The scales in the velocity keyswitches retuning Kontakt script

This page is work in progress, will describe all the scales in the examples list for Velecity keyswitches retuning

12 tone tunings
The droplist shows various twelve tone tunings starting with just intonation, and then a historical progression of tunings and well temperaments.

For an introduction to this subject, see Kyle Gann's An Introduction to Historical Tunings

Pythagorean
All the notes are based on the pure fifth, a frequency ratio of 3/2. When you add intervals you multiply ratios. So after twelve fifths you get to (3/2)^12 = 129.746337891. This is quite close to 2^7 (128) but not exactly the same, the notes differ by a Pythagorean comma - roughly an eighth tone, 23.46 cents.

If you follow a cycle of pure fifths you get ..., Cbb, Gbb, Dbb, Abb, Ebb, Bbb, Cb, Gb, Db, Ab, Eb, Bb, F, C, G, D, A, E, B, F#, C#, D#, A#, E#, B#, F##, C##, D##, A##, E##, B##, F##,..., where for instance, Cb, B and A## are different notes

The pythagorean twelve tone cycle was developed in the middle ages, gradually one note at a time, started with the white keys, then added Bb and then gradually added the other notes as time developed as the music got more chromatic.

They eventually stopped at twelve notes in Western music though in other cultures then musicians and theorists continued to more notes, for instance 17, or 53 notes. These numbers are the "moments of symmetry" with two step sizes. You also get a moment of symmetry after 5 notes for the pythagorean pentatonic, and after 7 notes for the diatonic scale with two step sizes whole tone and semitone. In the pythagorean 12 tone system you have two step sizes again, there are two sizes of semitone, the diatonic semitone (from e.g. E to F) of 90 cents, and the chromatic semitone (e.g. C to C#) of 114 cents, but they are similar in size so it is not that noticeable.

It is impossible to have all the fifths pure in Pythagorean tunings. So there is always one "wolf fifth" which is not pure. The wolf fifth in Pythagorean is not as extreme as the mean tone wolf, but has one of the fifths flat by about an eighth tone. It is usually placed in one of the remote keys rarely used.

In this tuning the fourths and fifths are consonances. The major and minor thirds in this tuning were considered dissonances in medieval music.

The only consonances in medieval music theory were the fourths and the fifths (and of course the octave), and music came to a rest on open fifths or fourths. Nowadays a modern listener might find the major and minor thirds in this tuning tolerable as they are only slightly sharp compared with the equal tempered thirds, and our ears are already used to the "bright" rapid beating you get in twelve equal thirds.

To find out more: Pythagorean tuning (wikipedia)

To find out more about how medieval composers used the Pythagorean tuning see Margo Schulter's Pythagorean Tuning and Medieval Polyphony

Quarter comma meantone
This is a tuning from the sixteenth and seventeenth centuries, also it is still used today for some organs (because the beating thirds of twelve equal are more noticeable in the long sustained notes of an organ).

In this tuning the idea is to adjust the fifths in order to achieve pure 5/4 major thirds. Eight of the major thirds are pure, the remaining four are sharp, a lot sharper than the major thirds of twelve equal. Like the Pythagorean tuning it has a wolf fifth, but this time it is sharp rather than flat (which you may find more noticeable) and it is sharp by more than a third of a tone. In period music this fifth wasn't used at all, you simply avoided that key. This was acceptable so long as modulation was restricted to a small range of keys.

To find out more, Quarter comma meantone on Wikipedia

The golden horogram tunings
This is a method of tuning developed by Erv Wilson. It uses a cycle of intervals just as for the Pythagorean and Mean tone approaches - but the aim isn't to try to approximate pure intervals. Instead you generate scales with two step sizes, large and small (a bit like our whole tones and semitones) but with the two step sizes in the ratio of the golden ratio.

You start with some formula involving the golden ratio, for instance the 3-5 horogram starts with the interval (1Phi+0)÷(5Phi+1) where Phi is the golden ratio. You then create a cycle of those intervals just as for the Pythagorean tuning, and you look for the "moments of symmetry" with two step sizes.

You can hear a couple of examples from David Finnamores golden horograms website. Best way to find out what they are is to read his site.

I thought it was nice to include a couple to give a taste of other kinds of microtonal music, in this case, using the golden ratio to construct intervals.

You can listen to examples on his listening page. The two tunings I included are the one for Ring 3-5, which you can hear here: Ring 3-5, and the one for ring 9-7 which you can hear here: Ring 9-7

Listen to examples of mirotonal music
See the Microtonal Listening List at the Xenharmonic wiki