256/255: Difference between revisions

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'''256/255''', the '''septendecimal kleisma''', '''charisma''', '''char comma''' or '''255th subharmonic''' is a [[small comma|small]] [[17-limit]] [[superparticular]] comma about 6.8 [[cent]]s in size. It is the difference between [[16/15]] (the classical diatonic semitone) and [[17/16]] (the large septendecimal semitone) and forms the amount by which a stack consisting of [[15/8]] and 17/16 falls short of an [[octave]]~~. It differs from [[352/351]] (the minthma) by [[936/935]] – an [[unnoticeable comma]] measuring about 1.85 cents~~.

'''256/255''', the '''septendecimal kleisma''', '''charisma''', '''char comma''' or '''255th subharmonic''' is a [[small comma|small]] [[17-limit]] [[superparticular]] comma about 6.8 [[cent]]s in size. It is the difference between [[16/15]] (the classical diatonic semitone) and [[17/16]] (the large septendecimal semitone) and forms the amount by which a stack consisting of [[15/8]] and 17/16 falls short of an [[octave]].

== Temperaments ==

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[[Subgroup]]: 2.3.5.17

Patent EDO tunings with [[relative error]] < 1/3 for all generators: 3, 9, 10, 12, 15, 21, 22, 24, 31, 32, 34, 43, 44, 46, 55, 56, 58, 65, 68, 77, 80, 111, 114, 145

Patent EDO tunings with [[relative error]] < 1/3 for all generators: {{Optimal ET sequence|3, 9, 10, 12, 15, 21, 22, 24, 31, 32, 34, 43, 44, 46, 55, 56, 58, 65, 68, 77, 80, 111, 114, 145 }}

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=== Charismic ===

[[Subgroup]]: [[17-limit]]

[[Subgroup]]: full [[17-limit]]

[[Mapping]]: [same as charic plus trivial pure extra primes]

[[Mapping]]: same as charic plus trivial pure extra primes

Patent EDO tunings with [[relative error]] < 1/3 for all generators: 9, 31, 43, 46, 56

Patent EDO tunings with [[relative error]] < 1/3 for all generators: {{Optimal ET sequence|9, 31, 43, 46, 56 }}

[[CTE]] generators: [same as charic plus trivial pure extra primes]

[[CTE]] generators: same as charic plus trivial pure extra primes

=== [[Srutal archagall]] ===

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The "char" in the name ''charisma'' (or ''char comma'') refers to the char data type in C-derived programming languages, where the char represents a byte of at least or exactly 8 bits. Thereby, the maximum unsigned value for an 8-bit char is 255 and the number of values an 8-bit char can take is 256, hence 256/255.

The former name ''diasemisma'' was proposed by [[User:Xenllium|Xenllium]] in May 2023. It is a contraction of ''diatonic semitone'' into a single word, ~~however~~, a rename to [[charisma]] was proposed as part of an effort to make naming more standardised and for a number of reasons including potential confusion with [[diasem]] and the former nonconforming naming of [[horcrux]] in the 11- and 13-limit (which were formerly named "charisma" and "charismic", creating a potential false impression that the former was a comma, not a temperament, and that the latter was the temperament defined by tempering that comma in the corresponding prime limit); specifically, see [[Talk:256/255]] and [[Temperament naming #Contemporary rules]] for details.

The former name ''diasemisma'' was proposed by [[User:Xenllium|Xenllium]] in May 2023. It is a contraction of ''diatonic semitone'' into a single word. In some contexts, both [[16/15]] and [[17/16]] are considered minor second (ie. [[diatonic semitone]]), namely classical diatonic semitone and minor diatonic semitone respectively. However, a rename to ''charisma'' was proposed as part of an effort to make naming more standardised and for a number of reasons including potential confusion with [[diasem]] and the former nonconforming naming of [[horcrux]] in the 11- and 13-limit (which were formerly named "charisma" and "charismic", creating a potential false impression that the former was a comma, not a temperament, and that the latter was the temperament defined by tempering that comma in the corresponding prime limit); specifically, see [[Talk:256/255]] and [[Temperament naming #Contemporary rules]] for details.

The rename took place as Starshine (from the [[XA Discord]] server) suggested (half-jokingly) that a chance had been missed to name it the ''charisma'' in December 2023, a name which [[User:Godtone|Godtone]] took favor to and championed which then caused awareness of nonconforming names of two [[horcrux]] temeraments. A revision to ''charsma'' (no-''i'' spelling) was proposed by Xenllium in January 2024 for disambiguation but this would cause inconsistency with the -ic/-ismic/-isma rule which is a reason that those same temperaments were already being proposed to be renamed.

