|
|
| (66 intermediate revisions by 17 users not shown) |
| Line 1: |
Line 1: |
| {{User:IlL/Template:RTT restriction}}
| | {{Infobox MOS}} |
| {{Infobox MOS | |
| | Name = mavila, superdiatonic
| |
| | Periods = 1
| |
| | nLargeSteps = 7
| |
| | nSmallSteps = 2
| |
| | Equalized = 5
| |
| | Paucitonic = 4
| |
| | Pattern = LLLsLLLLs
| |
| }} | |
| '''7L 2s''', '''mavila''' (/ˈmɑːvɪlə/ or /ˈmævɪlə/ ''MA(H)-vil-ə''), or '''superdiatonic''' refers to the structure of octave-equivalent [[MOS]] scales with generators ranging from 4\7 (four degrees of [[7edo]] = 685.71¢) to 5\9 (five degrees of [[9edo]] = 666.67¢) and associated harmonic framework. In the case of 9edo, L and s are the same size; in the case of 7edo, s becomes so small it disappears (and all that remains are the seven equal L's). Mavila was first discovered by Erv Wilson after studying the tuning of the "Timbila" music of the Chopi tribe in Mozambique. It is also closely related to the "pelog" scale in Indonesian and Balinese Gamelan music.
| |
| == Notation ==
| |
| In this article we use the Diamond MOS notation, with JKLMNOPQRJ = the symmetric Olympian mode (LLSLLLSLL), J = 261.6255653. &/@ = raise/lower by one chroma. So the fifth chain becomes ... P@ L@ Q M R N J O K P L Q& M& ...
| |
|
| |
|
| A possible alternative is to keep the 7-note fifth chain FCGDAEB from diatonic and extend it to a 9-note one, XFCGDAEBY, and to use &/@ for the 7L 2s chroma. So the extended chain becomes ... B@ Y@ X F C G D A E B Y X& F& ...
| | {{MOS intro}} |
| == Tunings == | | Scales of this form are strongly associated with [[Armodue theory]], as applied to septimal mavila and Hornbostel temperaments. [[Trismegistus]] is also a usable temperament. |
| Much like [[5L 2s|5L 2s diatonic]], mavila is supported by several low-numbered EDOs, which will basically be the same size as the MOS's listed above.
| | == Name == |
| | The [[TAMNAMS]] name for this pattern is '''armotonic''', in reference to Armodue theory. '''Superdiatonic''' is also in use. |
|
| |
|
| 7-EDO can be thought of as a primitive tuning, yielding a totally equal heptatonic scale that is equally diatonic and anti-diatonic.
| | == Scale properties == |
| | {{TAMNAMS use}} |
|
| |
|
| The next EDO supporting Mavila is 9-EDO, which can be thought of as the first mavila EDO (and the first EDO in general) differentiating between 4:5:6 major and 10:12:15 minor chords. This is fairly interesting, as there is no real equivalent in meantone terms. It is larger than the "diatonic" sized MOS, but smaller than the 16-tone "chromatic" MOS. It is best thought of as a "superdiatonic" scale. The fifth is 667 cents.
| | === Intervals === |
| | {{MOS intervals}} |
|
| |
|
| It is also supported by 16-EDO, which is probably the most common tuning for mavila. This can be thought of as the first EDO offering the potential for chromatic mavila harmony, similar to 12-EDO for meantone. This is also the usual setting for the aforementioned Armodue theory, although the Armodue theory can easily be extended to larger mavila scales such as mavila[23]. The fifth is 675 cents.
| | === Generator chain === |
| | {{MOS genchain}} |
|
| |
|
| The next EDO supporting mavila is 23-EDO, which is the second-most common tuning for mavila, used frequently by Igliashon Jones in his Cryptic Ruse albums. The fifth is 678 cents, and as a result the harmonic properties are slightly better than 16-EDO, although still fairly inharmonic compared to meantone. The anti-diatonic scale is more "quasi-equal" in this tuning than in 16-EDO.
| | === Modes === |
| | {{MOS mode degrees}} |
|
| |
|
| 25-EDO also contains mavila, although the tuning is 672 cents and hence very flat, even flatter than 16-EDO.
| | === Proposed mode names === |
| | | The Ad- mode names proposed by [[groundfault]] have the feature of matching up the middle 7 modes with the antidiatonic mode names in the generator arc. |
| The fifths of mavila are very flat - 16-EDO (675.0 cents) and 23-EDO (678.3 cents) are typical tunings, and the optimal 5-limit tuning is 679.8 cents. As a result, mavila is best played with specialized timbres: either timbres with a lot of rolloff (such as marimba, sine waves, ocarina, etc), or timbres with detuned partials (such as Gamelan or Timbila instruments), etc.
| | {{MOS modes |
| | | | Table Headers= |
| Mavila defines a tuning "spectrum", similarly to the meantone spectrum. The fifth of 7-EDO (~686 cents) is often thought of as a dividing line between diatonic and mavila: if the fifth is flatter than this, it will generate anti-diatonic scales but ''not'' [[7L 2s]] superdiatonic scales (it will generate [[2L 7s]] instead), and if it is sharper than this, it will generate diatonic scales. The fifth of 9-EDO is also often thought of as the other tuning endpoint on the mavila spectrum.
