|
|
| (79 intermediate revisions by 17 users not shown) |
| Line 1: |
Line 1: |
| {{Infobox MOS | | {{Infobox MOS}} |
| | Name = mavila, superdiatonic
| | |
| | Periods = 1
| | {{MOS intro}} |
| | nLargeSteps = 7
| | Scales of this form are strongly associated with [[Armodue theory]], as applied to septimal mavila and Hornbostel temperaments. [[Trismegistus]] is also a usable temperament. |
| | nSmallSteps = 2
| | == Name == |
| | Equalized = 5
| | The [[TAMNAMS]] name for this pattern is '''armotonic''', in reference to Armodue theory. '''Superdiatonic''' is also in use. |
| | Paucitonic = 4 | | |
| | Pattern = LLLsLLLLs | | == Scale properties == |
| | {{TAMNAMS use}} |
| | |
| | === Intervals === |
| | {{MOS intervals}} |
| | |
| | === Generator chain === |
| | {{MOS genchain}} |
| | |
| | === Modes === |
| | {{MOS mode degrees}} |
| | |
| | === 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. |
| | {{MOS modes |
| | | Table Headers= |
| | Super- Mode Names $ |
| | Ad- Mode Names (ground) $ |
| | | Table Entries= |
| | Superlydian $ |
| | TBD $ |
| | Superionian $ |
| | Adlocrian $ |
| | Supermixolydian $ |
| | Adphrygian $ |
| | Supercorinthian $ |
| | Adaeolian $ |
| | Superolympian $ |
| | Addorian $ |
| | Superdorian $ |
| | Admixolydian $ |
| | Superaeolian $ |
| | Adionian $ |
| | Superphrygian $ |
| | Adlydian $ |
| | Superlocrian $ |
| | TBD |
| }} | | }} |
|
| |
|
| '''7L 2s''', '''mavila superdiatonic''' 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¢). 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).
| | == Note names== |
| | | 7L 2s, when viewed under Armodue theory, can be notated using Armodue notation. |
| From a regular temperament perspective (i.e. approximating [[low JI]] intervals), this MOS pattern is essentially synonymous to [[mavila]]. If you're looking for highly accurate scales (that is, ones that approximate low JI closely), there are much better scale patterns to look at. However, if 678 cents is an acceptable 3/2 to you, then [[Pelogic_family|mavila]] is an important [[harmonic entropy]] minimum here. So a general name for this MOS pattern could be "mavila superdiatonic" or simply 'Superdiatonic'.
| |
|
| |
|
| These scales are strongly associated with [[mavila]] system, which can be divided into two systems:
| | == Theory == |
| * the [[Armodue|Armodue]] project/system and its associated [[armodue]] temperament, with fifths sharper than 5\9 (666.7¢) and flatter than 9\16 (675¢).
| | === Temperament interpretations === |
| * Hornbostel temperament, with fifths sharper than 9\16 (675¢) and flatter than 4\7 (685.71¢).
| | [[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. |
|
| |
|
| Some high JI approximations of the generator: 31/21, 34/23, 65/44, 71/48, 99/67, 105/71, 108/73, 133/90, 145/98, 176/119, 250/169. These could be used to guide the construction of neji versions of superdiatonic scales or edos.
| |
| == Scale tree == | | == Scale tree == |
| {| class="wikitable" | | {{MOS tuning spectrum |
| |-
| | | 1/1 = Near exact-7/6 [[Pelogic_family#Armodue|Armodue]] |
| ! colspan="5" | Generator
| | | 4/3 = Near exact-20/17 [[Pentagoth]] |
| ! | Generator size (cents)
| | | 7/5 = Near exact-5/4 [[Mavila]] |
| ! | L/s
| | | 3/2 = Near exact-13/11 Pentagoth |
| ! | Comments
| | | 7/4 = Near exact-7/4 [[Pelogic_family#Armodue|Armodue]] |
| |-
| | | 10/3 = Near exact-6/5 [[Mavila]] |
| | | 4\[[7edo|7]]
| | | 6/1 = [[Gravity]] ↓ |
| | | | | }} |
| | |
| |
| | |
| |
| | |
| |
| | | 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
| |
| | |
| |
| |}
| |
| | |
| == Primodal theory ==
| |
| === Neji versions of superdiatonic modes ===
| |
| * 40:48:52:54:59:64:70:77:80 Pental Superionian
| |
| === 16nejis ===
| |
| === 23nejis ===
| |
| === 25nejis ===
| |
|
| |
|
| [[Category:Theory]] | | [[Category:9-tone scales]] |
| [[Category:Scales]]
| |
| [[Category:MOS scales]]
| |
| [[Category:Abstract MOS patterns]]
| |
| [[Category:Mavila]] | | [[Category:Mavila]] |
| [[Category:Superdiatonic]]
| |