I've just submitted version 3.1 of pianoscope to the Apple App Store. It should go live within in the next 24 hours. The new version is all about temperaments.

By popular request, the Standard Edition now allows to create your own custom temperaments. In addition to this, eight new temperaments are coming with the new version:

Neidhardt Große Stadt 1724
Neidhardt Dorf 1732
Rameau 1737
Marpurg III 1776
Hummel Viennese 1829
Bach / Lehmann 2005
Meantone 1/3 Syntonic
Meantone 1/6 Syntonic

On devices running iOS 17 or later, you can now graphically visualize offsets and beat rates of intervals in the major triads of any temperament. You can find the new function in the temperament details panel.

When you tap on the Major Triads row, the following dialog opens:

The diagram shows all major triads from C3 to C4. Major thirds are shown in red, minor thirds in orange, and fifths in blue. By default, it shows the cent offsets of the first coincident partials of the intervals. The horizontal guide lines provide a reference with the interval offsets of a Pythagorean and an equal temperament.

If you place and hold your finger on one of the interval bars, you can read the exact numerical values of the offsets.

Tap on the ellipsis button in the toolbar for a menu with additional options.

By default, all triads are arranged horizontally in the order of the circle of fifths. By selecting the menu item Chromatic, you can also arrange them in semitone steps from C3 to C4.

Select the menu item Beat Rates to switch the display from cent offsets to beat rates in hertz.

If you choose the menu item Beat Synchrony, the diagram shows the ratios of the beat rates of minor to major thirds.

If you swipe your finger up or down in a diagram, you switch directly to the next or previous temperament from the list of all temperaments.