5L 2s/Muddles: Difference between revisions

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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, "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.

== ~~Ptolemaic-Auric Diatonic Scale ==~~

== 3L1 2L2 2s ==

~~The '''Ptolemaic-Auric Diatonic Scale''' can be denoted as~~ 3L1 2L2 2s~~, and, by default, has the pattern of L~~1L2~~sL1L1L2s. It is so~~-~~named~~ on account of the 3L1 2L2 2s step-size combination being shared by both ~~[[User:Aura|Aura]]'s preferred tuning of the Ionian scale and~~ the ~~more~~ well-known '''[[Zarlino|Ptolemaic Sequence]]''', albeit the exact step patterns differ between the two scales. ~~The~~ pattern L1L2sL1L1L2s 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 of the benefits offered by its [[5-limit]] version in particular.

The combination '''3L1 2L2 2s''' 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 [[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 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 offered by its 5-limit version in particular.

The 5-limit version of the Ptolemaic-Auric Diatonic Scale specifically can 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 5-limit version the Ptolemaic-Auric Diatonic 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]].]]

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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.
-== 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 and the more well-known '''[[Zarlino|Ptolemaic Sequence]]''', albeit the exact step patterns differ between the two scales.  The pattern L<sub>1</sub>L<sub>2</sub>sL<sub>1</sub>L<sub>1</sub>L<sub>2</sub>s 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 of the benefits offered by its [[5-limit]] version in particular.
+The combination '''3L<sub>1</sub> 2L<sub>2</sub> 2s''' 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 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 offered by its 5-limit version in particular.
-The 5-limit version of the Ptolemaic-Auric Diatonic Scale specifically can 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 5-limit version the Ptolemaic-Auric Diatonic 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]].]]