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" | ||
!# fifths | !# fifths | ||
! colspan="2" |-3 | |||
! colspan="2" |-2 | ! colspan="2" |-2 | ||
! colspan="2" |-1 | ! colspan="2" |-1 | ||
| Line 8: | Line 11: | ||
! colspan="2" |+1 | ! colspan="2" |+1 | ||
! colspan="2" |+2 | ! colspan="2" |+2 | ||
! colspan="2" |+3 | |||
|- | |- | ||
!# 5/4s | !# 5/4s | ||
!Cents* | |||
!JI | |||
!Cents* | |||
!JI | |||
!Cents* | !Cents* | ||
!JI | !JI | ||
| Line 22: | Line 30: | ||
|- | |- | ||
!3 | !3 | ||
|950. | |249.7 | ||
|125/108, 280/243 | |||
|950.3 | |||
|140/81 | |140/81 | ||
|450. | |450.9 | ||
|35/27 | |35/27 | ||
|1151. | |1151.4 | ||
|35/18 | |35/18, 64/33 | ||
|652. | |652.0 | ||
|35/24 | |35/24, 16/11 | ||
|152. | |152.6 | ||
|35/32 | |35/32, 12/11 | ||
|853.4 | |||
|105/64, 18/11 | |||
|- | |- | ||
!2 | !2 | ||
|566. | |1065.8 | ||
|50/27 | |||
|566.4 | |||
|25/18, 112/81 | |25/18, 112/81 | ||
|67. | |67.0 | ||
|28/27, 25/24 | |28/27, 25/24 | ||
|767. | |767.6 | ||
|14/9, 25/16 | |14/9, 25/16 | ||
|268. | |268.2 | ||
|7/6, 75/64 | |7/6, 75/64 | ||
|'''968. | |class="thl"|'''968.8''' | ||
|'''7/4''' | |class="thl"|'''7/4''' | ||
|469.6 | |||
|21/16 | |||
|- | |- | ||
!1 | !1 | ||
|182. | |682.0 | ||
|40/27 | |||
|182.6 | |||
|10/9 | |10/9 | ||
|883. | |883.2 | ||
|5/3 | |5/3 | ||
|'''383. | |class="thl"|'''383.8''' | ||
|'''5/4''' | |class="thl"|'''5/4''' | ||
|1084. | |1084.4 | ||
|15/8, 28/15 | |15/8, 28/15 | ||
|585. | |585.0 | ||
|7/5 | |7/5 | ||
|85.8 | |||
|21/20 | |||
|- | |- | ||
!0 | !0 | ||
|998. | |298.1 | ||
|32/27 | |||
|998.8 | |||
|16/9 | |16/9 | ||
|499. | |499.4 | ||
|4/3 | |4/3 | ||
|'''0''' | |class="thl"|'''0''' | ||
|'''1/1''' | |class="thl"|'''1/1''' | ||
|'''700. | |class="thl"|'''700.6''' | ||
|'''3/2''' | |class="thl"|'''3/2''' | ||
|201. | |201.2 | ||
|9/8 | |9/8 | ||
|901.9 | |||
|27/16 | |||
|- | |- | ||
!-1 | !-1 | ||
| | |1114.2 | ||
|40/21 | |||
|615.0 | |||
|10/7 | |10/7 | ||
|115. | |115.6 | ||
|16/15, 15/14 | |16/15, 15/14 | ||
|816. | |816.7 | ||
|8/5 | |8/5 | ||
|316. | |316.8 | ||
|6/5 | |6/5 | ||
|1017. | |1017.4 | ||
|9/5 | |9/5 | ||
|518.0 | |||
|27/20 | |||
|- | |- | ||
!-2 | !-2 | ||
|231. | |730.4 | ||
|32/21 | |||
|231.2 | |||
|8/7 | |8/7 | ||
|931. | |931.8 | ||
|12/7 | |12/7 | ||
|432. | |432.3 | ||
|9/7 | |9/7 | ||
| | |1133.0 | ||
|27/14 | |27/14 | ||
|633. | |633.6 | ||
|81/56 | |81/56 | ||
|134.2 | |||
|27/25 | |||
|- | |- | ||
!-3 | !-3 | ||
|1047. | |346.6 | ||
|64/35 | |128/105, 11/9 | ||
| | |1047.4 | ||
|48/35 | |64/35, 11/6 | ||
|48. | |class="thl"|'''548.0''' | ||
|36/35 | |class="thl"|48/35, '''11/8''' | ||
|749. | |48.6 | ||
|54/35 | |36/35 (33/32) | ||
|249. | |749.1 | ||
|54/35 (99/64) | |||
|249.7 | |||
|81/70 | |81/70 | ||
|950.3 | |||
|243/140 | |||
|} | |} | ||
(* Cent values in pure-2/1, pure-7/4 tuning. Note that ~64/63 = | (* 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 == | == Supporting temperaments == | ||
| Line 118: | Line 154: | ||
* 19 & 53, [[Kleismic|Catakleismic]] (Marvel + 4375/4374) | * 19 & 53, [[Kleismic|Catakleismic]] (Marvel + 4375/4374) | ||
== | == List of patent vals == | ||
:''Main article: [[Marvel/Patent vals]]'' | |||
{{Navbox regtemp}} | {{Navbox regtemp}} | ||
{{Cat|temperaments}} | {{Cat|temperaments}} | ||
Latest 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:
- 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
| 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 |
