3L 4s: Difference between revisions
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== Name == | == Name == | ||
[[TAMNAMS]] suggests the temperament-agnostic name '''mosh''' for this scale, adopted from an older [[Graham Breed's MOS naming scheme| | [[TAMNAMS]] suggests the temperament-agnostic name '''mosh''' for this scale, adopted from an older [[Graham Breed's MOS naming scheme|mos naming scheme]] by [[Graham Breed]]. The name is a contraction of "mohajira-ish". | ||
== Scale properties == | == Scale properties == | ||
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==== Proposed names ==== | ==== Proposed names ==== | ||
One set of mode nicknames was coined by [[Andrew Heathwaite]]. The other set was coined by [[User:CellularAutomaton|CellularAutomaton]] and follows the diatonic modes' naming convention by using ancient Greek toponyms that sound similar to the Heathwaite names. | One set of mode nicknames was coined by [[Andrew Heathwaite]]. The other set was coined by [[User:CellularAutomaton|CellularAutomaton]] and follows the diatonic modes' naming convention by using ancient Greek toponyms that sound similar to the Heathwaite names. | ||
{{MOS modes|Table Headers=Mode | {{MOS modes|Table Headers=Mode names<br>(Heathwaite); Mode names<br>(CA)|Table Entries=Dril; Dalmatian; Gil; Galatian; Kleeth; Cilician; Bish; Bithynian; Fish; Pisidian; Jwl; Illyrian; Led; Lycian}} | ||
== Theory == | == Theory == | ||
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== Tuning ranges == | == Tuning ranges == | ||
3\10 represents a dividing line between "neutral third scales" on the bottom (eg. 17edo neutral scale), and scales generated by submajor and major thirds at the top, with 10edo standing in between. The neutral third scales, after three more generators, make | 3\10 represents a dividing line between "neutral third scales" on the bottom (eg. 17edo neutral scale), and scales generated by submajor and major thirds at the top, with 10edo standing in between. The neutral third scales, after three more generators, make mos [[7L 3s]] (dicoid); the other scales make mos [[3L 7s]] (sephiroid). | ||
In dicoid, the generators are all "neutral thirds," and two of them make an approximation of the "perfect fifth." Additionally, the L of the scale is somewhere around a "whole tone" and the s of the scale is somewhere around a "neutral tone". | In dicoid, the generators are all "neutral thirds," and two of them make an approximation of the "perfect fifth." Additionally, the L of the scale is somewhere around a "whole tone" and the s of the scale is somewhere around a "neutral tone". | ||
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=== Ultrasoft === | === Ultrasoft === | ||
[[Ultrasoft]] mosh tunings have step ratios that are less than 4:3, which implies a generator flatter than {{nowrap|7\24 {{=}} 350{{c}}}}. | [[Ultrasoft]] mosh tunings have step ratios that are less than 4:3, which implies a generator flatter than {{nowrap| 7\24 {{=}} 350{{c}} }}. | ||
Ultrasoft mosh can be considered "meantone mosh". This is because the large step is a "meantone" in these tunings, somewhere between near-10/9 (as in [[38edo]]) and near-9/8 (as in [[24edo]]). | Ultrasoft mosh can be considered "meantone mosh". This is because the large step is a "meantone" in these tunings, somewhere between near-10/9 (as in [[38edo]]) and near-9/8 (as in [[24edo]]). | ||
Ultrasoft mosh | Ultrasoft mosh edos include [[24edo]], [[31edo]], [[38edo]], and [[55edo]]. | ||
* [[24edo]] can be used to make large and small steps more distinct (the step ratio is 4/3), or for its nearly pure 3/2. | * [[24edo]] can be used to make large and small steps more distinct (the step ratio is 4/3), or for its nearly pure 3/2. | ||
* [[38edo]] can be used to tune the diminished and perfect mosthirds near [[6/5]] and [[11/9]], respectively. | * [[38edo]] can be used to tune the diminished and perfect mosthirds near [[6/5]] and [[11/9]], respectively. | ||
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| [[11/9]] | | [[11/9]] | ||
|- | |- | ||
| L (4g - octave) | | L ({{nowrap| 4g - octave }}) | ||
