256/255: Difference between revisions

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=== Charic ===

[[Subgroup]]: 2.3.5.17

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 }}

~~{{mapping|legend=1| 1 1 2 5 | 0 1 0 -1 | 0 0 1 -1 }}~~

[[CTE]] generators: (2/1,) 3/2 = 702.647, 5/4 = 387.798

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

By also tempering the [[semitonisma~~]],~~ [[~~256~~/~~255~~]], an efficient temperament known as [[Srutal archagall]] is achieved, which is equivalently described as [[charic]] [[semitonic]].

By also tempering the semitonisma ([[289/288]]), an efficient temperament known as [[Srutal archagall]] is achieved, which is equivalently described as [[charic]] [[semitonic]].

This is because of a general fact of [[S-expression]]s; in this case it manifests as that: {[[diaschisma|S16<sup>2</sup> × S17]] , [[24576/24565|S16/S17]]} = {[[256/255|S16]], [[289/288|S17]]}

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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. 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 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 the [[Talk:256/255|talk page]] 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 13: / Line 13: @@
 === Charic ===
 [[Subgroup]]: 2.3.5.17
+{{Mapping|legend=1| 1 1 2 5 | 0 1 0 -1 | 0 0 1 -1 }}
 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 }}
 [[CTE]] generators: (2/1,) 3/2 = 702.647, 5/4 = 387.798
@@ Line 30: / Line 30: @@
 === [[Srutal archagall]] ===
-By also tempering the [[semitonisma]], [[256/255]], an efficient temperament known as [[Srutal archagall]] is achieved, which is equivalently described as [[charic]] [[semitonic]].
+By also tempering the semitonisma ([[289/288]]), an efficient temperament known as [[Srutal archagall]] is achieved, which is equivalently described as [[charic]] [[semitonic]].
 This is because of a general fact of [[S-expression]]s; in this case it manifests as that: {[[diaschisma|S16<sup>2</sup> × S17]] , [[24576/24565|S16/S17]]} = {[[256/255|S16]], [[289/288|S17]]}
@@ 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. 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 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 the [[Talk:256/255|talk page]] 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.