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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Questions and formulas:
Question: If the just ratio is 11:8 and the cents size is 560, what is the interval name?
Formula: LET(query1,LET(query1,FILTER(A1:G1,D1="11:8"),SUMMARIZE(CHOOSECOLS(query1,1),SUMX(CHOOSECOLS(query1,3)))),FILTER(query1,CHOOSECOLS(query1,2)=560))
Formula2: LET(query1,LET(query1,FILTER(A2:G18,D2:D18="11:8"),SUMMARIZE(CHOOSECOLS(query1,1),SUMX(CHOOSECOLS(query1,3)))),FILTER(query1,CHOOSECOLS(query1,2)=560))
Level: hard
Question: If the just cents is 84.46, what is the just ratio?
Formula: LET(query1,SUMMARIZE(D1,SUMX(E1)),FILTER(query1,CHOOSECOLS(query1,2)=84.46))
Formula2: LET(query1,SUMMARIZE(D2:D18,SUMX(E2:E18)),FILTER(query1,CHOOSECOLS(query1,2)=84.46))
Level: hard
Question: If the just cents is 701.96, what is the interval name?
Formula: LET(query1,SUMMARIZE(A1,SUMX(E1)),FILTER(query1,CHOOSECOLS(query1,2)=701.96))
Formula2: LET(query1,SUMMARIZE(A2:A18,SUMX(E2:E18)),FILTER(query1,CHOOSECOLS(query1,2)=701.96))
Level: hard