Songs by Level

This page lists difficulty ratings and chart constants for all song charts in the game (excluding Tutorial and April Fools' charts). Default sorting of charts is by Difficulty, then by Chart Constant, then Version, and then alphabetically by name, but the sorting method can be changed by clicking the headings of each column (if viewing on desktop, sort by multiple fields by holding Shift when clicking secondary sort fields). For uses of chart constants, see Potential.

The methods used to determine chart constants are available below, after the chart list.
These methods are based on information from the Japanese Wiki.

## Songs

Past ⌧
Past ☐
Present ⌧
Present ☐
Future ⌧
Future ☐
Beyond ⌧
Beyond ☐

## Inferring Chart Constants

Chart constants can be inferred from World Mode plays by back-calculating from the steps gained.
This method was developed by robert\_cpp, and is based on the inverses of the formulas for steps gained in World Mode and Play Rating.
An online tool by YabaiYatsu is available here.
Spreadsheet alternatives are linked to below.

The method is as follows:

1. Select a Partner and note their STEP stat.
2. Note the minimum safe cutoff score corresponding to the chart level from the table below.
3. Play the chart in World Mode (Track Lost is allowed), making sure you exceed the above cutoff score.
4. Note the Score and Steps Gained.
5. Calculate the Score Modifier from the Score (see page for formula).
6. Calculate the Chart Constant using the formula:

# Chart Constant

(

Steps Gained
×

50
STEP Stat

−
2.5

2.45

)

2

−
Score Modifier

{\displaystyle \text{Chart Constant}=\left(\dfrac{\text{Steps Gained}\times\frac{50}{\text{STEP Stat}}-2.5}{2.45}\right)^2-\text{Score Modifier}}

Using a spreadsheet for the calculations is easier than doing them manually with a calculator. This method is also complicated by the presence of numerical errors, but should give an accurate estimate if the following tips are used:

* Choose a Partner with the highest available STEP stat (avoid Hikari (Fatalis) if you wish to probe multiple charts).
* When playing the chart in World Mode, aim for a score only slightly higher than the cutoff score from the table (no more than 0.5 to 1 million over).
* Try to activate map boosts (optional but increases precision). If boosts are used, replace Steps Gained with (Steps Gained)/(Map Boosts).

#### **Numerical Errors**

The displayed values for Base Steps, Steps Gained, Partner STEP, and Score are all rounded down from their actual internal values, meaning the displayed values generally underestimate the actual values. For this reason, the calculated Chart Constant will have an error margin. This margin can be greater than 0.1, and so these rounding errors need to be considered. Since the Score displayed in-game is typically accurate to 7 or 8 significant figures, versus the Base Steps, Steps Gained, and Partner STEP which are only accurate to 2 or 3, the error margin due to Score uncertainty is comparatively tiny, and in practice only the error margins of the displayed Steps Gained and Partner STEP need to be dealt with.

A quick lower and upper estimate for the Steps Gained and Partner STEP stat (assuming STEP > 10) can be obtained via

Steps Gained (Lower)

=
Steps Gained (Displayed)

Steps Gained (Upper)

=
Steps Gained (Displayed)
0.1

STEP Stat (Lower)

=
STEP Stat (Displayed)

STEP Stat (Upper)

=
STEP Stat (Displayed) + 1

.

{\displaystyle \begin{align}
\text{Steps Gained (Lower)} &= \text{Steps Gained (Displayed)} \\
\text{Steps Gained (Upper)} &= \text{Steps Gained (Displayed)} + 0.1 \\
\text{STEP Stat (Lower)} &= \text{STEP Stat (Displayed)} \\
\text{STEP Stat (Upper)} &= \text{STEP Stat (Displayed) + 1} \,. \end{align}}

These estimates can then be put into the following Chart Constant formulas to obtain an error margin for the Chart Constant:

Chart Constant (Lower)

=

(

Steps Gained (Lower)
×

50
STEP Stat (Upper)

−
2.5

2.45

)

2

−
Score Modifier

Chart Constant (Upper)

=

(

Steps Gained (Upper)
×

50
STEP Stat (Lower)

−
2.5

2.45

)

2

−
Score Modifier

.

