INHARMONIC Calculator


(by Alexander Galembo)
This tool calculates interval/frequency relationships in:
1) Scale with pure octaves (just enter the inharmonicity coefficient B=0)
2) Scale with octaves stretched (compressed) by string-like inharmonicity (based on the octave ratio between the fundamental and the first overtone)
Another option is calculating the frequency and beat rates in equal temperament with arbitrary octave ratio.

This tool deals with the string-like inharmonicity only, defined by the classical stretching formula:

fn = f0n(1+Bn2)0.5 .....(1)
where fn is the frequency of the n-th stretched partial, f0 is the fundamental frequency of the ideal string, and B is the inharmonicity coefficient.

There exists also a simplified formula:

fn = f0n(1+Jn2) .....(2)
This means, approximately, that
J=0.5*B

Formula (2) works well for low order partials, but gives significant discrepancy with formula (1) for larger B (or J) and n values. As example, for realistic B=0.0002 the discrepancy is about 6 cents at n = 30 and about 100 cents (a semitone) at n = 70.

It is important to know that in all our calculations, the B value and formula (1) is used. Therefore, if you operate by J value, don't forget at least to double it before entering as an inharmonicity coefficient value.

This program explores an equal temperatment and allows to convert Hertzs to cents and back for normal, stretched or compressed octaves in accordance with the entered zero, positive or negative value of the inharmonicity coefficient, respectively. The case with negative inharmonicity provides perhaps no practical interest for the most piano technicians, but it might interest scientists and electronic music experts.

Now CLICK on what you need to calculate:

1. Interval (semitones, cents, octaves) between two entered frequencies (Hz)

2. Frequency ratio corresponding to the entered numbers of semitones and cents

3. Sum (Hz) of the entered frequency (Hz) and interval (semitones and cents).

4. Frequency of an inharmonic partial

5. Inharmonicity between two known partials

6. Your own equal temperament - frequencies and beat rates

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