Tairitsu (Tempest)

Tairitsu (Tempest) is a Partner in Arcaea and a story variant of Tairitsu. She is available through after obtaining the Black Fate Main Story pack and completing the Tempestissimo Anomaly on any difficulty.
==Character==
===Name===
Main article: Tairitsu § Name
===Appearance===
Rather than having crows by her, Tairitsu (Tempest) sports some blue butterflies (most likely Blue Morpho butterflies) with one carrying a blue lamp. She also has a long black ribbon in addition to her umbrella, and her hair is now in two sharp buns resembling a tornado (tempest). There is now a blue-black crystal following her around, similar to the obsidian-like glass that follows Hikari (Fracture). Her eye colours are now neon-blue and compared to her previous appearances, her expression changes from a sorrowful appearance to a threatening glare. 
She wears a thigh-length black dress and the dress is thigh length with ruffles at the hem. She also wears an earring on her left ear that has a blue rose and a black cross with a blade at the bottom. The black collar is laced to the top of her dress and her sleeves go from the bottom of her shoulders to her hands. She also wears black gloves. Her black socks go at mid-thigh and down her black heels with a blue rose on top. She wears a blue bow on her bang with a gold spade on the top of the bow. Long black ribbons follow her tied to her back.
===Personality===
Tairitsu is now much more aggressive towards Hikari. Rather than complying with Hikari's attempts to cooperate, she is intent on murdering Hikari due to the prediction in the memory. She is also described to take sadistic glee in trying to brutalize Hikari as hard as she could, both physically and psychologically.
==Story==
Main article: Tairitsu § Story
Tairitsu is depicted in her Tempest form in illustrations from the Black Fate and Final Verdict Main Stories.
==Gameplay==
===Stats by level===
All STEP stat values listed are base values.
Tairitsu (Tempest)'s base STEP receives a bonus of +1 for every 10 levels possessed by every unlocked partner, including herself.
Therefore, bringing her to Level 10/20 will grant her a bonus of +1/+2 STEP in addition to her base value, regardless of any other partners' levels.
On reaching this maximum, her STEP stat will be displayed in red, indicating that the cap has been reached.
=== Skill ===
Tairitsu (Tempest) uses the unique Tempest Gauge. Like other HARD Gauges, the Tempest Gauge starts at 100, and causes immediate Track Lost if it reaches 0, but is otherwise significantly different in its mechanics. Unlike other HARD Gauges,
*Recollection Rate (RR) changes smoothly at a continuous rate, rather than an instantaneous fixed change with each note judgement.
*PURE/FAR and LOST notes affect the Gauge by temporarily changing the rate at which RR increases/decreases. LOST notes make RR drain faster, while PURE/FAR notes slow the drain and can reverse it so that RR increases instead.
* RR will tend to slowly decrease at a continuous passive rate.
** The effect of individual note judgements is temporary, and the rate of RR change will settle towards this slow base drain when no notes are present.
** The total cumulative RR gain or loss caused by each PURE/FAR or LOST note is roughly twice that for the default HARD Gauge.
* The passive RR drain starts immediately after beginning a chart, even before the first note.
==== Detailed description ====
With the Tempest Gauge, the RR (Recollection Rate) will decrease or increase passively at a continuous rate, rather than suddenly increasing/decreasing with each note.
When RR is less than 100, the rate V(t) at which RR changes is given by
V(t) = - NL(t) + \sum_{i=1}^{\text{Total Notes}} E_i (t - t_i)
where
* t is the time elapsed (in seconds) from when the chart begins to the current time in the chart,
* NL(t) is the Natural Loss, which is a constant base rate at which RR decreases,
* ti is the time at which the ith note judgement is registered, and
* Ei(Δt) describes the temporary effect that the ith note judgement has on V at some time Δt after the note judgement has been registered.
Natural Loss is calculated as
NL(t) = \begin{cases}
\text{Recollection Factor}\times \frac{\text{Total Notes}}{\text{Chart Length}+0.5} & \text{if }t < \text{Chart Length} \\
0 & \text{if }t\geq\text{Chart Length} \end{cases}
where
* Chart Length is the time elapsed (in seconds) from when the chart begins to when the final note or trace passes the judgement line;
* Recollection Factor (RF) is the gain in total RR when a PURE note is hit in a normal Gauge.
