|Jan 26, 2011||:||Version 1.7.7 — Universal Binary.|
|Jul 22, 2011||:||Runs on OS X Lion.|
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 IntervalCalcTM
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
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 IntervalCalcTM 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
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
working in Cents
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
- Example 3 (shown): Here we see
IntervalCalcTM 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
- IntervalCalcTM 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
- 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
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)
- "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
Version 1.6 introduced the following:
- - 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
- - 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
- - 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.