5L 2s/Muddles

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, "L₁" refers to the larger of two large step sizes while "L₂" refers to the smaller of two large step sizes, and likewise "s₁" refers to the larger of two small step sizes while "s₂" 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.

3L₁ 2L₂ 2s

The 3L₁ 2L₂ 2s muddle can be denoted as Ptolemaic-Auric Diatonic Scale on account of the 3L₁ 2L₂ 2s being the step-size combination being shared by both the well-known Ptolemaic Sequence, and 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 L₁L₂sL₁L₁L₂s, 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.

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.

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.

2L₁ 3L₂ 2s

Aside from the Ptolemaic-Auric Diatonic Scale, the 2L₁ 3L₂ 2s muddle is the one of them more frequently encountered 5L 2s muddles.