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The term "'''diatonic scale'''" is an umbrella term that not only refers to the [[5L 2s]] [[MOS scale]], but also to a group of [[muddles]] and [[MODmuddles]] that are related to it.  This page is for the cataloguing of these muddles.  For the sake of ease, "L<sub>1</sub>" refers to the larger of two large step sizes while "L<sub>2</sub>" refers to the smaller of two large step sizes, and likewise "s<sub>1</sub>" refers to the larger of two small step sizes while "s<sub>2</sub>" refers to the smaller of two small step sizes.  For muddles where there's only a single size of large step, a simple "L" will be used, and likewise, for muddles where there's only a single size of small step, a simple "s" will be used.
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The term "'''diatonic scale'''" is an umbrella term that not only refers to the [[5L&nbsp;2s]] [[MOS scale]], but also to the group of [[muddle]]s and [[MODmuddle]]s that both resemble it and are related to it.  This page is for the cataloguing of these muddles.  For the sake of ease, "L<sub>1</sub>" refers to the larger of two large step sizes while "L<sub>2</sub>" refers to the smaller of two large step sizes, and likewise "s<sub>1</sub>" refers to the larger of two small step sizes while "s<sub>2</sub>" refers to the smaller of two small step sizes.  For muddles where there's only a single size of large step, a simple "L" will be used, and likewise, for muddles where there's only a single size of small step, a simple "s" will be used.


== Ptolemaic-Auric Diatonic Scale ==
== 3L<sub>1</sub> 2L<sub>2</sub> 2s ==
The '''Ptolemaic-Auric Diatonic Scale''' can be denoted as 3L<sub>1</sub> 2L<sub>2</sub> 2s, and, by default, has the pattern of L<sub>1</sub>L<sub>2</sub>sL<sub>1</sub>L<sub>1</sub>L<sub>2</sub>s.  It is so-named on account of the 3L<sub>1</sub> 2L<sub>2</sub> 2s step-size combination being shared by both [[User:Aura|Aura]]'s preferred tuning of the Ionian scale- the '''Dualharmonic Ionian Scale'''- and the more well-known '''[[Zarlino|Ptolemaic Sequence]]''', albeit the exact step patterns differ between the two scales. 
{{see also|Nicetone}}


The [[5-limit]] Dualharmonic Ionian Scale ([[1/1]] [[9/8]] [[5/4]] [[4/3]] [[3/2]] [[27/16]] [[15/8]] [[2/1]]) is so-named on account of every scale degree being a member of either the Tonic's [[harmonic series]] or [[subharmonic series]] and was chosen as the standard arrangement for this particular step-size combination both because it uses two identical tetrachords just like the Pythagorean Diatonic Scale to which it's related, and because the Dualharmonic Ionian Scale actually seems to be the optimal form for the Ionian scale- which is often considered the default diatonic mode by non-microtonalists- in terms of harmonic construction.  This form can be considered optimal for a 5-limit Ionian scale because the [[27/20]] wolf fourth is placed between the third and sixth scale degrees, which has the effect of creating both a really strong VIm-IIm-VM-IM cadence and a really powerful deceptive cadence using the VIm chord, while the IVM chord is in some ways less likely to be accidentally tonicized on account of it having a more tense sound.
The {{nowrap|'''3L<sub>1</sub> 2L<sub>2</sub> 2s'''}} muddle can be denoted as the '''Ptolemaic diatonic scale''' or as '''[[Nicetone]]''' on account of the {{nowrap|3L<sub>1</sub> 2L<sub>2</sub> 2s}} being the step-size combination of the well-known '''[[Zarlino|Ptolemaic sequence]]'''. By default, the Ptolemaic diatonic scale has the pattern of L<sub>1</sub>L<sub>2</sub>sL<sub>1</sub>L<sub>2</sub>L<sub>1</sub>s, which was chosen as the standard arrangement for representing this particular step-size combination due to the Ptolemaic Sequence being a more evenly distributed [[MV3]] scale, though to be fair, it is a chiral scale that has the other variant of L<sub>2</sub>L<sub>1</sub>sL<sub>1</sub>L<sub>2</sub>L<sub>1</sub>s.


== 2L<sub>1</sub> 3L<sub>2</sub> 2s ==
{{see also|Interdia}}


Aside from the Ptolemaic diatonic scale, the {{nowrap|'''2L<sub>1</sub> 3L<sub>2</sub> 2s'''}} muddle, which can be denoted as '''[[Interdia]]''', is the one of the more frequently encountered 5L&nbsp;2s muddles.


[[File:Study in Ionian.mp3|thumb|none|A study piece by Aura using the Dualharmonic Ionian scale.]]
== 5L 1s<sub>1</sub> 1s<sub>2</sub> ==
The following [[18edo]] irregular diatonics, which are derived by stacking alternating 667{{c}} and 733{{c}} fifths, belong to this category: {{dash|0, 200, 400, 533, 733, 933, 1133, 1200}} and {{dash|0, 200, 400, 467, 667, 867, 1067, 1200}}.
 
[[Category:Diatonic]]
[[Category:MOS muddles]]
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