Marvel
From Xenharmonic Reference
Marvel, 19 & 22 & 31, is a 7-limit rank-3 temperament tempering out 225/224, thereby equating 16/15 with 15/14 and equating 25/16 (= 5/4 * 5/4) with 14/9. On account of enlarging 16/15, Marvel favors somewhat flat tunings for 3 and 5.
The canonical strong extension to the 11-limit adds 385/384 (equating 35/32 to 12/11). 72edo is usually considered the Undecimal Marvel tuning par excellence; however, smaller edo tunings that support it such as 22edo and 41edo are more popular in the xen community.
Intervals
| # fifths | -3 | -2 | -1 | 0 | +1 | +2 | +3 | |||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| # 5/4s | Cents* | JI | Cents* | JI | Cents* | JI | Cents* | JI | Cents* | JI | Cents* | JI | Cents* | JI |
| 3 | 249.7 | 125/108, 280/243 | 950.3 | 140/81 | 450.9 | 35/27 | 1151.4 | 35/18, 64/33 | 652.0 | 35/24, 16/11 | 152.6 | 35/32, 12/11 | 853.4 | 105/64, 18/11 |
| 2 | 1065.8 | 50/27 | 566.4 | 25/18, 112/81 | 67.0 | 28/27, 25/24 | 767.6 | 14/9, 25/16 | 268.2 | 7/6, 75/64 | 968.8 | 7/4 | 469.6 | 21/16 |
| 1 | 682.0 | 40/27 | 182.6 | 10/9 | 883.2 | 5/3 | 383.8 | 5/4 | 1084.4 | 15/8, 28/15 | 585.0 | 7/5 | 85.8 | 21/20 |
| 0 | 298.1 | 32/27 | 998.8 | 16/9 | 499.4 | 4/3 | 0 | 1/1 | 700.6 | 3/2 | 201.2 | 9/8 | 901.9 | 27/16 |
| -1 | 1114.2 | 40/21 | 615.0 | 10/7 | 115.6 | 16/15, 15/14 | 816.7 | 8/5 | 316.8 | 6/5 | 1017.4 | 9/5 | 518.0 | 27/20 |
| -2 | 730.4 | 32/21 | 231.2 | 8/7 | 931.8 | 12/7 | 432.3 | 9/7 | 1133.0 | 27/14 | 633.6 | 81/56 | 134.2 | 27/25 |
| -3 | 346.6 | 128/105, 11/9 | 1047.4 | 64/35, 11/6 | 548.0 | 48/35, 11/8 | 48.6 | 36/35 (33/32) | 749.1 | 54/35 (99/64) | 249.7 | 81/70 | 950.3 | 243/140 |
(* Cent values in pure-2/1, pure-7/4 tuning. Note that ~64/63 = 30.0c and ~81/80 = 18.6c in this tuning. 11-limit JI interpretations use 385/384 tempering.)
Supporting temperaments
Many rank-2 temperaments supported by small-to-medium-sized edos support Marvel:
- 19 & 31, Septimal Meantone (Marvel + Meantone or + Didacus)
- 19 & 22, Magic (Marvel + Sensamagic)
- 22 & 31, Orwell
- 31 & 41, Miracle (Marvel + Slendric or + 2401/2400)
- 41 & 53, Garibaldi (Marvel + Schismic or + Aberschismic)
- 19 & 29, Negri (Marvel + Semaphore)
- 10 & 22, Pajara (Marvel + Diaschismic)
- 19 & 53, Catakleismic (Marvel + 4375/4374)
List of patent vals
- Main article: Marvel/Patent vals
