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
The following are patent vals that support 7-limit Marvel. Vals contorted in the 7-limit are not included.
| Edo | Extension to 11 | 3/2 tuning | 5/4 tuning | 7/4 tuning |
|---|---|---|---|---|
| 2 | 600.000 | 600.000 | 1200.000 | |
| 11 | 654.545 | 436.364 | 981.818 | |
| 9 | 19 & 22 & 31 | 666.667 | 400.000 | 933.333 |
| 21 | 685.714 | 400.000 | 971.429 | |
| 40 | 19 & 22 & 31 | 690.000 | 390.000 | 960.000 |
| 33 | 690.909 | 400.000 | 981.818 | |
| 52 | 692.308 | 392.308 | 969.231 | |
| 64 | 693.750 | 393.750 | 975.000 | |
| 19 | 19 & 22 & 31 | 694.737 | 378.947 | 947.368 |
| 50 | 19 & 22 & 31 | 696.000 | 384.000 | 960.000 |
| 81 | 19 & 22 & 31 | 696.296 | 385.185 | 962.963 |
| 31 | 19 & 22 & 31 | 696.774 | 387.097 | 967.742 |
| 105 | 697.143 | 388.571 | 971.429 | |
| 74 | 697.297 | 389.189 | 972.973 | |
| 43 | 697.674 | 390.698 | 976.744 | |
| 122 | 19 & 22 & 31 | 698.361 | 383.607 | 963.934 |
| 134 | 698.507 | 385.075 | 967.164 | |
| 146 | 698.630 | 386.301 | 969.863 | |
| 158 | 698.734 | 387.342 | 972.152 | |
| 91 | 19 & 22 & 31 | 698.901 | 382.418 | 962.637 |
| 103 | 19 & 22 & 31 | 699.029 | 384.466 | 966.990 |
| 115 | 699.130 | 386.087 | 970.435 | |
| 127 | 699.213 | 387.402 | 973.228 | |
| 175 | 19 & 22 & 31 | 699.429 | 384.000 | 966.857 |
| 187 | 699.465 | 385.027 | 968.984 | |
| 199 | 699.497 | 385.930 | 970.854 | |
| 12 | 700.000 | 400.000 | 1000.000 | |
| 60 | 19 & 22 & 31 | 700.000 | 380.000 | 960.000 |
| 72 | 19 & 22 & 31 | 700.000 | 383.333 | 966.667 |
| 84 | 700.000 | 385.714 | 971.429 | |
| 96 | 700.000 | 387.500 | 975.000 | |
| 156 | 700.000 | 384.615 | 969.231 | |
| 168 | 700.000 | 385.714 | 971.429 | |
| 228 | 700.000 | 384.211 | 968.421 | |
| 240 | 700.000 | 385.000 | 970.000 | |
| 293 | 700.341 | 384.983 | 970.648 | |
| 281 | 700.356 | 384.342 | 969.395 | |
| 209 | 700.478 | 384.689 | 970.335 | |
| 197 | 700.508 | 383.756 | 968.528 | |
| 137 | 700.730 | 385.401 | 972.263 | |
| 262 | 700.763 | 384.733 | 970.992 | |
| 125 | 19 & 22 & 31 | 700.800 | 384.000 | 969.600 |
| 113 | 19 & 22 & 31 | 700.885 | 382.301 | 966.372 |
| 178 | 701.124 | 384.270 | 970.787 | |
| 166 | 19 & 22 & 31 | 701.205 | 383.133 | 968.675 |
| 53 | 19 & 22 & 31 | 701.887 | 384.906 | 973.585 |
| 147 | 702.041 | 383.673 | 971.429 | |
| 94 | 19 & 22 & 31 | 702.128 | 382.979 | 970.213 |
| 135 | 19 & 22 & 31 | 702.222 | 382.222 | 968.889 |
| 41 | 19 & 22 & 31 | 702.439 | 380.488 | 965.854 |
| 29 | 703.448 | 372.414 | 951.724 | |
| 116 | 19 & 22 & 31 | 703.448 | 382.759 | 972.414 |
| 104 | 19 & 22 & 31 | 703.846 | 380.769 | 969.231 |
| 75 | 19 & 22 & 31 | 704.000 | 384.000 | 976.000 |
| 63 | 19 & 22 & 31 | 704.762 | 380.952 | 971.429 |
| 51 | 705.882 | 376.471 | 964.706 | |
| 85 | 19 & 22 & 31 | 705.882 | 381.176 | 974.118 |
| 22 | 19 & 22 & 31 | 709.091 | 381.818 | 981.818 |
| 44 | 19 & 22 & 31 | 709.091 | 381.818 | 981.818 |
| 54 | 19 & 22 & 31 | 711.111 | 377.778 | 977.778 |
| 32 | 19 & 22 & 31 | 712.500 | 375.000 | 975.000 |
| 10 | 19 & 22 & 31 | 720.000 | 360.000 | 960.000 |
| 1 | 1200.000 | 0.000 | 1200.000 |
| View • Talk • EditRegular temperaments | |
|---|---|
| Rank-2 | |
| Acot | Blackwood (1/5-octave) • Whitewood (1/7-octave) • Compton (1/12-octave) |
| Monocot | Meantone • Schismic • Gentle-fifth temperaments • Archy |
| Complexity 2 | Diaschismic (diploid monocot) • Pajara (diploid monocot) • Injera (diploid monocot) • Rastmatic (dicot) • Mohajira (dicot) • Intertridecimal (dicot) • Interseptimal (alpha-dicot) |
| Complexity 3 | Augmented (triploid) • Misty (triploid) • Slendric (tricot) • Porcupine (omega-tricot) |
| Complexity 4 | Diminished (tetraploid) • Tetracot (tetracot) • Buzzard (alpha-tetracot) • Squares (beta-tetracot) • Negri (omega-tetracot) |
| Complexity 5-6 | Magic (alpha-pentacot) • Amity (gamma-pentacot) • Kleismic (alpha-hexacot) • Miracle (hexacot) |
| Higher complexity | Orwell (alpha-heptacot) • Sensi (beta-heptacot) • Octacot (octacot) • Wurschmidt (beta-octacot) • Valentine (enneacot) • Ammonite (epsilon-enneacot) • Myna (beta-decacot) • Ennealimmal (enneaploid dicot) |
| Straddle-3 | A-Team (alter-tricot) • Machine (alter-monocot) |
| No-3 | Trismegistus (alpha-triseph) • Orgone (trimech) • Didacus (diseph) |
| No-octaves | Sensamagic (monogem) |
| Exotemperament | Dicot • Mavila • Father |
| Higher-rank | |
| Rank-3 | Hemifamity • Marvel • Parapyth |
