256/255: Difference between revisions

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{{Infobox Interval

| Name = septendecimal kleisma, ~~<br>char(i)sma, <br>diasemisma, <br>~~255th subharmonic

| Name = charisma, charic comma, septendecimal kleisma, octave-reduced 255th subharmonic

| Color name = 17ug1, sugu 1sn, ~~<br>~~Sugu comma

| Color name = 17ug1, sugu 1sn, Sugu comma

| Comma = yes

}}

'''256/255''', the '''~~septendecimal kleisma~~''', '''~~char(i)sma''', '''diasemisma~~''' 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]] (classical diatonic semitone) and [[17/16]] (large septendecimal semitone, ~~also called as ''minor diatonic 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 '''charisma''', '''charic comma''' or '''septendecimal kleisma''' 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), the difference between [[128/85]] (the archagall fifth) and [[3/2]] (the just perfect fifth), and the amount by which a stack consisting of [[15/8]] and 17/16 falls short of an [[octave]]. It is a [[Mersenne comma]].

By tempering it out is defined the ~~'''char(i)smic temperament''' (~~full 17-limit rank-6~~) or~~ '''~~charic~~ temperament''' (2.3.5.17 subgroup rank-3), which enables the [[~~diasemismic　chords|char(i)smic~~ chords]].

== Temperaments ==

By tempering it out is defined the full 17-limit rank-6 '''charismic temperament''' or 2.3.5.17 subgroup rank-3 '''charic temperament''', which enables the [[charismic chords]].

== ~~Etymology~~ ==

=== Charic ===

~~The name ''diasemisma'' was named by~~ [[~~User:Xenllium|Xenllium~~]] ~~in May 2023~~. ~~It is a contraction of ''diatonic semitone'' into a single word; it is unrelated to the [[diasem]] scale structure~~. ~~However, ''septendecimal kleisma'' and ''255th subharmonic'' were attested much earlier~~.

[[Subgroup]]: 2.3.5.17

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. A revision to ''charsma'' (no-''i'' spelling) was proposed by Xenllium in January 2024 for disambiguation ~~(formerly ''charisma'' and ''charismic'' were used for [[Magic family #Horcrux|horcrux extensions]]); the only issue taken with~~ this ~~is its~~ inconsistency with the -ic -ismic -isma rule ~~and~~ that ~~the~~ temperaments were already ~~suggested~~ to be renamed in the proposal by Godtone for this and other reasons. The "char" in the name "charisma" 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]].

: sval mapping generators: ~2, ~3, ~5

[[Optimal tuning]]s:

* [[CTE]]: ~2 = 1200.000, 3/2 = 702.647, 5/4 = 387.798

* [[CWE]]: ~2 = 1200.000, 3/2 = 703.015, 5/4 = 388.071

{{Optimal ET sequence|legend=1| 5, 7, 9, 10, 12, 22, 31, 34, 65, 87, 99, 343cgg, 442cgg, 541bcggg, 640bcgggg }}

=== Charismic ===

[[Subgroup]]: 2.3.5.7.11.13.17

[[Mapping]]:

{| class="right-all"

|-

| [⟨ || 1 || 0 || 0 || 0 || 0 || 0 || 8 || ],

|-

| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || -1 || ],

|-

| ⟨ || 0 || 0 || 1 || 0 || 0 || 0 || -1 || ],

|-

| ⟨ || 0 || 0 || 0 || 1 || 0 || 0 || 0 || ],

|-

| ⟨ || 0 || 0 || 0 || 0 || 1 || 0 || 0 || ],

|-

| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ]]

|}

: mapping generators: ~2, ~3, ~5, ~7, ~11, ~13

[[Optimal tuning]]s:

* [[CTE]]: ~2 = 1200.000, 3/2 = 702.647, 5/4 = 387.798, ~7/4, ~11/8, ~13/8

* [[CWE]]: ~2 = 1200.000, 3/2 = 703.015, 5/4 = 388.071, ~7/4, ~11/8, ~13/8

{{Optimal ET sequence|legend=1| 15, 19, 22, 31, 41, 46, 58, 77, 80, 87, 99ef, 111, 121, 152fg, 167, 198g, 256cfg, 319fgg, 377cdefgg, 507cdeefggg, 705bccdeeffggg }}

=== Srutal archagall ===

By also tempering out the semitonisma ([[289/288]] = S17), an efficient but lower accuracy temperament known as [[srutal archagall]] is achieved, which has [[17/15]]~[[9/8]] and therefore makes the minor third reached by the circle of fifths equal to ~[[20/17]].

=== Char ===

The charic temperament has an immediate 2.3.5.7.17 subgroup extension, the [[Marvel family #Char|char]] temperament. It tempers out both [[225/224|S15]] and S16, as well as their sum, [[120/119]], which induces the equivalences [[17/15]]~[[8/7]] and [[20/17]]~[[7/6]].

== Etymology and history ==

Before 2023, this interval was known as ''septendecimal kleisma'' or ''255th subharmonic''.

The "char" in the name ''charisma'' (or ''charic 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 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.

