5L 2s/Muddles: Difference between revisions

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== Ptolemaic-Auric Diatonic Scale ==

The '''Ptolemaic-Auric Diatonic Scale''' can be denoted as 3L1 2L2 2s, and, by default, has the pattern of L1L2sL1L1L2s. 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~~- the '''Dualharmonic Ionian Scale'''-~~ and the more well-known '''[[Zarlino|Ptolemaic Sequence]]''', albeit the exact step patterns differ between the two scales.

The '''Ptolemaic-Auric Diatonic Scale''' can be denoted as 3L1 2L2 2s, and, by default, has the pattern of L1L2sL1L1L2s. 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 [[5-limit]] Dualharmonic Ionian Scale ~~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 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.

[[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]].]]

[[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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 == Ptolemaic-Auric Diatonic Scale ==
-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.
+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 [[5-limit]] Dualharmonic Ionian Scale 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 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.
-[[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]].]]
+[[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]].]]