Robert Inventor

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Microtonal Scales and Tunings
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Microtonal scales and tunings
One of the many features that come as part of Fractal Tune Smithy

  • Try out an incredible range of tunings - historical baroque tunings, Gamelan tunings, Indian music, tunings based on vertex patterns of 3D shapes, and other special ones invented by modern scale designers
  • Make new tunings for scales using Tune Smithy

Motivations - Intro - Working with the scales - Scale construction features - Example of a scale


There are many reasons why one may want to venture away from the well trodden path of the twelve equal tuning.

For some its because they discover that if you slightly flatten the major third in a chord then it sounds more mellow, which leads into an investigation of the harmonic series, and just intonation harmony, and the various "commas" and "dieses" (minute fraction of a semitones pitch discrepancies) that arise.

You may discover that three pure harmonic series based major thirds take you to a note that's very noticeably flatter than the octave. Or you may wonder why it is that when tuning a piano, harpsichord or the like to equal temperament you have to tune all the fifths slightly flatter than pure.

Or - sometimes string players discover this - if you ascend by four pure fifths such as C G D A E (e.g. on a Cello, the C G D and A can be open strings, and the E can be the E harmonic on the A string) then the E that results is noticeably sharp compared to the pure harmonic series major third (e.g. the "E" harmonics on the Cello C string).

This leads one into a fascination with just intonation, temperaments, maybe baroque and medieval tunings and the notion of well temperings and key colour - or maybe modern twelve tone temperaments e.g. based on golden ratio, pi, etc - or perhaps the many equal divisions of the octave with more than twelve notes to an octave.

For some it's because they discover the unusual harmonies involving the seventh, eleventh or thirteenth harmonic and start to explore the tunings that use them. Or one may come to it via geometrical ideas such as the Lambdoma or the musical geometries of the Wilson CPS sets.

Or maybe you come to this through a wish to make musical harmonies from astronomical or scientific data. Or perhaps you are inspired by bird song and other natural sounds which are microtonal, as one can hardly expect that a bird or animal will naturally sing in twelve equal, or any other equal temperament, so one may find the resolution of twelve pitches to an octave isn't sufficiently fine to match what you hear.

Or maybe you are a musician in the great Indian, Japanese, Indonesian, Thai, or Arabic musical traditions - or perhaps one of the many African musical cultures, ... Or you have developed an interest in one of those cultures. So you want to use the tunings natural to your music rather than to try and retune it to the Western twelve equal tuning.

Or you are a composer who has trained in twelve equal, but you find it refreshing to explore other tunings as a new direction and inspiration for a fresh look at music. It may turn all your ideas on their heads, some tunings particularly, maybe you have to start from scratch which can be scary but also stimulating, and that may be what attracts you to this area.

To find out a bit about some of the others who are exploring this area take a look at the microtonal wiki (external web site, opens in a new window).



In this context, a "scale" specifies the exact intervals to play from a given fixed pitch, the "1/1". (often the intervals are given in hundredths of a semitone or as frequency ratios) - see the Pygmie scale at the bottom of this page for an example.

The usual "A major", "C minor" etc in this context are usually referred to as "Modes". In Tune Smithy I refer to them using the more general term "Arpeggio".


Working with the scales

You can choose from many scales that come with the program, and can also make a drop list of all the thousands of scales in the SCALA archive. You can save and open scales in the standard SCALA file format.

Then, you can enter new scales as well, using the usual notations such as cents (hundredths of a semitone), ratios (of frequencies), Hertz, and other less commonly encountered notations such as lattice notation and decimal midi, as well as a special notation which makes it easy to enter equal tempered scales.

You can immediately preview your scale - click the play button to play it - or play it using any figuration, or you can use the fractal tune generator with your scale.


Scale construction features

This is not a dedicated scale construction tool like Scala, but there is quite alot that you can do in Tune Smithy and you can also easily move scales between the two programs.