== See also ==

* [[Small comma]]

* [[List of superparticular intervals]]

* [[255/128]] – its [[octave complement]]

* [[85/64]] – its [[fourth complement]]

[[Category:~~Charsmic~~]]

[[Category:Charismic]]

[[Category:Commas named after their interval size]]

[[Category:Commas referencing a famous use of a number]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Name = septendecimal kleisma, <br>char(i)sma, <br>diasemisma, <br>255th subharmonic
+| Name = charisma, charic comma, septendecimal kleisma, octave-reduced 255th subharmonic
-| Color name = 17ug1, sugu 1sn, <br>Sugu comma
+| Color name = 17ug1, sugu 1sn, Sugu comma
 | Comma = yes
 }}
+{{Redirect-distinguish|Charisma|Horcrux}}
-'''256/255''', the '''septendecimal kleisma''', '''char(i)sma''', '''diasemisma''' 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]] (classical diatonic semitone) and [[17/16]] (large septendecimal semitone, also called as ''minor diatonic 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 '''charisma''', '''charic comma''' or '''septendecimal kleisma''' 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), the difference between [[128/85]] (the archagall fifth) and [[3/2]] (the just perfect fifth), and the amount by which a stack consisting of [[15/8]] and 17/16 falls short of an [[octave]]. It is a [[Mersenne comma]].
-By tempering it out is defined the '''char(i)smic temperament''' (full 17-limit rank-6) or '''charic temperament''' (2.3.5.17 subgroup rank-3), which enables the [[diasemismic　chords|char(i)smic chords]].
+== Temperaments ==
+By tempering it out is defined the full 17-limit rank-6 '''charismic temperament''' or 2.3.5.17 subgroup rank-3 '''charic temperament''', which enables the [[charismic chords]].
-== Etymology ==
+=== Charic ===
-The name ''diasemisma'' was named by [[User:Xenllium|Xenllium]] in May 2023. It is a contraction of ''diatonic semitone'' into a single word; it is unrelated to the [[diasem]] scale structure. However, ''septendecimal kleisma'' and ''255th subharmonic'' were attested much earlier.
+[[Subgroup]]: 2.3.5.17
-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. A revision to ''charsma'' (no-''i'' spelling) was proposed by Xenllium in January 2024 for disambiguation (formerly ''charisma'' and ''charismic'' were used for [[Magic family #Horcrux|horcrux extensions]]); the only issue taken with this is its inconsistency with the -ic -ismic -isma rule and that the temperaments were already suggested to be renamed in the proposal by Godtone for this and other reasons. The "char" in the name "charisma" 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]].
+{{Mapping|legend=2| 1 0 0 8 | 0 1 0 -1 | 0 0 1 -1 }}
+: sval mapping generators: ~2, ~3, ~5
+[[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1200.000, 3/2 = 702.647, 5/4 = 387.798
+* [[CWE]]: ~2 = 1200.000, 3/2 = 703.015, 5/4 = 388.071
+{{Optimal ET sequence|legend=1| 5, 7, 9, 10, 12, 22, 31, 34, 65, 87, 99, 343cgg, 442cgg, 541bcggg, 640bcgggg }}
+=== Charismic ===
+[[Subgroup]]: 2.3.5.7.11.13.17
+[[Mapping]]:
+{| class="right-all"
+|-
+| [⟨ || 1 || 0 || 0 || 0 || 0 || 0 || 8 || ],
+|-
+| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || -1 || ],
+|-
+| ⟨ || 0 || 0 || 1 || 0 || 0 || 0 || -1 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 1 || 0 || 0 || 0 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 0 || 1 || 0 || 0 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ]]
+|}
+: mapping generators: ~2, ~3, ~5, ~7, ~11, ~13
+[[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1200.000, 3/2 = 702.647, 5/4 = 387.798, ~7/4, ~11/8, ~13/8
+* [[CWE]]: ~2 = 1200.000, 3/2 = 703.015, 5/4 = 388.071, ~7/4, ~11/8, ~13/8
+{{Optimal ET sequence|legend=1| 15, 19, 22, 31, 41, 46, 58, 77, 80, 87, 99ef, 111, 121, 152fg, 167, 198g, 256cfg, 319fgg, 377cdefgg, 507cdeefggg, 705bccdeeffggg }}
+=== Srutal archagall ===
+By also tempering out the semitonisma ([[289/288]] = S17), an efficient but lower accuracy temperament known as [[srutal archagall]] is achieved, which has [[17/15]]~[[9/8]] and therefore makes the minor third reached by the circle of fifths equal to ~[[20/17]].
+=== Char ===
+The charic temperament has an immediate 2.3.5.7.17 subgroup extension, the [[Marvel family #Char|char]] temperament. It tempers out both [[225/224|S15]] and S16, as well as their sum, [[120/119]], which induces the equivalences [[17/15]]~[[8/7]] and [[20/17]]~[[7/6]].
+== Etymology and history ==
+Before 2023, this interval was known as ''septendecimal kleisma'' or ''255th subharmonic''.
+The "char" in the name ''charisma'' (or ''charic 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 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.
 == See also ==
 * [[Small comma]]
 * [[List of superparticular intervals]]
+* [[255/128]] – its [[octave complement]]
+* [[85/64]] – its [[fourth complement]]
-[[Category:Charsmic]]
+[[Category:Charismic]]
+[[Category:Commas named after their interval size]]
+[[Category:Commas referencing a famous use of a number]]