Marvel: Difference between revisions

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'''Marvel''', [[19edo|19]] & [[22edo|22]] & [[31edo|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.
'''Marvel''', [[19edo|19]] & [[22edo|22]] & [[31edo|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 ==
== Intervals ==
{| class="wikitable"
{| class="wikitable"
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* 19 & 53, [[Kleismic|Catakleismic]] (Marvel + 4375/4374)
* 19 & 53, [[Kleismic|Catakleismic]] (Marvel + 4375/4374)


== Extensions ==
== List of patent vals ==
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.
The following are patent vals that support 7-limit Marvel. Vals contorted in the 7-limit are not included.
 
{|class="wikitable sortable"
|-
!|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
|}
{{Navbox regtemp}}
{{Navbox regtemp}}
{{Cat|temperaments}}
{{Cat|temperaments}}

Revision as of 14:23, 7 April 2026

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:

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
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