5L 2s/Muddles: Difference between revisions

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== 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 '''[[Zarlino|Ptolemaic Sequence]]''', and [[User:Aura|Aura]]'s preferred 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 '''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 '''[[Zarlino|Ptolemaic Sequence]]''', and [[User:Aura|Aura]]'s preferred 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 L1L2sL1L2L1s, 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.

~~The 5-limit version~~ the Ptolemaic~~-Auric Diatonic Scale- the tuning of the Ionian scale 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.

~~[[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]]~~.]]

== 2L1 3L2 2s ==

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

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 == 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 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]].
+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 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>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.
-The 5-limit version the Ptolemaic-Auric Diatonic Scale- the tuning of the Ionian scale 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.
-[[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 ==
 Aside from the Ptolemaic-Auric Diatonic Scale, the '''2L<sub>1</sub> 3L<sub>2</sub> 2s''' muddle is the one of the more frequently encountered 5L 2s muddles.