Add music intervals

[bfinn]

I suggest you add units for musical intervals, used in music itself, scientific instruments such as electronic tuning meters, acoustics, psychoacoustics, etc. As your system includes bels and mentions the possibility of defining phons and sones, musical intervals would seem a natural addition.

Musical intervals are unitless logarithmic ratios of pitch frequencies. A useful set would be the following four:

octave = base 2 logarithm of frequency ratio; e.g. f1/f2 = 2 means the interval between f1 and f2 is 1 octave

cent = 1/1200 octave. So e.g. 600 cents denotes a frequency ratio of 2^{0.5 = 1.414...}

semitone (equal-tempered) or half step (equal-tempered) = 100 cents

tone (equal-tempered) or whole step (equal-tempered) = 200 cents

Semitone/tone are British terms, half/whole step are equivalent US terms. Note that like calendar months, these particular units can vary in size depending on the tuning system ('temperament') in use. However, nowadays 'equal temperament' is almost always used, in which semitones are of a fixed size of 100 cents. (They are hence rather like mean calendar months.) Cents and octaves are always of fixed size regardless of the tuning system.

The cent is a rather technical unit used in tuning rather than in everyday music. Semitone and, to a lesser extent, tone and octave are used in scientific as well as musical contexts. There are various other intervals used in musical rather than scientific contexts which are multiples of a semitone (e.g. minor third, fourth, tritone), but probably not worth including.

[Gunther Schadow]

It is indeed thinkable to add this.

Would the requestor please make a proposal that is ready to cut and paste into the specification? I.e., please define

1. each unit symbol
2. print name
3. formal definition
4. conversion function (logarithm, whatever is needed, if not already there)
5. any commentary you want to give
6. references to any scientific literature establishing the use of such units

I suspect it would be very difficult to do anything but equal temperament.

We do not have expertise in this field and our time to research this is limited. If the requester could provide this material, chances for this to go into the next revision are very good.