Mohajira: Difference between revisions
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{{ | {{Interwiki | ||
| en = Mohajira | |||
| de = Mohajira | | de = Mohajira | ||
| es = | | es = | ||
| ja = | | ja = | ||
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{{Infobox regtemp | |||
| Title = Mohajira | |||
| Subgroups = 2.3.5.7, 2.3.5.7.11 | |||
| Comma basis = [[81/80]], [[6144/6125]] (7-limit); <br>[[81/80]], [[121/120]], [[176/175]] (11-limit) | |||
| Edo join 1 = 24 | Edo join 2 = 31 | |||
| Mapping = 1; 2 8 -11 5 | |||
| Generators = 11/9 | |||
| Generators tuning = 348.5 | |||
| Optimization method = CWE | |||
| MOS scales = [[3L 4s]], [[7L 3s]], [[7L 10s]], [[7L 17s]] | |||
| Odd limit 1 = 9 | Mistuning 1 = 10.8 | Complexity 1 = 24 | |||
| Odd limit 2 = 11-limit 21 | Mistuning 2 = 10.8 | Complexity 2 = 24 | |||
}} | }} | ||
'''Mohajira'''<ref group="note">(/mʊˈhɑːdʒɪɹə, -hæ-/ ''muu-HA(H)-jirr-ə'' or /məˈhɑːdʒɪɹə, -hæ-/ ''mə-HA(H)-jirr-ə'', named by Jacques Dudon from Arabic مهاجرة ''Muhājirah'')</ref> is a [[Meantone_family#Mohajira|meantone]] temperament that splits [[3/2]] into two [[11/9]] generators and the [[6/5]] into two [[11/10]]'s, thus equating 11/10 with [[12/11]] and 11/9 with [[27/22]]. As a result, eight 11/9's reach [[5/4]], and five reach [[11/8]]. It [[tempering out|tempers out]] the biyatisma ([[121/120]]) and the [[rastma]] (along with meantone's [[syntonic comma]]). It can be thought of as meantone with [[quartertone]]s as it merely splits the generator 3/2 into two equally spaced neutral thirds. Among the most common is the 7-note mos Mohajira[7] which consists of the steps LsLsLss, as well as the [[modmos]] "Rast" which merely flats the fourth by one quartertone. | '''Mohajira'''<ref group="note">(/mʊˈhɑːdʒɪɹə, -hæ-/ ''muu-HA(H)-jirr-ə'' or /məˈhɑːdʒɪɹə, -hæ-/ ''mə-HA(H)-jirr-ə'', named by Jacques Dudon from Arabic مهاجرة ''Muhājirah'')</ref> is a [[Meantone_family#Mohajira|meantone]] temperament that splits [[3/2]] into two [[11/9]] generators and the [[6/5]] into two [[11/10]]'s, thus equating 11/10 with [[12/11]] and 11/9 with [[27/22]]. As a result, eight 11/9's reach [[5/4]], and five reach [[11/8]]. It [[tempering out|tempers out]] the biyatisma ([[121/120]]) and the [[rastma]] (along with meantone's [[syntonic comma]]). It can be thought of as meantone with [[quartertone]]s as it merely splits the generator 3/2 into two equally spaced neutral thirds. Among the most common is the 7-note mos Mohajira[7] which consists of the steps LsLsLss, as well as the [[modmos]] "Rast" which merely flats the fourth by one quartertone. | ||
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The simplest form of this temperament, in 2.3.5.11, is sometimes called '''mohaha'''. To extend mohaha into full 11-limit mohajira, 7 is found at 11 neutral thirds down, tempering out the [[valinorsma]] such that 14/11 is equated with 32/25. Mohaha is tuned best sharp of 31edo's neutral third. An alternate extension, ''migration'', is optimized for flatter tunings and finds 7 at 20 generators up, the same mapping as in [[septimal meantone]] which tempers out [[225/224]]. | The simplest form of this temperament, in 2.3.5.11, is sometimes called '''mohaha'''. To extend mohaha into full 11-limit mohajira, 7 is found at 11 neutral thirds down, tempering out the [[valinorsma]] such that 14/11 is equated with 32/25. Mohaha is tuned best sharp of 31edo's neutral third. An alternate extension, ''migration'', is optimized for flatter tunings and finds 7 at 20 generators up, the same mapping as in [[septimal meantone]] which tempers out [[225/224]]. | ||
As mohajira is a neutral third system, 13 also has a reasonable mapping at | As mohajira is a neutral third system, 13 also has a reasonable mapping at −1 generator, equating 11/9 and 16/13. Subsequently, 17 is mapped to −10 generators (the diatonic semitone) and 19 to −6 generators (the minor third). | ||
For technical data, see [[Meantone family #Mohajira]]. | For technical data, see [[Meantone family #Mohajira]]. | ||
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In the following tables, odd harmonics 1–11 are shown in '''bold'''. | In the following tables, odd harmonics 1–11 are shown in '''bold'''. | ||
<div style="display: inline-grid; margin-right: 25px;"> | |||
{| class="wikitable center-1 right-2" | {| class="wikitable center-1 right-2" | ||
|- | |- | ||
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| 4 | | 4 | ||
| 194.0 | | 194.0 | ||
| 9/8, 10/9 | | '''9/8''', 10/9 | ||
|- | |- | ||
| 5 | | 5 | ||
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| POTE: ~128/105 = 348.4149{{c}} | | POTE: ~128/105 = 348.4149{{c}} | ||
|} | |} | ||
{| class="wikitable mw-collapsible mw-collapsed" | {| class="wikitable mw-collapsible mw-collapsed" | ||
|+ style="font-size: 105%; white-space: nowrap;" | 11-limit norm-based tunings | |+ style="font-size: 105%; white-space: nowrap;" | 11-limit norm-based tunings | ||