User:Ganaram inukshuk/Methodologies: Difference between revisions

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The following list is some commentary on some of the basic edos shown in the table:

* '''19edo''': I've seen one musician describe it as a baby version of 31edo, and I'm inclined to agree in that it's basically an equalized 12L 7s.

* '''19edo''': I've seen one musician describe it as a baby version of 31edo, and I'm inclined to agree in that it's basically an equalized 12L 7s. It also introduces the idea that a note raised by two chromas can fall short of the next note one whole tone above it (for example, Cx falling short of D).

* '''31edo''': This, and 50edo to an extent, is currently my go-to edo for meantone temperament. Generally speaking, I like the mellow sound of meantone, which explains why I do absolutely nothing to date with 17edo and friends. It's also compatible with half-sharp and half-flat notation, so "quartertone" compositions are possible.

* '''45edo''': Like 19edo but more extreme. Whereas 19edo has Cx falling short of D but C#x being equivalent to D, in 45edo, C#x falls short of D, but the interval between C#x and D is its own smaller interval I'm dubbing the '''triesis''' for the purposes of this page.

=== 7L 5s ===

=== 7L 5s and 12L 7s ===

Given a chroma is the absolute difference between a large and small step (c = | L - s |), mathematically speaking, the large steps can be broken into a chroma and small step, the small and large steps of 7L 5s. Depending on the order, this produces two ways each of the seven modes can be broken down into the m-chromatic modes, with some overlap.

Given a chroma is the absolute difference between a large and small step (c = | L - s |), mathematically speaking, the large steps can be broken into a chroma and small step, the small and large steps of 7L 5s. Depending on the order, this produces two ways each of the seven modes can be broken down into the m-chromatic modes, with some overlap. Basically, a chroma and small step are not the same size, more commonly described with the terms "diatonic and chromatic semitones". This unevenness manifests itself as the m-chromatic scale, a scale I admittedly don't use as often compared to 12L 7s. I see this mos as an incomplete form of 12L 7s. Nonetheless, a mode table is still provided, providing a guide as to how these 12 modes relate back to the more familiar 7 modes.

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Basically, a chroma and small step are not the same size, more commonly described with the terms "diatonic and chromatic semitones". This unevenness manifests itself as the m-chromatic scale, a scale I admittedly don't use as often compared to 12L 7s. The mode "CS ionian" is basically an incomplete form of one of my favorite modes in 12L 7s.

This breakdown can be taken one step further by breaking down small steps into a chroma and diesis, where a diesis is defined as such: d = | L - 2s |. Ultimately, the large steps of 5L 2s are broken down into two chromas and a diesis, in some order. This produces the modes of 12L 7s and introduces an additional 7 modes on top of the previous 12. In either case, it's easier to think of these modes as some sort of extension of the seven modes of 5L 2s. There are, for example, 13 modes of 12L 7s that contain ionian as a subset (UDPs 17|1 to 5|13), so it's confusing and unhelpful to say there are 13 ionian modes. Therefore, saying that the large steps break down in a specific order (chroma-chroma-diesis, chroma-diesis-chroma, or diesis-chroma-chroma, or simply CCD, CDC, and DCC) helps to narrow down ionian-containing modes to 3 specific modes.

~~=== 12L 7s ===~~

This breakdown can be taken one step further by breaking down small steps into a chroma and diesis, where a diesis is defined as such: d = | L - 2s |. Ultimately, the large steps of 5L 2s are broken down into two chromas and a diesis, in some order. This produces the modes of 12L 7s and introduces an additional 7 modes. In either case, it's easier to think of these modes as some sort of extension of the seven modes of 5L 2s. ~~The use of "CS/SC" and "CCD/CDC/DCC" is to enforce how these modes are broken down; there~~ are 13 modes of 12L 7s that contain ionian as a subset (UDPs 17|1 to 5|13), so it's confusing to say there are 13 ionian modes.

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=== 19L 7s ===

Whereas a diesis is defined as d = | L - 2s |, a triesis is defined as t = | L - 3s |. As a summary, 19L 7s contains all the super-leading tone goodness I expect from 12L 7s, but with an additional step (literally) to get there.