| | Super- Mode Names $ |
| | | Ad- Mode Names (ground) $ |
| == Intervals == | | | Table Entries= |
| | | Superlydian $ |
| == Modes == | | TBD $ |
| :''See also [[Mavila modal harmony]]
| | Superionian $ |
| From brightest to darkest, the superdiatonic modes are:
| | Adlocrian $ |
| {| class="wikitable" | | Supermixolydian $ |
| |-
| | Adphrygian $ |
| | | LLLLsLLLs - (Super)Lydian
| | Supercorinthian $ |
| | |
| | Adaeolian $ |
| |-
| | Superolympian $ |
| | | LLLsLLLLs - (Super)Ionian
| | Addorian $ |
| | | | | Superdorian $ |
| |-
| | Admixolydian $ |
| | | LLLsLLLsL - (Super)Mixolydian
| | Superaeolian $ |
| | |
| | Adionian $ |
| |-
| | Superphrygian $ |
| | | LLsLLLLsL - (Super)Corinthian
| | Adlydian $ |
| | |
| | Superlocrian $ |
| |-
| | TBD |
| | | LLsLLLsLL - (Super)Olympian
| | }} |
| | | [[File:MavilaOlympian16edo.mp3]]
| |
| |-
| |
| | | LsLLLLsLL - (Super)Dorian
| |
| | |
| |
| |-
| |
| | | LsLLLsLLL - (Super)Aeolian
| |
| | |
| |
| |-
| |
| | | sLLLLsLLL - (Super)Phrygian
| |
| | |
| |
| |-
| |
| | | sLLLsLLLL - (Super)Locrian
| |
| | | [[File:MavilaSuperdiatonic16edo.mp3]]
| |
| |}
| |
| | |
| The modes of the antidiatonic scale are simply named after the existing diatonic scale modes, but with the "Anti-" prefix (e.g. Anti-ionian, Anti-aeolian, etc). The modes of the superdiatonic scale are also named after the existing modes, but contain the "Super" prefix (e.g. Superionian, Superaeolian, etc.). The "anti" and "super" prefixes can be left in to explicitly distinguish which MOS's modes you're talking about, or can be omitted for convention.
| |
| | |
| Each superdiatonic mode contains its corresponding mode in the antidiatonic scale. Additionally, the superdiatonic modes also resemble the "shape" of their meantone diatonic counterparts. This leads to a pattern: LLLsLLLLs both resembles the meantone LLsLLLs Ionian mode, and contains the mavila ssLsssL anti-Ionian mode as well. Additionally, sLLLsLLLL resembles the diatonic sLLsLLL Locrian mode, and also contains the mavila LssLsss anti-Ionian mode. Furthermore, every mavila mode contains a tonic triad of the -opposite- quality as the corresponding diatonic mode, so that Superionian and Anti-ionian contain a minor triad, and Superphrygian and Antiphrygian contain a major triad.
| |
| | |
| Since there are only seven diatonic modes, two of the superdiatonic modes need additional names and cannot reference any mode of the diatonic scale. These two modes present themselves as "mixed" modes, which begin with the LLs tetrachord, and so contain both the ~300 cent minor third and the ~375 cent major third (and hence both minor and major triads). These are the only two modes to exhibit this behavior. They're interspersed on the rotational continuum between Ionian and Dorian, and Mixolydian and Aeolian.
| |
| | |
| As were the original modes named after regions of ancient Greece, so are these new superdiatonic extensions. The one between Ionian and Dorian is called Corinthian, after the Greek island of Corinth, set up so that the Ionian -> Corinthian -> Dorian cyclic sequence will resemble the columns of ancient Greek architecture. The mode cyclically placed between Mixolydian and Aeolian, which is the symmetrical LLsLLLsLL scale, has a number of noteworthy theoretical properties, in that it contains every modal rotation of mavila[5], and hence the entire mavila-tempered 5-limit tonality diamond; it was given the name of Olympian to match its unique status in this regard.
| |
| === Table of modes ===
| |
|
| |
|
| == Chords and extended harmony == | | == Note names== |
| | 7L 2s, when viewed under Armodue theory, can be notated using Armodue notation. |
|
| |
|
| == Primodal theory == | | == Theory == |
| === Neji versions of superdiatonic modes === | | === Temperament interpretations === |
| * 40:48:52:54:59:64:70:77:80 Pental Superionian
| | [[Pelogic family#Mavila|Mavila]] is an important harmonic entropy minimum here, insofar as 670-680{{c}} can be considered a fifth. Other temperaments include septimal mavila, hornbostel, and trismegistus. |
| === 16nejis ===
| |
| === 23nejis ===
| |
| === 25nejis ===
| |
|
| |
|
| == Scale tree == | | == Scale tree == |
| In addition to the 7-note anti-diatonic scale described, Mavila also has a 9 note "superdiatonic" MOS, the "super-Ionian" mode of which looks LLLsLLLLs. This is the basis for the [[Armodue theory]].