| 4\24, 200.00 | | 4\24, 200.00 | ||
| 5\31, 193.55 | | 5\31, 193.55 | ||
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| [[9/8]], [[10/9]] | | [[9/8]], [[10/9]] | ||
|- | |- | ||
| s (octave - 3g) | | s ({{nowrap| octave - 3g }}) | ||
| 3\24, 150.00 | | 3\24, 150.00 | ||
| 4\31, 154.84 | | 4\31, 154.84 | ||
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=== Quasisoft === | === Quasisoft === | ||
Quasisoft tunings of mosh have a step ratio between 3/2 and 5/3, implying a generator sharper than 5\17 = 352. | Quasisoft tunings of mosh have a step ratio between 3/2 and 5/3, implying a generator sharper than {{nowrap| 5\17 {{=}} 352.94{{c}} }} and flatter than {{nowrap| 8\27 {{=}} 355.56{{c}} }}. | ||
The large step is a sharper major second in these tunings than in ultrasoft tunings. These tunings could be considered "parapyth mosh" or "archy mosh", in analogy to ultrasoft mosh being meantone mosh. | The large step is a sharper major second in these tunings than in ultrasoft tunings. These tunings could be considered "parapyth mosh" or "archy mosh", in analogy to ultrasoft mosh being meantone mosh. | ||
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| 16/13, 11/9 | | 16/13, 11/9 | ||
|- | |- | ||
| L (4g - octave) | | L ({{nowrap| 4g - octave }}) | ||
| 3\17, 211.76 | | 3\17, 211.76 | ||
| 5\27, 222.22 | | 5\27, 222.22 | ||
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| 9/8, 8/7 | | 9/8, 8/7 | ||
|- | |- | ||
| s (octave - 3g) | | s ({{nowrap| octave - 3g }}) | ||
| 2\17, 141.18 | | 2\17, 141.18 | ||
| 3\27, 133.33 | | 3\27, 133.33 | ||
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=== Hypohard === | === Hypohard === | ||
Hypohard tunings of mosh have a step ratio between 2 and 3, implying a generator sharper than 3\10 = | Hypohard tunings of mosh have a step ratio between 2 and 3, implying a generator sharper than {{nowrap| 3\10 {{=}} 360{{c}} }} and flatter than {{nowrap| 4\13 {{=}} 369.23{{c}} }}. | ||
The large step ranges from a semifourth to a subminor third in these tunings. The small step is now clearly a semitone, ranging from 1\10 ( | The large step ranges from a semifourth to a subminor third in these tunings. The small step is now clearly a semitone, ranging from 1\10 (120{{c}}) to 1\13 (92.31{{c}}). | ||
The symmetric mode sLsLsLs becomes a distorted double harmonic major in these tunings. | The symmetric mode sLsLsLs becomes a distorted double harmonic major in these tunings. | ||
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| 7\23, 365.22 | | 7\23, 365.22 | ||
|- | |- | ||
| L (4g - octave) | | L ({{nowrap| 4g - octave }}) | ||
| 2\10, 240.00 | | 2\10, 240.00 | ||
| 3\13, 276.92 | | 3\13, 276.92 | ||
| 5\23, 260.87 | | 5\23, 260.87 | ||
|- | |- | ||
| s (octave - 3g) | | s ({{nowrap| octave - 3g }}) | ||
| 1\10, 120.00 | | 1\10, 120.00 | ||
| 1\13, 92.31 | | 1\13, 92.31 | ||
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=== Ultrahard === | === Ultrahard === | ||
Ultra tunings of mosh have a step ratio greater than 4/1, implying a generator sharper than {{nowrap|5\16 {{=}} 375{{c}}}}. The generator is thus near a [[5/4]] major third, five of which add up to an approximate [[3/1]]. The 7-note | Ultra tunings of mosh have a step ratio greater than 4/1, implying a generator sharper than {{nowrap| 5\16 {{=}} 375{{c}} }}. The generator is thus near a [[5/4]] major third, five of which add up to an approximate [[3/1]]. The 7-note mos only has two perfect fifths, so extending the chain to bigger mosses, such as the [[3L 7s]] 10-note mos, is suggested for getting 5-limit harmony. | ||
This range is associated with [[magic]] temperament. | This range is associated with [[magic]] temperament. | ||
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| 5/4 | | 5/4 | ||
|- | |- | ||
| L (4g - octave) | | L ({{nowrap| 4g - octave }}) | ||
| 4\16, 300.00 | | 4\16, 300.00 | ||
| 5\19, 315.79 | | 5\19, 315.79 | ||
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| 6/5 | | 6/5 | ||
|- | |- | ||
| s (octave - 3g) | | s ({{nowrap| octave - 3g }}) | ||
| 1\16, 75.00 | | 1\16, 75.00 | ||
| 1\19, 63.16 | | 1\19, 63.16 | ||