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 The following list is some commentary on some of the basic edos shown in the table:
-* '''19edo''': I've seen one musician describe it as a baby version of 31edo, and I'm inclined to agree in that it's basically an equalized 12L 7s.
+* '''19edo''': I've seen one musician describe it as a baby version of 31edo, and I'm inclined to agree in that it's basically an equalized 12L 7s. It also introduces the idea that a note raised by two chromas can fall short of the next note one whole tone above it (for example, Cx falling short of D).
 * '''31edo''': This, and 50edo to an extent, is currently my go-to edo for meantone temperament. Generally speaking, I like the mellow sound of meantone, which explains why I do absolutely nothing to date with 17edo and friends. It's also compatible with half-sharp and half-flat notation, so "quartertone" compositions are possible.
+* '''45edo''': Like 19edo but more extreme. Whereas 19edo has Cx falling short of D but C#x being equivalent to D, in 45edo, C#x falls short of D, but the interval between C#x and D is its own smaller interval I'm dubbing the '''triesis''' for the purposes of this page.
-=== 7L 5s ===
+=== 7L 5s and 12L 7s ===
-Given a chroma is the absolute difference between a large and small step (c = | L - s |), mathematically speaking, the large steps can be broken into a chroma and small step, the small and large steps of 7L 5s. Depending on the order, this produces two ways each of the seven modes can be broken down into the m-chromatic modes, with some overlap.
+Given a chroma is the absolute difference between a large and small step (c = | L - s |), mathematically speaking, the large steps can be broken into a chroma and small step, the small and large steps of 7L 5s. Depending on the order, this produces two ways each of the seven modes can be broken down into the m-chromatic modes, with some overlap. Basically, a chroma and small step are not the same size, more commonly described with the terms "diatonic and chromatic semitones". This unevenness manifests itself as the m-chromatic scale, a scale I admittedly don't use as often compared to 12L 7s. I see this mos as an incomplete form of 12L 7s. Nonetheless, a mode table is still provided, providing a guide as to how these 12 modes relate back to the more familiar 7 modes.
 {| class="wikitable"
 !
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 |SC Locrian
 |}
-Basically, a chroma and small step are not the same size, more commonly described with the terms "diatonic and chromatic semitones". This unevenness manifests itself as the m-chromatic scale, a scale I admittedly don't use as often compared to 12L 7s. The mode "CS ionian" is basically an incomplete form of one of my favorite modes in 12L 7s.
+This breakdown can be taken one step further by breaking down small steps into a chroma and diesis, where a diesis is defined as such: d = | L - 2s |. Ultimately, the large steps of 5L 2s are broken down into two chromas and a diesis, in some order. This produces the modes of 12L 7s and introduces an additional 7 modes on top of the previous 12. In either case, it's easier to think of these modes as some sort of extension of the seven modes of 5L 2s. There are, for example, 13 modes of 12L 7s that contain ionian as a subset (UDPs 17|1 to 5|13), so it's confusing and unhelpful to say there are 13 ionian modes. Therefore, saying that the large steps break down in a specific order (chroma-chroma-diesis, chroma-diesis-chroma, or diesis-chroma-chroma, or simply CCD, CDC, and DCC) helps to narrow down ionian-containing modes to 3 specific modes.
-=== 12L 7s ===
-This breakdown can be taken one step further by breaking down small steps into a chroma and diesis, where a diesis is defined as such: d = | L - 2s |. Ultimately, the large steps of 5L 2s are broken down into two chromas and a diesis, in some order. This produces the modes of 12L 7s and introduces an additional 7 modes. In either case, it's easier to think of these modes as some sort of extension of the seven modes of 5L 2s. The use of "CS/SC" and "CCD/CDC/DCC" is to enforce how these modes are broken down; there are 13 modes of 12L 7s that contain ionian as a subset (UDPs 17|1 to 5|13), so it's confusing to say there are 13 ionian modes.
 {| class="wikitable"
 !
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 todo:examples
+=== 19L 7s ===
+Whereas a diesis is defined as d = | L - 2s |, a triesis is defined as t = | L - 3s |. As a summary, 19L 7s contains all the super-leading tone goodness I expect from 12L 7s, but with an additional step (literally) to get there.