| | {{MOS tuning spectrum |
| | | | 1/1 = Near exact-7/6 [[Pelogic_family#Armodue|Armodue]] |
| Mavila generates a 16 tone chromatic MOS. In a certain sense, much of mavila makes sense if viewed within the lens of a 16-tone chromatic gamut, similarly to how much of meantone is thought of in the setting of a 12-tone chromatic gamut.
| | | 4/3 = Near exact-20/17 [[Pentagoth]] |
| | | | 7/5 = Near exact-5/4 [[Mavila]] |
| After the 16 tone chromatic scale is the 23 tone enharmonic MOS, which can be thought of as an "extended mavila" analogous to the "extended meantone" 19-tone enharmonic scale. If the mavila fifth is flatter than that of 16-EDO (675 cents), it will instead generate an MOS at 25 notes. This is similar to how if the meantone fifth is tuned sharper than 12-EDO, it will instead generate a 17-tone MOS rather than a 19-tone one.
| | | 3/2 = Near exact-13/11 Pentagoth |
| | | | 7/4 = Near exact-7/4 [[Pelogic_family#Armodue|Armodue]] |
| {| class="wikitable"
| | | 10/3 = Near exact-6/5 [[Mavila]] |
| |-
| | | 6/1 = [[Gravity]] ↓ |
| ! colspan="5" | Generator
| | }} |
| ! | Generator size (cents)
| |
| ! | L/s
| |
| ! | Comments
| |
| |-
| |
| | | 4\[[7edo|7]]
| |
| | | | |
| | |
| |
| | |
| |
| | |
| |
| | | 685.714
| |
| | | 1/0
| |
| | |
| |
| |-
| |
| | |
| |
| | |
| |
| | |
| |
| | |
| |
| | | 21\37
| |
| | | 681.08
| |
| | | 5/1
| |
| | |
| |
| |-
| |
| | |
| |
| | |
| |
| | |
| |
| | | 17\30
| |
| | |
| |
| | | 680
| |
| | | 4/1
| |
| | |
| |
| |-
| |
| | |
| |
| | |
| |
| | | 13\23
| |
| | |
| |
| | |
| |
| | | 678.261
| |
| | | 3/1
| |
| | |
| |
| |-
| |
| | |
| |
| | |
| |
| | |
| |
| | | 22\39
| |
| | |
| |
| | | 676.923
| |
| | | 5/2
| |
| |-
| |
| | |
| |
| | | 9\16
| |
| | |
| |
| | |
| |
| | |
| |
| | | 675
| |
| | | 2/1
| |
| | | Boundary of propriety; smaller generators are strictly proper | |
| |-
| |
| | |
| |
| | |
| |
| | | 23\41
| |
| | |
| |
| | |
| |
| | | 673.171
| |
| | | 5/3
| |
| | |
| |
| |-
| |
| | |
| |
| | |
| |
| | |
| |
| | |
| |
| | |
| |
| | | 672.85
| |
| | | φ/1
| |
| | | Golden mavila
| |
| |-
| |
| | |
| |
| | |
| |
| | | 14\25
| |
| | |
| |
| | |
| |
| | | 672
| |
| | | 3/2
| |
| | |
| |
| |-
| |
| | |
| |
| | |
| |
| | |
| |
| | | 19\34
| |
| | |
| |
| | | 670.588
| |
| | | 4/3
| |
| | |
| |
| |-
| |
| | |
| |
| | |
| |
| | |
| |
| | |
| |
| | | 24\43
| |
| | | 669.767
| |
| | | 5/4
| |
| | |
| |
| |-
| |
| | | 5\[[9edo|9]]
| |
| | | | |
| | |
| |
| | |
| |
| | |
| |
| | | 666.667
| |
| | | 1/1
| |
| | |
| |
| |}
| |
| | |
| | |
| == Pieces == | |
| * [https://soundcloud.com/starshine99/undercity-ft-hatsune-miku (Undercity ft. Hatsune Miku)]
| |
| * [https://www.youtube.com/watch?v=bgnGZCQr5yE ks26 - Wallowing in Madness]
| |
| * [https://www.youtube.com/watch?v=2p3z9YEpW1k Sevish - Sea Poem]
| |
| * [https://www.youtube.com/watch?v=1tdHPqKPOWc Marooned at Home (mavila tuning)]
| |
| * [https://www.youtube.com/watch?v=QzZw-KCn2ig "Netbeans" (in a tuning of Mavila)]
| |
| * [https://en.xen.wiki/w/File:Mavila_Jazz_Rhodes_1.mp3 Mavila Jazz Rhodes 1]
| |
| * [https://cityoftheasleep.bandcamp.com/track/illegible-red-ink Illegible Red Ink]
| |
| * [https://cityoftheasleep.bandcamp.com/track/run-run-red-robot Run Run Red Robot]
| |
|
| |
|
| [[Category:Mavila| ]] <!-- main article --> | | [[Category:9-tone scales]] |
| [[Category:Theory]]
| | [[Category:Mavila]] |
| [[Category:Scales]]
| |
| [[Category:MOS scales]]
| |
| [[Category:Abstract MOS patterns]] | |
| [[Category:Superdiatonic]]
| |