Examples of what you can do in Tune Smithy:

  • Make Mean Tone Scales and Linear Temperaments, with any size of comma and any position of wolf fifth, which are very important in the context of historical tunings (example: quarter comma meantone which was at its height in the period just before Bach, which favours pure 5/4 major thirds).
  • Make Moment of Symmetry Scales, with any size of generating interval and any scale repeat, including non-octave (example, pythagorean chromatic twelve tone is a moment of symmmetry for the pure 3/2 fifth, as are the pythagorean pentatonic and diatonic scales and the Arabic seventeen tone pythagorean scale).
  • Explore Super Particular Scales, using the methods of David Canright (for some reason, many nice sounding scales are superparitcular, meaning that all scale steps are intervals between consecutive numbers in the harmonic series, 9/8, 10/9, 8/7 etc).
  • Make Harmonic Fragment Scales (with these, every single note is harmonious with all the others)
  • Explore the Pythagorean Lambdoma arrangement of pitches, also known as the Tonality Diamond (as used by Harry Partch)
  • Explore Dan Stearn's UO and LMN Scales (some special types of scale by this modern scale designer)
  • Explore Erv Wilson's CPS sets (musical geometries)
  • Lattice and Product Scales (ways of combining two scales to make a third)
  • Make a drop-list of all the scales in the Scala archive and search it for any scales of particular interest
  • To specify an equal temperament such as 31 equal you can just enter the scale as 1//31 - like a ratio but with two //s instead of one. Here 1//31 stands for an equal thirty first division of an octave. Or to specify e.g. the fifth step of 31 equal use 5//31.
  • Show your scale in SCALA using the Show in SCALA button, and you can also show scales you construct in SCALA in Tune Smithy using File | @ Tune Smithy in SCALA.
    (You may need to configure @ Tune Smithy first to work from SCALA - which you can do within Tune Smithy - the option to do this is in the window Locate SCALA and make all the SCALA related files - Ctrl + 16 in FTS - i.e. hold down the Ctrl key, type 16, then release the key)
  • Easily make any mode within the scale - in Tune Smithy these are referred to as Arpeggios, as a more general term.
  • Explore modes that ascend and descend using different notes - such as the melodic minor, and the Japanese Koto scales.
    The Indian Ragas also do this - however since there are so many of them and I don't have a database available of them, then the only ones included with the program are the ones from the SCALA archive which ignore distinctions of ascending / descending modes. If any of you are interested to provide a database of some of the Indian raga modes, I'll be delighted to include them in a future release of the program.


Example Scale

An example of a scale might be for instance, the Pygmie scale:

1/1 8/7 21/16 3/2 7/4 2/1
(as the ratios of the frequencies from the 1/1)

If the player chose to take the 1/1 as concert pitch C, the pitches to play would be:
261.626 Hz 299.001 Hz 343.384 Hz 392.438 Hz 457.845 Hz 523.251 Hz

There for instance, the 8/7 is the ratio of the first and second frequencies, 8/7 = 299.01 / 261.626.

As cents (hundredths of a twelve equal semitone), the same scale is:

0.0 231.174 470.781 701.955 968.826 1200.0

There you can see that the 8/7 is about 231 cents above the 1/1, that is to say, about two and a third semitones, so it is a "wide whole tone" or in some contexts it can behave like a very narrow minor third.

Since it uses the number seven, it is referred to as a "septimal" interval, and is the interval between the seventh and eight notes of the harmonic series - as a harmonic series based interval, it is harmonious, though unusual and unfamilar sounding to Western ears.

Other commonly used septimal intervals are 7/6 (the dark septimal minor third sometimes called subminor), 9/7 (the septimal major or super major) and their inversions 7/4, 12/7 and 14/9. The pygmie scale has a 7/6 interval between the 3/2 and the 7/4.

What to do next

Freeware / Shareware status: This feature is free.

To continue reading about Tune Smithy, go on to the Metronome for Rhythms and Polyrhythms

To find this feature after you download Tune Smithy:
Look in the Tune Smithy Tasks window for: Music kbd Retuning

The scales features are also available in many of the other tasks, the Scale Composer is just more dedicated towards scale construction than the others.

To download the program and take it for a Test drive (start the test drive at any time):

Download Tune Smithy



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To find this feature:
look in the
Tune Smithy Tasks window for:
The scales are used with many of the tasks

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