Table:
0
A
B
C
D
E
F
G
1
interval name
size (steps)
size (cents)
just ratio
just (cents)
error
audio
2
perfect fifth
9
720
3:2
701.96
+18.04
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3
septimal tritone
7
560
7:5
582.51
−22.51
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4
11:8 wide fourth
7
560
11:8
551.32
+8.68
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5
15:11 wide fourth
7
560
15:11
536.95
+23.05
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6
perfect fourth
6
480
4:3
498.04
−18.04
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7
septimal major third
5
400
9:7
435.08
−35.08
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8
undecimal major third
5
400
14:11
417.51
−17.51
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9
major third
5
400
5:4
386.31
+13.69
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10
minor third
4
320
6:5
315.64
+4.36
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11
septimal minor third
3
240
7:6
266.87
−26.87
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12
septimal whole tone
3
240
8:7
231.17
+8.83
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13
major tone
3
240
9:8
203.91
+36.09
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14
minor tone
2
160
10:9
182.40
−22.40
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15
greater undecimal neutral second
2
160
11:10
165.00
−5.00
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16
lesser undecimal neutral second
2
160
12:11
150.63
+9.36
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17
just diatonic semitone
1
80
16:15
111.73
−31.73
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18
septimal chromatic semitone
1
80
21:20
84.46
−4.47
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19
just chromatic semitone
1
80
25:24
70.67
+9.33
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Questions and formulas:
Question: What is the value of the size (steps) that has just ratio 10:9 and a size (cents) more than 160
Formula: SUM(FILTER(B1, (D1="10:9")*(C1>160)))
Formula2: SUM(FILTER(B2:B19, (D2:D19="10:9")*(C2:C19>160)))
Level: easy
Question: what is the value of the audio with a just ratio 21:20
Formula: UNIQUE(CHOOSECOLS(FILTER(A1:G1,D1="21:20"),7))
Formula2: UNIQUE(CHOOSECOLS(FILTER(A2:G19,D2:D19="21:20"),7))
Level: medium
Question: What is the error that has a size (steps) more than 5 and a just (cents) value 536.95
Formula: LET(query1,SUMMARIZE(F1,SUMX(B1),SUMX(E1)),FILTER(query1,(CHOOSECOLS(query1,2)>5)*(CHOOSECOLS(query1,3)=536.95)))
Formula2: LET(query1,SUMMARIZE(F2:F19,SUMX(B2:B19),SUMX(E2:E19)),FILTER(query1,(CHOOSECOLS(query1,2)>5)*(CHOOSECOLS(query1,3)=536.95)))
Level: hard
Question: What is the average size (cents) with an interval of major third and size (steps) more than 5
Formula: AVERAGE(FILTER(C1, (A1="major third")*(B1>5)))
Formula2: AVERAGE(FILTER(C2:C19, (A2:A19="major third")*(B2:B19>5)))
Level: easy