E q u a l - T e m p e r e d     C a l c u l a t o r
For a standard chromatic scale or subset thereof, the number of tones per octave is 12. More info on this. You can use more than one sample bar for greater accuracy. More info on this. There's no need to indicate length units (inches or cm). If you don't intend to cut a sample bar but just want to calculate the relative bar lengths, enter a 1 for your sample bar length.. More info on this.	Frequency Ratios Bar Lengths Number of tones per octave Sample Bar Length Number of steps to Calculate up the scale Number of steps to Calculate down the scale

J u s t - I n t o n a t i o n   C a l c u l a t o r
Enter the frequency ratios on this side of the calculator => More info on inputting ratios For example, here is 1 octave of a standard major scale: 1/1 9/8 5/4 4/3 3/2 5/3 15/8	Frequency Ratios Bar Lengths / / / / / / / Add bars to this calculator Number of bars for your instrument: (This will re-load this page with more entry fields in this calculator)	<= Enter your sample bar length(s) on this side. You can enter just one sample bar length, or more than one for greater accuracy. More info on sample bars. The sample bar(s) can be tuned to any pitch in your chosen the scale, and the length(s) entered opposite the appropriate ratios. There's no need to indicate units (inches or centimeters). But do remember to be consistent about what units you use. If you don't intend to cut a sample bar but just want to calculate the relative lengths of the bars, enter a 1 opposite one of the ratios (typically the firsts, or longest bar). More info on this.

This software will only work if certain conditions are met. These caveats are noted briefly here and discussed in more detail in the user notes. The bars must be uniform in shape over their full length -- e.g., uniformly cylindrical, or uniformly rectangular in cross section. The formula won't work, for example, for marimba bars with scallops underneath. All the bars must have the same cross-sectional shape and size as the sample bar. You can't for example, use 1" tubing for the sample bar and then apply the resulting calculation to 3/4" tubing. If you intend to use bars or tubes of several thicknesses or diameters, you must cut a sample for each size and do separate calculations for each. If the material is inconsistent - as with, say, wood which has some natural variance in rigidity from bar to bar - then the formula will be inaccurate to the degree of the variance. Tip: For the most accurate results, cut your bars a bit longer than the softwares calculated lengths and then tune them up to pitch (by shortening them) by ear or with an electronic tuner. With wooden bars, due to the inconsistencies of the material, this this approach is recommended. With metal bars manufactured to close tolerances, it may not be necessary. These considerations may make it sound like this formula won't be very useful, because it only works in limited circumstances, but I've actually found plenty of occasions to use it and I expect you will too.