{\displaystyle \begin{align}
\text{Chart Constant (Lower)} &= \left(\dfrac{\text{Steps Gained (Lower)}\times\frac{50}{\text{STEP Stat (Upper)}}-2.5}{2.45}\right)^2-\text{Score Modifier} \\
\text{Chart Constant (Upper)} &= \left(\dfrac{\text{Steps Gained (Upper)}\times\frac{50}{\text{STEP Stat (Lower)}}-2.5}{2.45}\right)^2-\text{Score Modifier} \,. \end{align}}

Explanations for why various tips reduce the error margin:

* High STEP stat means the STEP rounding error of up to +1 is smaller in comparison.
* Using map boosts to increase step progress means the Steps Gained rounding error of up to +0.1 is smaller in comparison.
* Achieving scores near the tabulated cutoff means the Play Rating will be close to 0, and the pre-STEP multiplier step progress will be close to the pity value of 2.5. The above Chart Constant formula is quadratic with respect to Steps Gained, where the parabola is flatter when pre-STEP multiplier steps are closer to 2.5. Since the parabola is flatter here, small errors in STEP and Steps Gained (x value) cause less uncertainty in the calculated Chart Constant output (y value).

Similar explanations (with plots) are given on the JP Wiki.

#### **Spreadsheets**

robert\_cpp's original spreadsheet is available here (does not allow grade EX scores), and an optimized version by Transendium is available here.

An extended version by GKWS is available here. Copies can be saved to your own Google Drive for personal use. Simply fill in the blanks in the 'Input' section and it will attempt to derive the Chart Constant at the 'Output'.

**Example:**

```
Chart: carmine:scythe [FTR]
  Score: 9,562,787 (AA)
  Base Steps: 10.1
  Steps Gained: 20.7
  STEP Stat: 102
  Base Steps (Lower): max(20.7/2.04, 10.1) = 10.147
  Base Steps (Upper): min((20.7+0.1)/2.04, 10.1+0.1) = 10.196
  Chart Constant (Lower): 9.524490036
  Chart Constant (Upper): 9.649682062

```

Since the only chart constant between the lower and upper bounds is 9.6, carmine:scythe [FTR] has a chart constant of **9.6**.

### **Fresh History Method**

*Developed by choka\_noah, deprecated since v3.0.0*

This method relies on the fact that Play Rating = Chart Constant when Score = 9,500,000.
It is advisable to first understand how Potential is calculated before understanding this method.

1. Create a new account.
2. Play the same chart 3 times in a row and try to score as close to 9,500,000 on each of them.
3. Multiply your Potential by 10 to obtain the Chart Constant of that chart.

**Explanation**

This method exploits the formula for calculating Potential, as detailed here.

* By playing the same chart 3 times in a row on a new account, we have 3 Play Ratings under Recent Entries, and 1 Play Rating under Best Entries.
* By scoring 9,500,000 on each play, we ensure that all 4 Play Ratings have the same value as the Chart Constant.

In this situation, the formula for calculating Potential becomes:

# Potential

4
×
Play Rating

40

=

Chart Constant
10

{\displaystyle \text{Potential}=\dfrac{4\times\text{Play Rating}}{40}=\dfrac{\text{Chart Constant}}{10}}

Hence, when we multiply the Potential by 10, this yields the Chart Constant.

**Example**

```
Chart: Dandelion [FTR]
Recent Entries
  Trial 1: 9,501,391
  Trial 2: 9,501,390
  Trial 3: 9,501,385
Best Entries
  Trial 1: 9,501,391
Potential
  Trial 1: 0.43 (+0.43)
  Trial 2: 0.64 (+0.21)
  Trial 3: 0.86 (+0.22)

```

Therefore, Dandelion [FTR] has a chart constant of **8.6**.

*Note: dropdead's Past chart has a very low note count of 44, so it is impossible to score close to 9,500,000.*

This method is simple to understand and perform, but is impractical since it requires creation of a new account for every chart.

Since v3.0.0, all repeated entries in the recent 10 entries will not stack with old entries but rather replace them, rendering this method useless.