User:Godtone: Difference between revisions

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# (classic) minor

# supraminor

# minor neutral

# subneutral (or "minor neutral" if you prefer)

# major neutral

# superneutral (or "major neutral" if you prefer)

# submajor

# (classic) major

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# (ultraminor or) superminor, minor, neutral, major, supermajor (or ultramajor) (5 types)

# (ultraminor,) superminor, novaminor/neominor, minor, neutral, major, novamajor/neomajor, supermajor(, ultramajor) (7 (or 9) types)

# [same as 7 (or 9) types but with neutral split into ~~minor neutral~~ & ~~major neutral~~] (8 (or 10) types)

# [same as 7 (or 9) types but with neutral split into subneutral & superneutral] (8 (or 10) types)

# [same as 8 (or 10) types but with either neo- & nova- distinguished (+2) or with supraminor & submajor added (+2)] (10 (or 12) types)

# [both neo- & nova- and supraminor & submajor distinguished] (12 (or 14) types)

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</ol>

<br/>

=== Colourful EDOs ===

My above progression of "types"/"colours" can be used as a perhaps-interesting alternative to finding "good" EDOs for music by judging them not based on approximation of rationals of interest but instead based on their "colour palette"; not that these two methods are contradictory, and in fact I believe a combination of both is desirable. However, as a demonstration and a starting point, we will look at EDOs providing progressively more complex colour palettes, starting from a broad equalised 7-note approximation of the 5L2s diatonic scale (AKA 7 EDO) and considering only the 'seconds' and 'thirds' (and thus by octave complement, their inversions), with fourths and fifths not considered except to the extent that they should ideally not be too "out of tune", with "out-of-tune-ness" judged relative to approximating either 4/3 or 11/8 (but not both), as these are the simplest J.I fourths. Furthermore, we want the colour palettes to be generally symmetric for the thirds, so this excludes a large number of EDOs; this is intentional, as otherwise we would end up listing every EDO, and as it is a symmetry which I think is important or at least an interesting restriction.

# 7 EDO is the simplest/"trivial" EDO as it provides only the (at times very approximate) "neutral" colour. Note that its fourths are very out-of-tune; this EDO is mainly included as a trivial case. This corresponds to "1 type".

# 12 EDO is the next simplest as it provides (nova)major and (nova)minor seconds and thirds. Also a tone-efficient pure Pyth approximation so very good fourths. This corresponds to "2 types".

# 15 EDO, in terms of colours, is similar to 12 EDO except that its minor third is a little sharper and that it now has 3 types of second which are roughly subminor, neutral and supermajor. The "subminor" and "supermajor" designations are used due to symmetry; in actuality the subminor second is closer to a neominor second and the supermajor second is closer to an ultramajor second. The prefixes may be omitted, or more exact colour terms may be used, making it have a "superneutral second".

# 17 EDO is the first EDO to truly have minor, neutral and major for both seconds and thirds, and is thus quite significant as a potential next step up from 12 EDO. More exactly, these come in the flavours of neominor, neutral and neomajor.

# 19 EDO is the next step up, having seconds and thirds of the ultraminor, minor, major and ultramajor varieties. It does this by conflating an ultramajor second as an ultraminor third, creating quite a distinct interval that escapes 5L2s categorisation. Note that 18 EDO does this too, but is less symmetric. Thus 19 (or 18 - if you are so inclined - which represents a sharpening of seconds and thirds) is the next step up as corresponding to "4 types".

<br/>Note that in the EDOs

=== Philosophy ===

@@ Line 25: / Line 25: @@
 # (classic) minor
 # supraminor
-# minor neutral
+# subneutral (or "minor neutral" if you prefer)
-# major neutral
+# superneutral (or "major neutral" if you prefer)
 # submajor
 # (classic) major
@@ Line 40: / Line 40: @@
 # (ultraminor or) superminor, minor, neutral, major, supermajor (or ultramajor) (5 types)
 # (ultraminor,) superminor, novaminor/neominor, minor, neutral, major, novamajor/neomajor, supermajor(, ultramajor) (7 (or 9) types)
-# [same as 7 (or 9) types but with neutral split into minor neutral & major neutral] (8 (or 10) types)
+# [same as 7 (or 9) types but with neutral split into subneutral & superneutral] (8 (or 10) types)
 # [same as 8 (or 10) types but with either neo- & nova- distinguished (+2) or with supraminor & submajor added (+2)] (10 (or 12) types)
 # [both neo- & nova- and supraminor & submajor distinguished] (12 (or 14) types)
@@ Line 49: / Line 49: @@
 </ol>
 <br/>
+=== Colourful EDOs ===
+My above progression of "types"/"colours" can be used as a perhaps-interesting alternative to finding "good" EDOs for music by judging them not based on approximation of rationals of interest but instead based on their "colour palette"; not that these two methods are contradictory, and in fact I believe a combination of both is desirable. However, as a demonstration and a starting point, we will look at EDOs providing progressively more complex colour palettes, starting from a broad equalised 7-note approximation of the 5L2s diatonic scale (AKA 7 EDO) and considering only the 'seconds' and 'thirds' (and thus by octave complement, their inversions), with fourths and fifths not considered except to the extent that they should ideally not be too "out of tune", with "out-of-tune-ness" judged relative to approximating either 4/3 or 11/8 (but not both), as these are the simplest J.I fourths. Furthermore, we want the colour palettes to be generally symmetric for the thirds, so this excludes a large number of EDOs; this is intentional, as otherwise we would end up listing every EDO, and as it is a symmetry which I think is important or at least an interesting restriction.
+# 7 EDO is the simplest/"trivial" EDO as it provides only the (at times very approximate) "neutral" colour. Note that its fourths are very out-of-tune; this EDO is mainly included as a trivial case. This corresponds to "1 type".
+# 12 EDO is the next simplest as it provides (nova)major and (nova)minor seconds and thirds. Also a tone-efficient pure Pyth approximation so very good fourths. This corresponds to "2 types".
+# 15 EDO, in terms of colours, is similar to 12 EDO except that its minor third is a little sharper and that it now has 3 types of second which are roughly subminor, neutral and supermajor. The "subminor" and "supermajor" designations are used due to symmetry; in actuality the subminor second is closer to a neominor second and the supermajor second is closer to an ultramajor second. The prefixes may be omitted, or more exact colour terms may be used, making it have a "superneutral second".
+# 17 EDO is the first EDO to truly have minor, neutral and major for both seconds and thirds, and is thus quite significant as a potential next step up from 12 EDO. More exactly, these come in the flavours of neominor, neutral and neomajor.
+# 19 EDO is the next step up, having seconds and thirds of the ultraminor, minor, major and ultramajor varieties. It does this by conflating an ultramajor second as an ultraminor third, creating quite a distinct interval that escapes 5L2s categorisation. Note that 18 EDO does this too, but is less symmetric. Thus 19 (or 18 - if you are so inclined - which represents a sharpening of seconds and thirds) is the next step up as corresponding to "4 types".
+<br/>Note that in the EDOs
 === Philosophy ===