User:Nick Vuci/Moments of Symmetry: Difference between revisions

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== Construction ==

File:1-1 MOS Construction.png|An interval is chosen to be the period (the 1200 cent octave in this example). The period is represented with a circle; intervals are represented with purple lines and points radiating out from the middle which move clockwise.

File:1-1 MOS Construction.png|An interval is chosen to be the period (the '''1200 cent octave''' in this example). The period is represented with a circle; intervals are represented with purple lines and points radiating out from the middle which move clockwise.

File:1-2 MOS Construction.png|An interval is chosen to be a generator (the 700 cent perfect fifth in this example). This is the 1L 2s MOS pattern.

File:1-2 MOS Construction.png|An interval is chosen to be a generator (the '''700 cent perfect fifth''' in this example). This is the '''1L 2s''' MOS pattern.

File:1-3 MOS Construction.png|Stacking the generator upon itself yields a scale with 2 step sizes. This is the 2L 1s MOS pattern.

File:1-3 MOS Construction.png|Stacking the generator upon itself yields a scale with 2 step sizes. This is the '''2L 1s''' MOS pattern.

File:1-4 MOS Construction.png|Stacking the generator 2 times yields a scale with 3 step sizes (not MOS).

File:1-4 MOS Construction.png|Stacking the generator 2 times yields a scale with 3 step sizes ('''not MOS''').

File:1-5 MOS Construction.png|Stacking the generator 3 times yields a scale with 2 step sizes. This is the 2L 3s MOS pattern.

File:1-5 MOS Construction.png|Stacking the generator 3 times yields a scale with 2 step sizes. This is the '''2L 3s''' MOS pattern.

File:1-6 MOS Construction.png|Stacking the generator five times yields a scale with ~~three~~ step sizes (not MOS).

File:1-6 MOS Construction.png|Stacking the generator five times yields a scale with 3 step sizes ('''not MOS''').

File:1-7 MOS Construction.png|Stacking the generator 6 times yields a scale with 2 step sizes. This is the 5L 2s MOS pattern.

File:1-7 MOS Construction.png|Stacking the generator 6 times yields a scale with 2 step sizes. This is the '''5L 2s''' MOS pattern.

File:700centMOS.gif|The generator sequence animated with the moments of symmetry labelled.

</gallery>

== Step Ratios ==

The [[step ratio]] ~~(also simply called~~ the ''hardness''~~) of~~ MOS denote the relative sizes of the large and small steps and is ~~an important~~ factor ~~for~~ classifying MOS patterns. ~~The~~ step ratio of 2:1 ~~— which means that~~ the large steps are ~~double~~ the size of the small steps — is ~~called~~ the ''basic'' form of the MOS. When the difference between the large and small steps increases (i.e., the large step becomes larger and the small step smaller) the MOS is considered harder, as the contrast in ~~size is~~ more pronounced. Conversely, when the size difference decreases (~~meaning~~ the large step becomes smaller and the small step larger) the MOS is considered softer, due to the ~~subtler~~ contrast.

The [[step ratio]]—also referred to as the ''hardness''—of MOS denote the relative sizes of the large and small steps and is a key factor in classifying MOS patterns. A step ratio of 2:1, meaning the large steps are twice the size of the small steps, is considered the ''basic'' form of the MOS. When the difference between the large and small steps increases (i.e., the large step becomes larger and the small step smaller), the MOS is considered ''harder'', as the contrast in step sizes becomes more pronounced. Conversely, when the size difference decreases (i.e., the large step becomes smaller and the small step larger), the MOS is considered ''softer'', due to the more subtle contrast.

To find the equal tuning of some hardness of an MOS, simply input the relative size of the steps and multiply them by the number of steps. For example if we want to find the tuning which contains the 5L 2s pattern with the hardness of 2:1, we simply calculate 5(2)+2(1)=12, showing us that 12-EDO contains it.

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 == Construction ==
 <gallery mode="nolines" widths="200" heights="200">
-File:1-1 MOS Construction.png|An interval is chosen to be the period (the 1200 cent octave in this example). The period is represented with a circle; intervals are represented with purple lines and points radiating out from the middle which move clockwise.
+File:1-1 MOS Construction.png|An interval is chosen to be the period (the '''1200 cent octave''' in this example). The period is represented with a circle; intervals are represented with purple lines and points radiating out from the middle which move clockwise.
-File:1-2 MOS Construction.png|An interval is chosen to be a generator (the 700 cent perfect fifth in this example). This is the 1L 2s MOS pattern.
+File:1-2 MOS Construction.png|An interval is chosen to be a generator (the '''700 cent perfect fifth''' in this example). This is the '''1L 2s''' MOS pattern.
-File:1-3 MOS Construction.png|Stacking the generator upon itself yields a scale with 2 step sizes. This is the 2L 1s MOS pattern.
+File:1-3 MOS Construction.png|Stacking the generator upon itself yields a scale with <u>2 step sizes</u>. This is the '''2L 1s''' MOS pattern.
-File:1-4 MOS Construction.png|Stacking the generator 2 times yields a scale with 3 step sizes (not MOS).
+File:1-4 MOS Construction.png|Stacking the generator 2 times yields a scale with 3 step sizes ('''not MOS''').
-File:1-5 MOS Construction.png|Stacking the generator 3 times yields a scale with 2 step sizes. This is the 2L 3s MOS pattern.
+File:1-5 MOS Construction.png|Stacking the generator 3 times yields a scale with <u>2 step sizes</u>. This is the '''2L 3s''' MOS pattern.
-File:1-6 MOS Construction.png|Stacking the generator five times yields a scale with three step sizes (not MOS).
+File:1-6 MOS Construction.png|Stacking the generator five times yields a scale with 3 step sizes ('''not MOS''').
-File:1-7 MOS Construction.png|Stacking the generator 6 times yields a scale with 2 step sizes. This is the 5L 2s MOS pattern.
+File:1-7 MOS Construction.png|Stacking the generator 6 times yields a scale with <u>2 step sizes</u>. This is the '''5L 2s''' MOS pattern.
 File:700centMOS.gif|The generator sequence animated with the moments of symmetry labelled.
 </gallery>
 == Step Ratios ==
-The [[step ratio]] (also simply called the ''hardness'') of MOS denote the relative sizes of the large and small steps and is an important factor for classifying MOS patterns. The step ratio of 2:1 — which means that the large steps are double the size of the small steps — is called the ''basic'' form of the MOS. When the difference between the large and small steps increases (i.e., the large step becomes larger and the small step smaller) the MOS is considered harder, as the contrast in size is more pronounced. Conversely, when the size difference decreases (meaning the large step becomes smaller and the small step larger) the MOS is considered softer, due to the subtler contrast.
+The [[step ratio]]—also referred to as the ''hardness''—of MOS denote the relative sizes of the large and small steps and is a key factor in classifying MOS patterns. A step ratio of 2:1, meaning the large steps are twice the size of the small steps, is considered the ''basic'' form of the MOS. When the difference between the large and small steps increases (i.e., the large step becomes larger and the small step smaller), the MOS is considered ''harder'', as the contrast in step sizes becomes more pronounced. Conversely, when the size difference decreases (i.e., the large step becomes smaller and the small step larger), the MOS is considered ''softer'', due to the more subtle contrast.
 To find the equal tuning of some hardness of an MOS, simply input the relative size of the steps and multiply them by the number of steps. For example if we want to find the tuning which contains the 5L 2s pattern with the hardness of 2:1, we simply calculate 5(2)+2(1)=12, showing us that 12-EDO contains it.