Marvel: Difference between revisions
Cmloegcmluin (talk | contribs) unchanged interval → unchanged-interval |
Briefly discuss 13-limit extensions; rework chords section; style; mark a dead link |
||
| Line 2: | Line 2: | ||
The temperament was named by [[Gene Ward Smith]] in 2002–2003, when the 11-limit version was found first<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5145.html#5184 Yahoo! Tuning Group | ''Relative complexity and scale construction''] – first mention of ''marvel''.</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5687.html Yahoo! Tuning Group | ''Top 135 11-limit planar temperaments''] – establishment as an 11-limit temperament.</ref>. Gene carried it to the 7-limit restriction in 2004<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_50829.html Yahoo! Tuning Group | ''Marvel'']</ref>. | The temperament was named by [[Gene Ward Smith]] in 2002–2003, when the 11-limit version was found first<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5145.html#5184 Yahoo! Tuning Group | ''Relative complexity and scale construction''] – first mention of ''marvel''.</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5687.html Yahoo! Tuning Group | ''Top 135 11-limit planar temperaments''] – establishment as an 11-limit temperament.</ref>. Gene carried it to the 7-limit restriction in 2004<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_50829.html Yahoo! Tuning Group | ''Marvel'']</ref>. | ||
Extending marvel to the 13-limit is not as obvious. While Gene has chosen [[351/350]] as the canonical extension, '''hecate''', tempering out [[325/324]], arguably makes more sense as it is closer in tuning<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101722.html Yahoo! Tuning Group | ''13-limit marvel'']</ref>. | |||
See [[Marvel family #Marvel]] for technical data. | See [[Marvel family #Marvel]] for technical data. | ||
| Line 39: | Line 41: | ||
== Chords == | == Chords == | ||
Marvel enables [[essentially tempered chord]]s of [[Marvel chords|marvel]], [[Keenanismic chords|keenanismic]], [[Swetismic chords|swetismic]], and [[Undecimal marvel chords|undecimal marvel]]. Extending the temperament to the 13-limit through 325/324, resulting in hecate, enables chords of [[Marveltwin chords|marveltwin]] and [[Squbemic chords|squbemic]]. [[Hecate hexad]] is a chord peculiar to this temperament. | |||
Alternative 11-limit extensions give different sets of chords. One notable example, tempering out [[441/440]], enables [[prodigy chords]]. | |||
== Scales == | == Scales == | ||
| Line 73: | Line 74: | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
|- | |- | ||
! [[ | ! [[Eigenmonzo|Eigenmonzo<br>(Unchanged-interval)]] | ||
! | ! Fifth<br>(¢) | ||
! | ! Major<br>Third (¢) | ||
! | ! Comments | ||
|- | |- | ||
| 5/4 | | 5/4 | ||
| Line 155: | Line 156: | ||
== Music == | == Music == | ||
; [[Billy Stiltner]] | |||
* [http://micro.soonlabel.com/gene_ward_smith/Others/Stiltner/marvel10_2.mp3 notJoelTaylorsTreeSpirit-Marvel10-2] | * [http://micro.soonlabel.com/gene_ward_smith/Others/Stiltner/marvel10_2.mp3 notJoelTaylorsTreeSpirit-Marvel10-2]{{dead link}} | ||
* [http://chrisvaisvil.com/?p=314 Semimarvelous Blue Drawf] | ; [[Chris Vaisvil]] | ||
* [http://chrisvaisvil.com/?p=314 ''Semimarvelous Blue Drawf''] | |||
== Notes == | == Notes == | ||
Revision as of 10:17, 5 September 2023
The marvel temperament is the rank-3 temperament tempering out 225/224, the marvel comma. It has a canonical 11-limit extension adding 385/384 and 540/539 to the comma list.
The temperament was named by Gene Ward Smith in 2002–2003, when the 11-limit version was found first[1][2]. Gene carried it to the 7-limit restriction in 2004[3].
Extending marvel to the 13-limit is not as obvious. While Gene has chosen 351/350 as the canonical extension, hecate, tempering out 325/324, arguably makes more sense as it is closer in tuning[4].
See Marvel family #Marvel for technical data.
Interval lattice
Notation
Marvel can be notated the same as 5-limit just intonation since they share the same lattice structure.
One way to do this is to take the conventional circle-of-fifths notation with an additional module of accidentals for the 81/80 comma. In this system, 5/4 is a major third, 7/4 an augmented sixth, and 11/8 a double diminished 5th.
| Ratio | Nominal | Example |
|---|---|---|
| 3/2 | Perfect 5th | C-G |
| 5/4 | Down major 3rd | C-vE |
| 7/4 | Dudaugmented 6th | C-vvA# |
| 11/8 | Trup double-diminished 5th | C-^3Gbb |
Alternatively, it can be notated the same as full prime-limit just intonation, with a distinct accidental pair for each prime. That makes some intervals more intuitive, at the cost of hiding the structure of marvel tempering. For example, it is customary of the 5/4 to be a major third, and 7/4 to be a minor seventh. As a result, the fact that the 14/9 is a stack of two 5/4's is not revealed, and the related chords can be confusing.
Chords
Marvel enables essentially tempered chords of marvel, keenanismic, swetismic, and undecimal marvel. Extending the temperament to the 13-limit through 325/324, resulting in hecate, enables chords of marveltwin and squbemic. Hecate hexad is a chord peculiar to this temperament.
Alternative 11-limit extensions give different sets of chords. One notable example, tempering out 441/440, enables prodigy chords.
Scales
Marvel hobbit scales
Undecimal marvel hobbit scales
Other marvel scales
Tuning spectrum
This spectrum assumes pure 2 and 7.
| Eigenmonzo (Unchanged-interval) |
Fifth (¢) |
Major Third (¢) |
Comments |
|---|---|---|---|
| 5/4 | 698.099 | 386.314 | |
| 6/5 | 700.027 | 384.386 | 7-odd-limit minimax |
| 15/11 | 700.351 | 384.062 | |
| 10/9 | 700.670 | 383.743 | 9-odd-limit minimax |
| 11/10 | 700.885 | 383.528 | |
| 15/13 | 700.916 | 383.497 | 15-odd-limit hecate minimax |
| 13/10 | 701.065 | 383.348 | 13-odd-limit hecate minimax |
| 13/11 | 701.199 | 383.214 | |
| 18/13 | 701.361 | 383.052 | |
| 13/12 | 701.480 | 382.933 | |
| 16/13 | 701.559 | 382.854 | |
| 4/3 | 701.955 | 382.458 | |
| 14/11 | 702.278 | 382.135 | |
| 11/8 | 702.278 | 382.135 | |
| 12/11 | 702.602 | 381.811 |
Music
Notes
- ↑ Yahoo! Tuning Group | Relative complexity and scale construction – first mention of marvel.
- ↑ Yahoo! Tuning Group | Top 135 11-limit planar temperaments – establishment as an 11-limit temperament.
- ↑ Yahoo! Tuning Group | Marvel
- ↑ Yahoo! Tuning Group | 13-limit marvel