Selecting and creating musical scales
The Justonic Pitch Palette loads with a default harmonic scale and includes
more than 50 additional harmonic scales, including blues scales, Arabic scales,
modern harmonic scales and historic scales. You can choose any one of these
scales, and you can also create your own scales.
When you choose the Scale Editor from your tool bar, you will see this screen:
On the left side is the name of the currently selected scale. The left and right spin buttons can be used for scrolling through all of the scales in the Pitch Palette.
Below the scale name there are 12 ratio input boxes arranged in the form of one octave of a piano keyboard in the Key of C. This is where you can view the ratios of the selected scale or input your own scale. These ratios are used in every Key and every Root.
Notice that the scale is entered as a series of fractions (or ratios): 1/1, 16/15, 9/8, etc. All pure harmonic scales are formed by these perfect whole-number ratios. If you have a scale that is described in cents or in Hertz (Hz), you can convert it to ratios using The Calculator . With The Calculator, you enter your scale in cents, decimals or Hertz and the calculator will calculate the ratio. Alternatively, you can enter the ratio into the calculator and read out the scale in the other units. Also, see the appendix for a Table of Intervals.
Scale #1 is perhaps the most classic harmonic scale, and the one we consider to be the most appropriate harmonic scale to start on because all of the intervals are directly related to the low harmonics of the tonic. The basis for this scale in its diatonic major mode dates back to Claudius Ptolemy (90-168 AD). This is what we call a "7-limit" just intonation scale, because all the harmonic ratios can be created using prime numbers no higher than seven (1,2,3,5, and 7). It has been used by many modern just intonation composers.
On the right-hand side of the screen you see a graph that compares the current scale to equal temperament. The black bars represent black notes from the octave, and the white bars white notes. You will notice with the default harmonic scale that the minor Third and Sixth are sharper than equal temperament and that the major Thirds and Sixths are flatter. These adjustments correct the faulty placement of these intervals in equal temperament. These Thirds will give you full, harmonious chords. The Fifth is only slightly sharp of equal temperament, but this small adjustment makes a big difference in the smoothness of chords.
Perhaps the most distinctive feature of this default scale is the very flat flat-seventh. In equal temperament this note is the most out of tune with natural harmonics. In fact, on a piano the seventh harmonic of the strings is purposefully damped so that it does not conflict with the mistuned equal tempered flat seven. The major seven is also flat of equal temperament. Try playing a major seven chord, and a minor seven chord with this scale. You will hear a richness in these chords that is completely obliterated in equal temperament. The flatter flat-seventh here is derived directly from the seventh harmonic of the tonic. To the ear used to equal temperament, this scale degree will sound the most exotic in this scale. If you want a flat seven that is closer to equal temperament, you can choose scale #2, the Inversion Harmonic Scale, which uses the 16/9 flat-seven, the inversion of the 9/8 harmonic whole tone.
A word of clarification might help in distinguishing between "scale" and "mode." These terms can be used interchangeably in some cases. That is, all modes are scales, and all scales are modes. Scales are modes of larger scales containing their notes, and of any scale using the same notes but a different tonic. Furthermore, all modes are scales in their own right. It will help to set some ground rules and definitions for using these terms.
In the classical ecclesiastical usage, a mode of a scale is simply defined by moving the tonic to a new scale degree. The most common example that Western musicians know is that every natural minor scale is a mode (starting on the sixth) of a major diatonic scale. So an A-minor scale uses the same notes as a C-major scale. The same notes can be used to play a D-dorian.
In its broadest definition, a mode is simply a selection of tones from a scale. So the diatonic scale or the natural minor scale can also be seen as a selection from a chromatic scale or a mode of a chromatic scale. In both cases, it is important to distinguish between a mode and a scale. If, for example, you want to play music in a diatonic major mode, or minor mode, or a Lydian, pentatonic, Dorian, etc., you do not have to change "scale." You can play any of these modes using any of the scales in the Justonic Scale Menu, or with any other 12-tone scale that you create.
Modal changes can add depth to your music. You will notice, for example, that each mode takes on a somewhat different feel in the various scales. A natural minor mode sounds quite different in the Harmonic Classic scale than it does in the Inversion Harmonic scale and sounds different again in the blues or Arabic scales.
