I have created a tool for Sibelius users to help with creating justly-tuned playback. This should be helpful if you’re interested in experimenting with just intonation tuning, and want computer playback to reflect the proper tunings. In order for this spreadsheet to be helpful, you probably need to have a basic understanding of what just intonation is: how in just-intonation-speak, intervals are usually described as fractions rather than as stepwise counts, as when counting adjacent keys on a keyboard. If this is new to you, I recommend you check out Wikipedia or Kyle Gann’s Just Intonation Explained page. Both are excellent resources. Anyway, the spreadsheet:

Ratio To MIDI Pitch Bend Calculator

JI Numerator and JI Denominator represent the upper and lower parts of a fraction which describes a relative pitch. For example, if you want the info on a perfect fifth, the JI Numerator would be 3 and the JI Denominator would be 2.

12ET Half Steps tells the algorithm how many half-steps to subtract from the pitch bend. So, a 3:2 is bent by 1.955 cents instead of 701.955 cents by subtracting 7 half-steps.

~B(*x*,y) and ~B(x,*y*) represent the scripting that you would add to Sibelius to affect the pitch bend. The number under ~B(*x*,y) is the *x*, and the number under ~B(x,*y*) is the *y*. Thus, if under ~B(*x*,y) you see 80 and under ~B(x,*y*) you see 64, the script you want is ~B(80,64). You then go to Sibelius and enter the text attached to the note you want bent. Sibelius will then bend every subsequent pitch on the same stave by the same amount until you tell it to change the pitch bend again. And, capitalization counts.

The rest of the spreadsheet really is just parts of the calculation functions.

To test and see if this spreadsheet works with your program, test a major third. On one stave, input a held C and on another stave, input a held E a major third above where the C is on the other stave. Above the E, enter in the text

~B(79,59)

Play it back. If it sounds skunky, something is wrong, and you may need to tweak the function in the ‘Cents to Pitch Bend Units’ column. Ask me if you need to and can’t figure it out yourself. If it sounds clear, vibrant, and resonant, it’s working as intended.

### Like this:

Like Loading...

Hi Andrew,

Thanks so much for this! I’m a Sibelius user (8.0), and I’ve been searching for a way to adjust the playback tuning of individual pitches based on just intonation ratios. This is exactly what I needed, and it still works in version 8.0: you just need to omit the parentheses. I’m wondering how to calculate the ~B(x,y) values for other JI ratios that are not in your spreadsheet, as I need several others, such as 256/135, 105/64, and so on. If you could let me know how to calculate the pitch bend values from the ratios, I would be extremely grateful!

You should be able to either replace the numerator and denominator in an existing row, or copy and paste a row and then edit the newly pasted row. Most spreadsheet software, include in my experience Open Office, will automatically update references in formulas in paste operations.

Thanks! Adding a new row below the list didn’t work, but editing an existing row does.