## Latest News

Jan 26, 2011 | : | Version 1.7.7 — Universal Binary. |
---|---|---|

Jul 22, 2011 | : | Runs on OS X Lion. |

*IntervalCalc ^{TM}*
is a calculator which is arranged so that it is very useful for working
with musical tuning systems. It

**converts cents to ratios and back**— yes. And so can any other calculator or slide rule that can handle logarithms. It can also

**describe those ratios using terms in english**. That’s pretty neat too, sure.

But what makes IntervalCalc^{TM}
*extra special* is the way it is set up. Every field you can
type in can **handle not just regular numbers, but mathematical
expressions as well**. By *mathematical expressions,* I
mean things like `7*13` and `(7:5)^(1/13)` (seven times thirteen
and seven-fifths raised to the one-thirteenth power.) And if
that’s not cool enough, **the individual numbers within your
expression can be incremented and decremented very quickly by
using the up and down arrows**. A subtle change from the usual
method of entering numbers, but what a world of difference it
makes.

I wouldn’t have gone to the trouble of writing a custom
application to do this simple task if it didn’t generate a
**massive improvement in my ability to search for interesting
tuning systems** — which it does. And it can do so for you too
if you are a composer or theoretician who is interested in
composing **interesting, mind-blowing, haunting, striking,
mesmerizing, intense, or just plain beautiful music**.

For example, let’s say you have become enamored with the
lovely *minor septimal tritone* interval (7:5) and you want
to use it as the base for an entire tuning system. If you want to
see what sort of just ratios you approximate by dividing the
ratio of 7:5 into — say — 13 equal parts, you can do so very
easily. You start in *ratio-to-cents* mode and type in `7` and
`5`. Right away, you see that that interval is equal to 582.51
cents. Next you move into *cents-to-ratio* mode — you’ll see
that the 582.51 cents has been automatically entered in the edit
field. Now you can edit the entry to read `582.51*1/13`. Hit the
calculate button and you see that that interval is 4.1 cents flat
of the just ratio 13:12. Put the cursor next to the number ‘1’
and press the up arrow (or use the mouse wheel if your mouse has one). The 1
increments to 2. The calculation again shows a nearby just interval and the
difference. Press the up arrow again — the 2 increments to 3. When the
interval has a name in english (such as the fifth, 3:2; or the subminor 3rd,
7:6), that name is also displayed. **Very quickly you can zoom through all of
the intervallic resources you will have** by basing a tuning on the 13th root
of 7/5 — or any other base. (In the thirteenth root of 7:5, you’d
quickly discover that you have more than a bucketful of awesome harmonic and
melodic possibilities available.)

You just have to try it to **see how much more efficient this
method is** than using a regular calculator or spreadsheet. It’s **a
genuinely useful musical tool**.

Below we see IntervalCalc^{TM} working in *Ratio to Cents* mode. This
mode takes a ratio — like 2:1, 3:2, 4:3, 5:4, 6:5, 7:6, or even
7:5, 7:4, 12:7, or 13:11 — and converts that value to cents, the
unit which is used in music as a way of precisely measuring
intervals. There are 1200 cents in the octave which is a ratio of
2:1.

Here we see that the interval of 7 to 5 is
equivalent to 582.51 cents. Also, we see 7 cycles of a sine wave
and 5 cycles of a sine wave, then what it looks like when those
two waveforms are added together.

Below we see IntervalCalc

^{TM}working in

*Cents to Ratio*mode. This mode not only shows which ratio is nearest the value in cents which is typed in, but it also describes that interval in English if it can.

- Example 1: If you give it the interval of 700 cents, it will tell you that 700 cents is two cents flat of a pure fifth — which is the ratio of 3 to 2 (3:2).
- Example 2: Type in 1200 cents, and it tells you that there are 1200 cents in an octave and that the octave is just another name for the ratio of 2 to 1 (2:1).
- Example 3 (shown): Here we see
IntervalCalc
^{TM}identifying the interval which is 6/13 of the septimal tritone — turns out that that interval is a mere two cents sharp from the subminor third — that extra flat third used in jazz which is a ratio of 7 to 6 (7:6).

### Other Features

- IntervalCalc
^{TM}also reduces expressions (shows what they are equal to) when you press " ". Expressions with ratios and integers get reduced to lowest terms. In other words, if you type in`11:3-5:12`and reduce, you will get`13:4`. - Holding down the shift button while using the arrow keys to increment or decrement a number in an expression causes the number to change in steps of 10 instead of 1.
- Graphical display can be drawn using sine, square, or sawtooth waveforms.

### More about Expressions

IntervalCalc is a general purpose calculator, including logarithmic
and trigonometric functions.

Examples of expressions it can handle:

`3 log 100``log (3:2) / log (2^(1/1200))``sin (2 pi / 360 * 51.72)``2 + 7 choose 3 * 14``1 + factorial(11)``e^4``"71077345" base 9``"11111110" base 2`

*Released: Jan 26, 2011*

Version 1.7.7 introduces the following:

- - universal binary
- - new icon

*Released: Jan 20, 2004*

Version 1.7 introduced the following:

- - os x compatible
- - improved appearance

- - harmonograph
- A new and interesting way to look at intervals when in the
*Ratio to Cents*mode. - - better math handling
- Some bugs in the calculator have been fixed and now when you type things it doesn’t understand, it tries to explain what it thinks is wrong.
- - improved waveform display
- The square and sawtooth waveforms are drawn in a different way which makes them look much better. The waveforms are also all lined up better and are now color coded.
- - new about box
- Includes a pretty kinesthetic sculpture.
- - persistent preferences
- Changes to preferences are now saved.
- - larger entry fields
- You now have more room to type in formulas and expressions.
- - smaller and faster
- The program is smaller in size even though it does many more things. Being smaller also means the program launches open faster.
- - fine number control
- Incrementing numbers with arrow keys now has two
additional step sizes: 0.1 size steps when the control key
is held down with an arrow key (because finer
*control*is now possible), and 0.01 size steps when control and shift are held down with an arrow key. Try the small steps and change a value in*Ratio to Cents*mode. It’s fun to watch the complete range of shapes which the new harmonograph moves through when the numerator or denominator is scrolled at small step values with this feature.

### Obtaining IntervalCalc 1.7:

- IntervalCalc is no longer available. This page is retained as a reference of features for those still using it.