@@ Line 6: / Line 6: @@
 {{Redirect-distinguish|Charisma|Horcrux}}
-'''256/255''', the '''septendecimal kleisma''', '''charisma''', '''char comma''' or '''255th subharmonic''' is a [[small comma|small]] [[17-limit]] [[superparticular]] comma about 6.8 [[cent]]s in size. It is the difference between [[16/15]] (the classical diatonic semitone) and [[17/16]] (the large septendecimal semitone) and forms the amount by which a stack consisting of [[15/8]] and 17/16 falls short of an [[octave]]. It differs from [[352/351]] (the minthma) by [[936/935]] – an [[unnoticeable comma]] measuring about 1.85 cents.
+'''256/255''', the '''septendecimal kleisma''', '''charisma''', '''char comma''' or '''255th subharmonic''' is a [[small comma|small]] [[17-limit]] [[superparticular]] comma about 6.8 [[cent]]s in size. It is the difference between [[16/15]] (the classical diatonic semitone) and [[17/16]] (the large septendecimal semitone) and forms the amount by which a stack consisting of [[15/8]] and 17/16 falls short of an [[octave]].
 == Temperaments ==
@@ Line 14: / Line 14: @@
 [[Subgroup]]: 2.3.5.17
-Patent EDO tunings with [[relative error]] &lt; 1/3 for all generators: 3, 9, 10, 12, 15, 21, 22, 24, 31, 32, 34, 43, 44, 46, 55, 56, 58, 65, 68, 77, 80, 111, 114, 145
+Patent EDO tunings with [[relative error]] &lt; 1/3 for all generators: {{Optimal ET sequence|3, 9, 10, 12, 15, 21, 22, 24, 31, 32, 34, 43, 44, 46, 55, 56, 58, 65, 68, 77, 80, 111, 114, 145 }}
 {{mapping|legend=1| 1 1 2 5 | 0 1 0 -1 | 0 0 1 -1 }}
@@ Line 21: / Line 21: @@
 === Charismic ===
-[[Subgroup]]: [[17-limit]]
+[[Subgroup]]: full [[17-limit]]
-[[Mapping]]: [same as charic plus trivial pure extra primes]
+[[Mapping]]: same as charic plus trivial pure extra primes
-Patent EDO tunings with [[relative error]] &lt; 1/3 for all generators: 9, 31, 43, 46, 56
+Patent EDO tunings with [[relative error]] &lt; 1/3 for all generators: {{Optimal ET sequence|9, 31, 43, 46, 56 }}
-[[CTE]] generators: [same as charic plus trivial pure extra primes]
+[[CTE]] generators: same as charic plus trivial pure extra primes
 === [[Srutal archagall]] ===
@@ Line 39: / Line 39: @@
 The "char" in the name ''charisma'' (or ''char comma'') refers to the char data type in C-derived programming languages, where the char represents a byte of at least or exactly 8 bits. Thereby, the maximum unsigned value for an 8-bit char is 255 and the number of values an 8-bit char can take is 256, hence 256/255.
-The former name ''diasemisma'' was proposed by [[User:Xenllium|Xenllium]] in May 2023. It is a contraction of ''diatonic semitone'' into a single word, however, a rename to [[charisma]] was proposed as part of an effort to make naming more standardised and for a number of reasons including potential confusion with [[diasem]] and the former nonconforming naming of [[horcrux]] in the 11- and 13-limit (which were formerly named "charisma" and "charismic", creating a potential false impression that the former was a comma, not a temperament, and that the latter was the temperament defined by tempering that comma in the corresponding prime limit); specifically, see [[Talk:256/255]] and [[Temperament naming #Contemporary rules]] for details.
+The former name ''diasemisma'' was proposed by [[User:Xenllium|Xenllium]] in May 2023. It is a contraction of ''diatonic semitone'' into a single word. In some contexts, both [[16/15]] and [[17/16]] are considered minor second (ie. [[diatonic semitone]]), namely classical diatonic semitone and minor diatonic semitone respectively. However, a rename to ''charisma'' was proposed as part of an effort to make naming more standardised and for a number of reasons including potential confusion with [[diasem]] and the former nonconforming naming of [[horcrux]] in the 11- and 13-limit (which were formerly named "charisma" and "charismic", creating a potential false impression that the former was a comma, not a temperament, and that the latter was the temperament defined by tempering that comma in the corresponding prime limit); specifically, see [[Talk:256/255]] and [[Temperament naming #Contemporary rules]] for details.
 The rename took place as Starshine (from the [[XA Discord]] server) suggested (half-jokingly) that a chance had been missed to name it the ''charisma'' in December 2023, a name which [[User:Godtone|Godtone]] took favor to and championed which then caused awareness of nonconforming names of two [[horcrux]] temeraments. A revision to ''charsma'' (no-''i'' spelling) was proposed by Xenllium in January 2024 for disambiguation but this would cause inconsistency with the -ic/-ismic/-isma rule which is a reason that those same temperaments were already being proposed to be renamed.