Ei(Δt) can take one of three forms, depending on whether the ith note judgement was a PURE/FAR/LOST. In every case, it takes the form of an exponential decay function, so that the effect of Ei is temporary and V(t) is generally pulled towards the Natural Loss rate.
A PURE/FAR note judgement will immediately increase V(t), while a LOST judgement will decrease it.
Specifically,
E_i(\Delta t) = \begin{cases}
0 & \text{if }\Delta t < 0\text{, i.e. note judgement hasn't occurred yet} \\
+ 2\ln(2) \cdot \text{RF} \cdot 2^{-\Delta t} & \text{if judgement is PURE} \\
+ \ln(2) \cdot \text{RF} \cdot 2^{-\Delta t} & \text{if judgement is FAR} \\
- 9\ln(2) \cdot 2^{-0.5 \Delta t} & \text{if judgement is LOST.} \end{cases}
Note that like the default HARD Gauge, the gain for PURE/FAR notes depends on RF, with FAR notes being half as beneficial as PURE notes, while LOST notes incur a harsher fixed penalty. The penalty for a LOST note also lasts longer due to the slower decay.
Since the Rate cannot increase past 100, the rate at which RR actually increases or decreases is given by:
\begin{align}
\frac{\text{d}\text{RR}}{\text{d}t} &= \text{Rate of change of RR at time }t \\ 
&= \begin{cases}
0 & \text{if }V(t) > 0\text{ and RR} = 100 \\
V(t) & \text{otherwise} \end{cases}
\end{align}
In the case where RR is 100 while V(t) is positive, RR will remain at 100, and start dropping again once V(t) drops back into negative values.
After the final chart object has fully passed the judgement line, Natural Loss is set to 0, and the play will continue for roughly 7 seconds before ending. During this time, the RR may continue to increase or decrease due to recent note judgements, and Track Lost can still occur.
Integrating under the area of Ei(Δt) gives a finite size for the total effect that the ith note has on the value of RR (this calculation is more of a heuristic since it won't apply if RR reaches 100 at any point). This total effect size is equal to
\int_0^\infty E_i(\Delta t) \text{d} \Delta t = \begin{cases}
+ 2\cdot \text{RF} & \text{if judgement is PURE} \\
+ \text{RF} & \text{if judgement is FAR} \\
- 18 & \text{if judgement is LOST.} \end{cases}
The Tempest Gauge therefore effectively causes double the RR gain/loss per note compared to the regular HARD Gauge, but distributes this gain/loss over a longer time period instead of making it instantaneous. This riskier double effect is in addition to the constant Natural Loss RR drain.
===Notes===
An efficient strategy to boost her STEP stat is to use Ether Drops on low level partners. One Ether Drop is sufficient to raise a Level 1 partner to Level 5. This immediately adds 0.4 to Tairitsu (Tempest)'s STEP stat per partner. She is the perfect partner to have when min-maxing for World Mode.
Due to the nature of Tairitsu (Tempest)'s skill, missing consecutive notes is even more dangerous than other HARD partners due to the rapid Rate drain.
==Artwork==
Story vs tempest.jpg|Story Entry VS-7
Tempestissimo.jpg|Tempestissimo jacket art
File:F-2cg.jpg|Story Entry F-2
File:F-5cg.jpg|Story Entry F-5
Defection.jpg|Defection jacket art
Infinite Strife.jpg|Infinite Strife, jacket art
Pentiment.jpg|Pentiment jacket art
Arcana Eden.jpg|Arcana Eden jacket art
File:F-6 (Cutscene).jpg|Story Entry F-6
V4 countdown 1 day.jpeg|Image by すずなし (Suzunashi) for the version 4.0 update
Switch v2 release.jpeg|Image by がわこ (Gawako) for the Switch version 2.0 update
Partner Tairitsu Tempest large.png|Full body artwork
Temp tai angry.png|Annoyed expression from Tempestissimo anomaly
Temp tai twisted.png|Smiling expression from Tempestissimo anomaly
Partner Tairitsu Tempest.png|Icon in the partner select screen