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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. | | {{breadcrumb}} |
| | The term "'''diatonic scale'''" is an umbrella term that not only refers to the [[5L 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. |
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| == 3L<sub>1</sub> 2L<sub>2</sub> 2s == | | == 3L<sub>1</sub> 2L<sub>2</sub> 2s == |
| The '''3L<sub>1</sub> 2L<sub>2</sub> 2s''' muddle can be denoted as '''Ptolemaic-Auric Diatonic Scale''' on account of the 3L<sub>1</sub> 2L<sub>2</sub> 2s being the step-size combination being shared by both the well-known '''[[Zarlino|Ptolemaic Sequence]]''', and [[User:Aura|Aura]]'s preferred [[5-limit]] tuning of the Ionian scale, albeit the exact step patterns differ between the two scales. By default, the Ptolemaic-Auric Diatonic Scale 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, which was chosen as the standard arrangement for representing 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 of the benefits this arrangement offers in the 5-limit.
| | {{see also|Nicetone}} |
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| The 5-limit version the Ptolemaic-Auric Diatonic Scale- the tuning preferred by Aura- may be referred to as the '''Dualharmonic Ionian Scale''' on account of every scale degree being a member of either the Tonic's [[harmonic series]] or [[subharmonic series]]. 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. |
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| [[File:Study in Ionian.mp3|thumb|none|A study piece by Aura using the Dualharmonic Ionian Scale, which has the following intervals: [[1/1]] [[9/8]] [[5/4]] [[4/3]] [[3/2]] [[27/16]] [[15/8]] [[2/1]].]]
| | == 2L<sub>1</sub> 3L<sub>2</sub> 2s == |
| | {{see also|Interdia}} |
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| | 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 2s muddles. |
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| | == 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}}. |
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| == 2L<sub>1</sub> 3L<sub>2</sub> 2s ==
| | [[Category:Diatonic]] |
| Aside from the Ptolemaic-Auric Diatonic Scale, the '''2L<sub>1</sub> 3L<sub>2</sub> 2s''' muddle is the one of them more frequently encountered 5L 2s muddles.
| | [[Category:MOS muddles]] |