5L 2s: Difference between revisions
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{{MOS intro}} | {{MOS intro}} | ||
The familiar pattern of 5 whole steps and 2 half steps, commonly written as WWHWWWH for the major scale, takes on a generalized form of LLsLLLs, where the large and small steps—denoted as ''L''{{'}} | The familiar pattern of 5 whole steps and 2 half steps, commonly written as WWHWWWH for the major scale, takes on a generalized form of LLsLLLs, where the large and small steps—denoted as ''L''{{'s}} and ''s''{{`s}}—represent whole number step sizes, thus producing different [[edo]]s. These [[step ratio]]s affect the sizes of the diatonic scale's intervals and correspond to different tuning systems. | ||
Among the most well-known forms of this scale are the Pythagorean diatonic scale, and scales produced by meantone systems (including [[12edo]]). | Among the most well-known forms of this scale are the Pythagorean diatonic scale, and scales produced by meantone systems (including [[12edo]]). | ||
== Name == | == Name == | ||
{{TAMNAMS name}} | {{TAMNAMS name}} "Mosdiatonic" may also be used for the sake of specificity. | ||
== Notation == | == Notation == | ||
: ''This article assumes [[TAMNAMS]] for naming step ratios.'' | : ''This article assumes [[TAMNAMS]] for naming step ratios.'' | ||
== Scale characteristics == | |||
{{TAMNAMS use}} | |||
=== Intervals === | === Intervals === | ||
{{MOS intervals}} | {{MOS intervals}} | ||
=== Generator chain === | |||
{{MOS genchain}} | |||
=== Modes === | |||
{{MOS mode degrees}} | |||
Diatonic modes have standard names from classical music theory. | |||
{{MOS modes}} | |||
=== Note names === | === Note names === | ||
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== Theory == | == Theory == | ||
=== Temperament interpretations === | === Temperament interpretations === | ||
{{Main| | {{Main| {{PAGENAME}}/Temperaments }} | ||
5L 2s has several rank-2 temperament interpretations, such as: | 5L 2s has several rank-2 temperament interpretations, such as: | ||
* [[Meantone]], with generators around 696.2{{c}}. This includes: | * [[Meantone]], with generators around 696.2{{c}}. This includes: | ||
** [[Flattone]], with generators around 693.7{{c}}. | ** [[Flattone]], with generators around 693.7{{c}}. | ||
* [[Schismic]], with generators around 702{{c}}. | * [[Schismic]], with generators around 702{{c}}. | ||
* [[ | * [[Leapfrog]], with generators around 704.7{{c}}. | ||
* [[Archy]], with generators around 709.3{{c}}. This includes: | * [[Archy]], with generators around 709.3{{c}}. This includes: | ||
** Supra, with generators around 707.2{{c}} | ** Supra, with generators around 707.2{{c}} | ||
** Superpyth, with generators around 710.3{{c}} | ** [[Superpyth]], with generators around 710.3{{c}} | ||
** Ultrapyth, with generators around 713.7{{c}}. | ** [[Ultrapyth]], with generators around 713.7{{c}}. | ||
=== Generator chain === | === Generator chain === | ||
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A larger scale can be constructed so that it contains chains of 5L 2s, but then breaks the pattern, exploiting that pareidolic effect to surprise and disorient the listener. Scales which have this effect are called [[warped diatonic]] scales. | A larger scale can be constructed so that it contains chains of 5L 2s, but then breaks the pattern, exploiting that pareidolic effect to surprise and disorient the listener. Scales which have this effect are called [[warped diatonic]] scales. | ||
=== Interval categories === | |||
''See [[5L 2s/Interval categories]]''. | |||
== Tuning ranges == | == Tuning ranges == | ||
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=== Ultrasoft tunings === | === Ultrasoft tunings === | ||
{{See also| Superflat }} | |||
In this range, the major third is so flat that it can best be approximated by [[16/13]], tempering out [[1053/1024]]. | |||
{{MOS tunings|Step Ratios=Ultrasoft|JI Ratios=NONE}} | {{MOS tunings|Step Ratios=Ultrasoft|JI Ratios=NONE}} | ||
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Edos include [[17edo]], [[22edo]], [[27edo]], and [[32edo]], among others. | Edos include [[17edo]], [[22edo]], [[27edo]], and [[32edo]], among others. | ||
{{MOS tunings|Step Ratios=3/1; 4/1; 5/1; 6/1|JI Ratios=Subgroup: 2.3.7 ; Int Limit: 80; Complements Only: 1|Tolerance=15}} | {{MOS tunings|Step Ratios=3/1; 4/1; 5/1; 6/1|JI Ratios=Subgroup: 2.3.7 ; Int Limit: 80; Complements Only: 1|Tolerance=15}} | ||
== Scales == | == Scales == | ||
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=== MODMOS scales and muddles === | === MODMOS scales and muddles === | ||
{{Main|5L 2s MODMOSes|5L 2s Muddles}} | {{Main|5L 2s/MODMOSes|5L 2s/Muddles}} | ||
=== Scala files === | === Scala files === | ||
* [[Meantone7]] | * [[Meantone7]] – 19edo and 31edo tunings | ||
* [[Nestoria7]] | * [[Nestoria7]] – 171edo tuning | ||
* [[Pythagorean7]] | * [[Pythagorean7]] – Pythagorean tuning | ||
* [[Garibaldi7]] | * [[Garibaldi7]] – 94edo tuning | ||
* [[Cotoneum7]] | * [[Cotoneum7]] – 217edo tuning | ||
* [[Edson7]] | * [[Edson7]] – 29edo tuning | ||
* [[Pepperoni7]] | * [[Pepperoni7]] – 271edo tuning | ||
* [[Supra7]] | * [[Supra7]] – 56edo tuning | ||
* [[Archy7]] | * [[Archy7]] – 49edo tuning | ||
== Scale tree == | == Scale tree == | ||
{{ | {{MOS tuning spectrum | ||
7/5 | | Depth = 6 | ||
21/13 | | 7/5 = [[Flattone]] region | ||
5/3 | | 21/13 = [[Golden meantone]] (696.214{{c}}) | ||
9/4 | | 5/3 = [[Meantone]] region | ||
16/7 | | 9/4 = [[Pythagorean tuning]] (701.955{{c}}) | ||
5/2 | | 16/7 = [[Garibaldi]] / [[cassandra]] | ||
21/8 | | 5/2 = [[Dominant (temperament)|Dominant]] region | ||
8/3 | | 21/8 = Golden neogothic (704.096{{c}}) | ||
| 8/3 = [[Neogothic]] region | |||
| 7/2 = [[Quasisuper]] region | |||
| 9/2 = [[Superpyth]] region | |||
| 11/2 = [[Quasiultra]] region | |||
| 7/1 = [[Ultrapyth]] region | |||
}} | }} | ||