UPDATE
Previous Ranking System: Lowest Common Multiple of Ratio's Numbers
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This ranking system breaks down for intervals beyond the Octave such as the Major Seventeenth. Therefore, I have devised a new ranking system that overcomes this problem.
Frequency Ratios
Semitones
|
Note |
Interval |
Ratio |
0 |
C |
Unison |
1:1 |
1 |
C# |
Minor Second |
16:15 |
2 |
D |
Major Second |
9:8 |
3 |
D# |
Minor Third |
6:5 |
4 |
E |
Major Third |
5:4 |
5 |
F |
Perfect Fourth |
4:3 |
6 |
F# |
Tritone |
25:18 |
7 |
G |
Perfect Fifth |
3:2 |
8 |
G# |
Minor Sixth |
8:5 |
9 |
A |
Major Sixth |
5:3 |
10 |
A# |
Minor Seventh |
9:5 |
11 |
B |
Major Seventh |
15:8 |
12 |
C |
Octave |
2:1 |
Source: https://fundamentals-of-piano-practice.readthedocs.io/en/latest/chapter2/CH2.2.html
New Ranking System: Lowest 1st Number then Lowest 2nd Number of Ratio
Rank |
Interval |
Ratio |
Number 1 |
Number 2 |
1 |
Octave |
2/1 |
2 |
1 |
2 |
Perfect Twelfth |
3/1 |
3 |
1 |
3 |
Perfect Fifth |
3/2 |
3 |
2 |
4 |
Perfect Fourth |
4/3 |
4 |
3 |
5 |
Major Seventeenth |
5/1 |
5 |
1 |
6 |
Major Sixth |
5/3 |
5 |
3 |
7 |
Major Third |
5/4 |
5 |
4 |
8 |
Minor Third |
6/5 |
6 |
5 |
9 |
Minor Sixth |
8/5 |
8 |
5 |
10 |
Minor Seventh |
9/5 |
9 |
5 |
11 |
Major Second |
9/8 |
9 |
8 |
12 |
Major Seventh |
15/8 |
15 |
8 |
13 |
Minor Second |
16/15 |
16 |
15 |
14 |
Tritone |
25/18 |
25 |
18 |
This new system is compatible with the order in which harmonics coincide.
Examples
1. 2nd harmonic of Unison coincides with 1st harmonic of Octave.
2. 3rd harmonic of Unison coincides with 1st harmonic of Perfect Twelfth.
3. 3rd harmonic of Unison coincides with 2nd harmonic of Perfect Fifth.
4. 4th harmonic of Unison coincides with 3rd harmonic of Perfect Fourth.
5. 5th harmonic of Unison coincides with 1st harmonic of Major Seventeenth.
6. 5th harmonic of Unison coincides with 3rd harmonic of Major Sixth.
7. 5th harmonic of Unison coincides with 4th harmonic of Major Third.
8. 6th harmonic of Unison coincides with 5th harmonic of Minor Third.
9. 8th harmonic of Unison coincides with 5th harmonic of Minor Sixth.
10. 9th harmonic of Unison coincides with 5th harmonic of Minor Seventh.
11. 9th harmonic of Unison coincides with 8th harmonic of Major Second.
12. 15th harmonic of Unison coincides with 8th harmonic of Major Seventh.
13. 16th harmonic of Unison coincides with 15th harmonic of Minor Second.
14. 25th harmonic of Unison coincides with 18th harmonic of Tritone.
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Roshan Kakiya
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