Okay. Let's view a few scales. Open The
Scale Editor. First, you can click your mouse on the Next >or Previous
< buttons which are to the right of the scale name to move through the Justonic
Scale Menu, or you can click on the Scale Menu arrow on the Toolbar and simply
select a scale from the drop-down list. (You can also select a scale using the
Scale Editor, as described at the beginning of this chapter.)
As you click through the menu or select from the drop-down list, notice that
the bars in the graph move up and down indicating the relative sharpness or
flatness of each interval in each scale.
You will see that the Arabic scales use quartertone thirds and sixths. The blues
scales also use flat thirds, sixths and sevenths. The more you experiment with
these scales, the more you will realize how restrictive and out-of-tune the
equal tempered scale really is.
To enter your own scale, click on New, Insert or Clone.
Once you have your new octave ready, whether a clone or a blank scale, you can now enter new ratios. The scale editor will only take ratios, so if you don't know the ratio, but only know the frequency in Hertz or the interval in cents, open The Calculator to calculate the ratios or see the table in Appendix for the closest ratio.
You enter the ratios by clicking your cursor into the appropriate box, and typing in the number. When you enter a number into a box, after you press Tab, your cursor jumps to the next box. Every ratio requires two numbers, one in the top box and one in the lower box. The top number must be larger than the bottom number.
There are some other rules we've incorporated into The Scale Editor to help you check that your scale makes sense. (If you find these rules cramp your creativity, we created The Tuning Board . If you want to get really radical with your scales, contact us, and we will try to build your requirements into future versions of the software. For most purposes, we think you'll find these scale rules both logical and helpful.)
Rules for Type 1 scales:
- Intervals are entered as ratios of two numbers. These numbers represent the size of the interval in relation to the tonic, which is the ratio 1/1.
- The first ratio, the tonic, is always 1/1.
- The top number in each ratio (fraction) must be larger than the bottom number (that is, each ratio is greater than one).
- The top number cannot be more than twice the size of the bottom number (that is, each ratio is less than two.) Rules 3 and 4 ensure that the scale is contained within the compass of one octave, 1/1 to 2/1.
- Each interval must be larger than the previous interval. This rule ensures that the scale ascends from the tonic to the octave, and does not retrograde backwards.
If you are not used to working with ratios, you may not immediately know if one ratio is larger or smaller than another. Don't worry about it. The software will let you know if you violate a rule, will inform you what you have done and will assist you in correcting it. (In Appendix Two of this manual there is a table of ratios of various size.)
The Pitch Palette creates and recognizes three types of scales:
Type 1
- Created with Pitch Palette Scale Editor
- Follows the above Scale Editor rules
- Created for Synthesizer or Pitch Bend Tuning Method
- Shows first note or Root as a ratio of 1/1
- Shows remaining 11 notes as ratios of their frequency to the Root
- Uses tuning features of current synthesizer - range, resolution, SysEx
Type 2
- Created with The Tuning Board
- Created for Synthesizer Tuning Method
- Always created in the Key of A
- Saves Root as part of Scale name
- Changes Base Pitch A from 440 to whatever is necessary to preserve the interval between note A and the Root
- Shows first note or Root as: Frequency in Hertz/1
- Shows remaining 11 notes as ratios of their frequency to the Root
- Uses tuning features of current synthesizer - range, resolution, SysEx
Type 3
- Created with The Tuning Board
- Created for Pitch Bend Tuning Method
- Allows use of MIDI Pitch Bend range of up to 24 semitones per semitone
- Always created in the Key of A
- Saves Root as part of Scale name
- Changes Base Pitch A from 440 to whatever is necessary to preserve the interval between note A and the Root
- Shows first note or Root as: Frequency in Hertz/1
- Shows remaining 11 notes as ratios of their frequency to the Root
- Uses tuning features of MIDI Pitch Bend available on ALL synthesizers
The scale editor has additional options that are available to you by clicking on the appropriate button:
Scales are saved in a file called PPalette2.SCL, which is loaded automatically each time the Pitch Palette program starts. You might want to make a backup copy of that file.
When saving the file, the previous version of the file is sent to the Recycle
Bin. For security reasons, you will be asked to confirm this action. If you
are sure, you should confirm it.