311edo: Difference between revisions

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== Intervals ==

The 41-limit add-73 add-89 add-101 add-109 add-113 ~~125~~-odd-limit is represented very close to completely consistently, and as aforementioned, the 77-odd-limit subset of that odd-limit is perfectly consistent, to which a variety of odds can be added that keep perfect consistency, but for comprehensiveness and practical use as a temperament approximating the low-to-mid end of the harmonic series, we consider a larger odd-limit than that which seeks to be more complete.

The 41-limit add-73 add-89 add-101 add-109 add-113 123-odd-limit is represented very close to completely consistently, and as aforementioned, the 77-odd-limit subset of that odd-limit is perfectly consistent, to which a variety of odds can be added that keep perfect consistency, but for comprehensiveness and practical use as a temperament approximating the low-to-mid end of the harmonic series, we consider a larger odd-limit than that which seeks to be more complete.

There is 884 interval pairs in that [[odd-limit]] (the [[41-limit]] add-73 add-89 add-101 add-109 add-113 ~~125~~-odd-limit), where "pairs" refers to that each interval has an [[octave complement]] with equal and opposite error.

There is 884 interval pairs in that [[odd-limit]] (the [[41-limit]] add-73 add-89 add-101 add-109 add-113 123-odd-limit), where "pairs" refers to that each interval has an [[octave complement]] with equal and opposite error.

That odd-limit can be described explicitly as the...

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The below table was generated by writing a simple Python 3 script to print it in plaintext using [[User:Godtone#My_Python_3_code|this code]] to simplify certain steps.

It should be noted that while almost all intervals shown in the table are intervals of the ~~125~~-odd-limit restricted to the aforementioned prime subgroup, the [[square-particular]]s up to [[1681/1680|S41 = (41/40)/(42/41)]] were added manually for completeness and reference in understanding the mapping of the [[41-odd-limit]] by [[311edo]]. Therefore, the very beginning of the table (from 0\311 to 3\311 inclusive) is the only part that is not algorithmically generated.

It should be noted that while almost all intervals shown in the table are intervals of the 123-odd-limit restricted to the aforementioned prime subgroup, the [[square-particular]]s up to [[1681/1680|S41 = (41/40)/(42/41)]] were added manually for completeness and reference in understanding the mapping of the [[41-odd-limit]] by [[311edo]]. Therefore, the very beginning of the table (from 0\311 to 3\311 inclusive) is the only part that is not algorithmically generated.

{| class="mw-collapsible mw-collapsed wikitable center-1"

|+ style=white-space:nowrap | Table of 311edo intervals

| style="text-align:center;" | genes

| style="text-align:center;" | [[41-limit]] add-73 add-89 add-101 add-109 add-113 ~~125~~-odd-limit intervals (/2^n and 2^n/ in bold & linked, inconsistent in italics, else, if [[23-limit]], linked)

| style="text-align:center;" | [[41-limit]] add-73 add-89 add-101 add-109 add-113 123-odd-limit intervals (/2^n and 2^n/ in bold & linked, inconsistent in italics, else, if [[23-limit]], linked)

|-

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@@ Line 20: / Line 20: @@
 == Intervals ==
-The 41-limit add-73 add-89 add-101 add-109 add-113 125-odd-limit is represented very close to completely consistently, and as aforementioned, the 77-odd-limit subset of that odd-limit is perfectly consistent, to which a variety of odds can be added that keep perfect consistency, but for comprehensiveness and practical use as a temperament approximating the low-to-mid end of the harmonic series, we consider a larger odd-limit than that which seeks to be more complete.
+The 41-limit add-73 add-89 add-101 add-109 add-113 123-odd-limit is represented very close to completely consistently, and as aforementioned, the 77-odd-limit subset of that odd-limit is perfectly consistent, to which a variety of odds can be added that keep perfect consistency, but for comprehensiveness and practical use as a temperament approximating the low-to-mid end of the harmonic series, we consider a larger odd-limit than that which seeks to be more complete.
-There is 884 interval pairs in that [[odd-limit]] (the [[41-limit]] add-73 add-89 add-101 add-109 add-113 125-odd-limit), where "pairs" refers to that each interval has an [[octave complement]] with equal and opposite error.
+There is 884 interval pairs in that [[odd-limit]] (the [[41-limit]] add-73 add-89 add-101 add-109 add-113 123-odd-limit), where "pairs" refers to that each interval has an [[octave complement]] with equal and opposite error.
 That odd-limit can be described explicitly as the...
@@ Line 46: / Line 46: @@
 The below table was generated by writing a simple Python 3 script to print it in plaintext using [[User:Godtone#My_Python_3_code|this code]] to simplify certain steps.
-It should be noted that while almost all intervals shown in the table are intervals of the 125-odd-limit restricted to the aforementioned prime subgroup, the [[square-particular]]s up to [[1681/1680|S41 = (41/40)/(42/41)]] were added manually for completeness and reference in understanding the mapping of the [[41-odd-limit]] by [[311edo]]. Therefore, the very beginning of the table (from 0\311 to 3\311 inclusive) is the only part that is not algorithmically generated.
+It should be noted that while almost all intervals shown in the table are intervals of the 123-odd-limit restricted to the aforementioned prime subgroup, the [[square-particular]]s up to [[1681/1680|S41 = (41/40)/(42/41)]] were added manually for completeness and reference in understanding the mapping of the [[41-odd-limit]] by [[311edo]]. Therefore, the very beginning of the table (from 0\311 to 3\311 inclusive) is the only part that is not algorithmically generated.
 {| class="mw-collapsible mw-collapsed wikitable center-1"
 |+ style=white-space:nowrap | Table of 311edo intervals
 | style="text-align:center;" | genes
-| style="text-align:center;" | [[41-limit]] add-73 add-89 add-101 add-109 add-113 125-odd-limit intervals (/2^n and 2^n/ in bold & linked, inconsistent in italics, else, if [[23-limit]], linked)
+| style="text-align:center;" | [[41-limit]] add-73 add-89 add-101 add-109 add-113 123-odd-limit intervals (/2^n and 2^n/ in bold & linked, inconsistent in italics, else, if [[23-limit]], linked)
 |-
 | 0