You can use this web application to compare notes and chords of the equal temperament with the just temperament (including the pythagorean temperament), demonstrate the phenomen of beats (acoustics), use it for ear training, frequency calculations or as a drone for tuning or practicing.
Hover over a note, select the octave by clicking on its octave number and then the name, the frequency and a graphic of the selected note will show up below the control bar. Use the control bar or the individual play buttons to play your selection (for more information about the control see below).
The just temperament is based on the harmonic series. The shown 13 x 5 grid of notes is a section of an infinite (imaginary) two-dimensional toneweb generated only by the frequency ratio of a just fifth (3/2) in the x-axis (derived from the 3rd harmonic) and the frequency ratio of a just major third (5/4) in the y-axis (derived from the 5th harmonic). If you exclude the second dimension (y-axis) and look exclusively at one row, you get a pythagorean system. So by choosing notes only from one row you can show/play pythagorean intervals or chords as well.
In theory you could even extend this two-dimensional toneweb to a third dimension taking the harmonic sevenths (derived from the 7th harmonic and accordingly the next prime number in the harmonic series) into account.
The notes of the central note's ("A") row are added with a ° sign to indicate that this is the row of null (a.k.a the base or central row). The notes of the row above the °-row are added with a ` sign to indicate that they are a syntonic comma (≈21.5 cents) lower than their namesakes of the °-row. The syntonic comma can therefore be described as the difference between a pythagorean major third and a just major third. Conversely the notes of the row below the °-row are a syntonic comma higher than their namesakes of the °-row.
The equal temperament divides the octave into 12 equal steps. Therefore the frequency ratio of any pair of adjacent notes is equal to the 12th root of 2 (12√2) and unlike in the just temperament there is no difference in enharmonic notes (e.g. C♯ is exactly the same as D♭). While this tuning system is pretty handy for instruments with fixed pitches like the piano or the harp, musicians with the possibility to intonate freely are likely to prefer the just intervals over the equal tempered and use them whenever they can.
Dropdown menu to choose between different sound types.
Select the notes that you want to display or hear by clicking on its octave number. Start the sound of your selection by clicking the PLAY button. If you deselect a note the sound will continue. This allows you to select the next notes you want to hear without having a pause between your sound selections. To stop the sound use the STOP button.
Click the STOP button to stop any sounding notes. If you want to switch for example from one chord to another you can use the PLAY button instead.
Deselects all of your selected notes at once.
Shows the deviation from a just note to its equal equivalent in cents. One cent is a hundreth of an equal semitone. Note: all cents numbers refers to the tonewebs central note which in this case is the "A" but in theory you could choose any note as central note. The cent deviation is also represented by the notes background color. The less green it is the bigger the difference.
Change the standart respectively concert pitch. It changes not while playing.
Main volume slider
Starts respectively pauses the selected note.
Volume slider for the selected note.
Note that the individual sliders adjust the volume automatically when selecting/deselecting more respectively less notes. This is to prevent the sound from distorting when you start a bunch of notes at the same time. Odds are you want to decrease the volume of higher pitched notes and increase the volume of lower pitched notes, especially with SINE notes to level the notes' loudness.