 | 191.8456041 |
| 11 * 13 * 17 | 2431/2048 | 1.187011719 | 296.8010136 |
| 19 | 19/16 | 1.1875 | 297.5130161 |
| 17 * 19 | 323/256 | 1.26171875 | 402.4684256 |
| 11 * 13 * 19 | 2717/2048 | 1.326660156 | 489.3586203 |
| 11 | 11/8 | 1.375 | 551.3179424 |
| 11 * 13 * 17 * 19 | 46189/32768 | 1.409576416 | 594.3140298 |
| 11 * 17 | 187/128 | 1.4609375 | 656.2733519 |
| 13 | 13/8 | 1.625 | 840.5276618 |
| 11 * 19 | 209/128 | 1.6328125 | 848.8309585 |
| 13 * 17 | 221/128 | 1.7265625 | 945.4830713 |
| 11 * 17 * 19 | 3553/2048 | 1.734863281 | 953.786368 |
| 13 * 19 | 247/128 | 1.9296875 | 1138.040678 |
Commas
Yer features two unusual commas:
| name | value | cents | monzo |
|---|---|---|---|
| Blumeyer comma | 2432/2431 | 0.71200249782 | | 7 0 0 0 -1 -1 -1 1 > |
| Blume comma | 2057/2048 | 7.59129422992 | | -11 0 0 0 2 0 1 > |
Yer supports 240 possible comma pumps (which are zero comma pumps via comma shifts by the comma-wide intervals present in the tuning).
Scala file
! blumeyer_ji.scl ! Blumeyer JI scale, combination of CPS's of 11, 13, 17, 19 16 ! 4199/4096 17/16 143/128 2431/2048 19/16 323/256 2717/2048 11/8 46189/32768 187/128 13/8 209/128 221/128 3553/2048 247/128 2/1
Video explanation
More details are presented in this video: Yer (pitch system)
Listening
Douglas Blumeyer - Tsraxcfaubdj