Scales of interest to musicians

If you are a complete beginner to the idea of musical pitch intervals, you may like to read Some basic concepts .

The program uses the MIDI pitch bend feature to play scales with pure ratios as well as in the equal tempered tuning. You can choose from a selection of scales, or else specify your own scales by typing in the ratios or the values in cents. You can use the usual notation, for instance this is the Pythagorean diatonic scale as you could type it into the program (though it has it already, so you don't need to):

If the ratio notation for musical intervals is new to you, or you want to see details of how the just temperament scale is constructed from the harmonic series, with pictures and sound clips, see Harmonics and just temperament .

Here is the same tune as is shown at the top of this page, with an intervals notation, using the Pythagorean temperament.

Some MIDI players (noteably, old versions of Windows MPlayer) will need a reset to get back to ordinary twelve tone equal temperament.

Play: B flat then c . Now play Two notes . Do you hear the same note (middle c) twice? If so your player is okay.

If you hear two pitches, you can upgrade your player to one with automatic resets

Windows Media Player (it's free) :)

Alternatively, play Reset after listening to the clips. More details.

And here it is again, this time showing the ratio of each note with the previous one, so that each number shows the size of the interval immediately below it:

You can also specify well tempered, mean-tone, or equal temperament scales, or microtonal systems with as many notes to an octave as you like, or any other scale defined using ratios or cents.

This is to help train your ear to hear the distinction between the types of major third.

Click on any of the pictures to hear a four minute midi clip of the tune in that temperament. Can you hear any difference between the equal temperament, Pythagorean temperament, and just temperament tunes?

The easiest distinction to hear is that the Pythagorean temperament major third, the third note of the tune, is brighter, and sharper, while the one for the just temperament is more mellow.

Also, it is probably easier to hear the distinction in a chord, rather than in a melody. So if you don't hear it yet, or aren't sure, here are some chords to listen to.

You will hear some just, and some pythagorean chords. The puzzle is to try to identify them.

The a1, a2 etc identify the answers. See if you can recognise which chord is which, rather than just guess.

To check your answers, scroll down, and follow the link you can find at the end of this page.

Now try listening to the tunes again. Perhaps you can hear that the equal temperament one is a bit brighter than the mellow just temperament one, and the Pythagorean temperament one brighter still?

Try both, and listen especially to the third note of the tune. Which do you think sounds most mellow, and which sounds brightest?

Best of all is to try playing in the various scales yourself, which you can do with Fractal Tune Smithy from a MIDI music keyboard, or from your ordinary p.c. keyboard enabled for sound .

The Pythagorean major third was considered way too bright to even use back in Medieval times, but is quite acceptable to modern ears, used as we are to the bright equal temperament major third. In medieval times, one of the favourite tunings was the quarter comma mean-tone temperament, which is designed to favour just temperament major thirds, at the expense of leaving one of the twelve major scales completely unplayable. That was considered a small price to pay for it in those times. The quarter comma mean-tone scale continued in use for church organs for a while after it was no longer in common use otherwise, perhaps because of its particularly sonorous chords.

You can try playing your favourite keyboard music in the Pythagorean scale, quarter comma mean-tone scale, historically authentic tunings from the time of Bach, or Mozart, and so on, using Fractal Tune Smithy . You just need to choose the tuning from a drop list. You can use a MIDI music keyboard.

You can also play in any of the scales from an ordinary p.c. keyboard using successive keys for the notes of the scale / mode. You can play single notes and two note chords in this way, and some of the three note chords. Some chords of three or more notes can't be played from a standard p.c. keyboard (see the program's help under Seeds | Playing along ). If you find a make of p.c. keyboard that can play them, let me know so that I can recommend it in future versions.

An archive of over 2000 scales from all round the world is included with the freeware SCALA program by Manuel Op de Coul. Also includes a list of modes for many scales. His program, run from the MSDOS prompt, also has a wide range of commands to use to make new scales. You can use any of these scales and modes in FTS, either via the drop lists that come with the program, or other ones you can make from the SCALA archive by clicking buttons in FTS after you download the archive.. To find the SCALA options in FTS, look at Fractal Tune Smithy | File | Scales Options | SCALA Scales .

Examples with equal temperament and other temperaments, to compare, utilities for changing the tuning of a MIDI file, original compositions, and links to other tuning sites: Fred Nachbaur's web site