Tuning observatory
Temperament Visualizer
Put rival tunings on the same pitch rail. The distance is measured in cents; the shimmer you hear is their beat frequency.
Markers coincide when both systems assign the same pitch.
Temperament Visualizer is an interactive tool that allows you to compare various tuning systems to standard equal temperament, both aurally and visually. Using either your computer keyboard or the mouse, you can navigate around interface and trigger sounds. It also plots competing tunings next to each other on a single pitch rail to point out small variations in terms of beat frequencies and number of cents.
From there you can use row of buttons along the top to choose your tuning lens. The options are Quarter-comma meantone, Pythagorean chain, Pure ratios, and Equal divisions. Each will change the mathematics that it is basing its calculations on. Pure ratios is based around small integer relationships whereas Quarter-comma meantone slightly constricts fifths. The colored marker will sit on pitch rail in relation to the baseline twelve-tone equal temperament line, depending on which one you select.
How to Use the Temperament Visualizer
Underneath the set of tuning lenses is another grid of interval stones. Each of these buttons represent a common musical interval. Examples include the octave, major third, and perfect fifth. Use your mouse to click on an interval button and then the arrow keys to scroll through available choices. When you select an interval, the display change to show its frequency and cent deviation. This deviation is number of cents the interval differs from root note. The rail visualizer displays the extent to which the tuning vary away from the equal-tempered pitch for each interval.
On the right hand side, the Reference anchor slider will set starting frequency of the bottom note. It does that by dragging it up and down scale. The reason for that is because beat frequency depends on the absolute Hz values. So if you want to hear what happens when the beats are at a different pitch level, use this slider. The Observatory level slider control the overall volume so that sound remains comfortabley.
To play, simply choose an interval and tuning from the main panel, then press one or more of the buttons along the bottom. Each time you do, it will play the interval you’ve chosen on standard equal-tempered scale (the Audit 12-TET button). It will also play your choice of tuning using that same interval (Taste this tuning). Finally, the Expose the beating option play both tones together so you can hear how they clash. That’s what we call the audible ‘shimmer’ of the slightly different frequencies in each of the two tunings.
In the sidebar is a Measurement log which details accurate information about whatever you’ve selected. This includes: This is the upper-note beat frequency. It is offset from twelve-tone equal temperament. Aim for target cents. This provides some numeric feedback for you to quantify what you’re hearing. Below the log is the Four-lens comparison ledger, where you can easily switch through different tunings and hear how they differ than before. Simply click on a row in the ledger to hear current interval and select a new tuning. Survey all four tuning lenses, If you want to get an overview, you can press this button which will play your chosen interval from each of the four tuning systems in turn back on itself using same reference pitch. This is a speedy method for listening to the nature of each system without having to click through the menus one by one.
You can also expand the help panel at any time to review the conventions and controls within the widget. If you like, you can use keyboard to move around more quickly. The arrow keys steps forward/back through the interval stones. The tab key step from control to control. The space bar/Enter key sound out whichever interval is in focus. You can also jump straight to each of the first nine intervals by pressing one to nine on the number keys, speeding things up as you explore. With this mapping, you wouldn’t of need to remove your hands from the keyboard while you try out different tunings and intervals.
Slow down the beat frequency by reducing the reference pitch. Lower frequencies produces slower beats, which can be more easily distinguished by ear. Listen how clearly different a Pythagorean major third sounds compared with a pure one where offset of the cent is audible. Alternatively, look at the markers along the rail aligning and separating when you alter the tunings. This visual feedback reinforce what you are hearing from the audio output.
Experiment with various interval and tuning combinations. Each tuning system has its own unique characteristics; try to develop an ear for these differences. You can adjust the reference pitch and volume until you are comfortable listening. Remember this is an exploration tool. Take time out to listen and observe how the beats changes when traveling through the scale. Try it now: how do these historic tunings sound to you?