Marvel: Difference between revisions
From Xenharmonic Reference
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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. | ||
== Intervals == | == Intervals == | ||
{| class="wikitable" | |||
!# fifths | |||
! colspan="2" |-2 | |||
! colspan="2" |-1 | |||
! colspan="2" |0 | |||
! colspan="2" |+1 | |||
! colspan="2" |+2 | |||
|- | |||
!# 5/4s | |||
!Cents* | |||
!JI | |||
!Cents* | |||
!JI | |||
!Cents* | |||
!JI | |||
!Cents* | |||
!JI | |||
!Cents* | |||
!JI | |||
|- | |||
!-3 | |||
|950.254 | |||
|140/81 | |||
|450.851 | |||
|35/27 | |||
|1151.448 | |||
|35/18 | |||
|652.045 | |||
|35/24 | |||
|152.642 | |||
|35/32 | |||
|- | |||
!-2 | |||
|566.438 | |||
|25/18, 112/81 | |||
|67.035 | |||
|28/27, 25/24 | |||
|767.632 | |||
|14/9, 25/16 | |||
|268.229 | |||
|7/6, 75/64 | |||
|'''968.826''' | |||
|'''7/4''' | |||
|- | |||
!-1 | |||
|182.622 | |||
|10/9 | |||
|883.219 | |||
|5/3 | |||
|'''383.816''' | |||
|'''5/4''' | |||
|1084.413 | |||
|15/8, 28/15 | |||
|585.01 | |||
|7/5 | |||
|- | |||
!0 | |||
|998.806 | |||
|16/9 | |||
|499.403 | |||
|4/3 | |||
|'''0''' | |||
|'''1/1''' | |||
|'''700.597''' | |||
|'''3/2''' | |||
|201.194 | |||
|9/8 | |||
|- | |||
!1 | |||
|614.99 | |||
|10/7 | |||
|115.587 | |||
|16/15, 15/14 | |||
|816.684 | |||
|8/5 | |||
|316.781 | |||
|6/5 | |||
|1017.378 | |||
|9/5 | |||
|- | |||
!2 | |||
|231.174 | |||
|8/7 | |||
|931.771 | |||
|12/7 | |||
|432.368 | |||
|9/7 | |||
|1132.965 | |||
|27/14 | |||
|633.562 | |||
|81/56 | |||
|- | |||
!3 | |||
|1047.358 | |||
|64/35 | |||
|547.955 | |||
|48/35 | |||
|48.552 | |||
|36/35 | |||
|749.149 | |||
|54/35 | |||
|249.746 | |||
|81/70 | |||
|} | |||
(* Cent values in pure-2/1, pure-7/4 tuning) | |||
== Supporting temperaments == | == Supporting temperaments == | ||
Revision as of 03:16, 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.
Intervals
| # fifths | -2 | -1 | 0 | +1 | +2 | |||||
|---|---|---|---|---|---|---|---|---|---|---|
| # 5/4s | Cents* | JI | Cents* | JI | Cents* | JI | Cents* | JI | Cents* | JI |
| -3 | 950.254 | 140/81 | 450.851 | 35/27 | 1151.448 | 35/18 | 652.045 | 35/24 | 152.642 | 35/32 |
| -2 | 566.438 | 25/18, 112/81 | 67.035 | 28/27, 25/24 | 767.632 | 14/9, 25/16 | 268.229 | 7/6, 75/64 | 968.826 | 7/4 |
| -1 | 182.622 | 10/9 | 883.219 | 5/3 | 383.816 | 5/4 | 1084.413 | 15/8, 28/15 | 585.01 | 7/5 |
| 0 | 998.806 | 16/9 | 499.403 | 4/3 | 0 | 1/1 | 700.597 | 3/2 | 201.194 | 9/8 |
| 1 | 614.99 | 10/7 | 115.587 | 16/15, 15/14 | 816.684 | 8/5 | 316.781 | 6/5 | 1017.378 | 9/5 |
| 2 | 231.174 | 8/7 | 931.771 | 12/7 | 432.368 | 9/7 | 1132.965 | 27/14 | 633.562 | 81/56 |
| 3 | 1047.358 | 64/35 | 547.955 | 48/35 | 48.552 | 36/35 | 749.149 | 54/35 | 249.746 | 81/70 |
(* Cent values in pure-2/1, pure-7/4 tuning)
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)
Extensions
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, 41edo is more ergonomic and popular.
| 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 |
