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Scales

Scales options window , Superparticular scales , SCALA scales , Search scales or modes list , Sort scales or modes list .

Scales options window

File | Scales options

This is the starting point from which you can get to any of these windows:

Superparticular scales , SCALA scales , Search scales or modes list , Sort scales or modes list .

It also has a few buttons and tick boxes of its own.

Reset to default Scales list

Reset to default Modes / arpeggios

These reset the Scales and Arpeggios or modes drop down lists for the main window.

The default list of scales is the one that ends with the Indian shruti scale.

The default for the modes is the first 12 tone list.

Place new windows in front of main window - tick to make most new windows (such as the various scales options, and the new Seed / Scale / Arpeggio windows) children of the main window. This means they are always in front of it,. You can minimise them, or move them out of the way, to get to the main window.

Untick if you want them to be siblings of the main window, so that they can go behind it.

Whether a new windows is a child or a sibling will depend on whether the box is ticked before it is created. Doesn't affect windows already created.

Some windows ignore this tick box. (e.g. about box, unregistered message, and a few of the ones you get to from other windows).

Find all arrangements of selected scales steps - finds all the ways of re-arranging the steps of the scale.

Show as steps in description - used with the search for all re-arrangements.

Tick to show the steps of the scale in the Scales drop list (which has the scale descriptions). Untick to show ratios from the first note of the scale.

The Intervals drop list shows the ratio from the first note of the scale, whatever your choice for the Scales drop list.

Find all arrangements of ALL scales steps - finds all the ways of re-arranging the steps of each scale in the drop list, and puts them all in a single drop list. Skips duplicates of ones already found.

Add reduce buttons to New Scale windows - adds a button and two boxes to the New Scale windows.

More about the Reduce button for New Scale windows:

The notes box specifies how many of the scale you wish to reduce - remaining notes are left out altogether.

The Max ratio box specifies the maximum ratio for the new scale.

You can alternatively enter two numbers like this:

3/2 2

The first number then is the minimum ratio for the new scale, and the second one is the maximum ratio.

The Reduce button moves all notes up to the number specified into the specified range.

How it works: multiplies the old ratios by any number of multiples of b/a where b is the max ratio and a is the min ratio for the new scale.

It adds in the max ratio as a new note to the scale, if not already present.

If you want the new scale to be ordered in ascending order, select Ascending Order from the select Ascending Order / Order clicked drop list.

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Superparticular scales

File | Scales options | Superparticular scales...

A scale is superparticular if all the steps are of the form (n+1)/n for some n.

Examples of superparticular scales:

just intonation diatonic: 1 9/8 5/4 4/3 3/2 5/3 15/8 2 steps 9/8 10/9 16/15 9/8 10/9 9/8 16/15

pentatonic: 1 9/8 5/4 3/2 5/3 2 steps 9/8 10/9 6/5 10/9 6/5

Superparticular scales tend to sound good. If two notes are related to each other by a superparticular interval, then they belong to the same harmonic series. So the two notes, and their difference tone, can all sound together with without any beats (provided they are sufficiently far apart from each other).

The difference tone is the difference of the two frequencies. It isn't actually present as a separate note (won't show up on frequency analysers), but is heard as an extra low note below them, if you listen carefully. It can sometimes be rather quiet, but is often fairly loud when the notes are perfectly in tune. Try the recorder voice to hear them particularly clearly, this is because of the purity of the sound of the recorder - when playing recorder duets (esp. without vibrato), one often hears them rather strongly like an extra base part, sometimes with unwanted notes!

To find out what the difference tone is for two notes by tick Show beats in the scale window, then play them. For a fifth, the difference tone is an octave below the lowest note. For major thirds, two octaves below. For minor thirds, it is two octaves plus a major third below the lowest note (completes them to make a major chord).

Click on the button to find a complete lists of superparticular scales using David Canright 's algorithm, as described in Superparticular Pentatonics .

This can also be used to make another scale into a superparticular one by adding extra steps. Let's see an example of this.

The Pygmie scale: 1 8/7 21/16 3/2 7/4 2 steps 8/7 147/128 8/7 7/6 8/7 has four superparticular steps, and one wide step which is not superparticular: 147/128

Enter 147/128 into the Top interval box.

Set the number of notes to 2 , and leave the smallest interval (or range) at its default of 81/80 - 5/4.

Click the Find all superparticular scales button.

There is only one solution 9/8 49/48

Pygmie scale with superparticular interpolation: 1 8/7 9/7 21/16 3/2 7/4 2 steps 8/7 9/8 49/48 8/7 7/6 8/7

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SCALA scales

File | Scales options | SCALA scales...

You can make new Lists of Modes (LMD) files and Lists of scales (LSC) from files in the SCALA archives.

All the lists of modes that come with FTS, except the short 12 tone list, are from Manuel Op de Coul's modes lists, with his kind permission. For the most up to date versions, visit modename.html , which is updated more frequently than the file in the SCALA archive.

This file also has modes for many microtonal equal temperament scales. To make the modes lists, save modename.html file in any folder, enter it's folder in the Location of SCALA program box or browse to find it using the Browse button for that box, then click Make LMD files from SCALA list of modes .

To add the list of all the modes lists made to Scales box | More scales , tick File | Scales options | SCALA Scales | Add LSC files to "More scales..." drop list on Save or Open before you make it.

You can sort the lists in the same way as the default modes lists that come with FTS by ticking Auto sort modes by . with n+~i in the box next to it (least notes first, smallest steps first, most of the smallest steps 1st). For other sort methods, see Sort scales or modes list .

This makes many more modes lists than the ones that come with FTS. They are all saved in the same folder as the Fractal Tune Smithy.exe application, which will be your Fractal Tune Smithy folder if you chose the default location when you installed it.

You can also open SCALA Modes.lsc using File | Open , again, in the Fractal Tune Smithy folder.

The modes lists can also be edited by hand - each line in the file corresponds to an entry in the list. For details of the format:

LMD files format

You can add tags to the html file to specify default scales for the modes lists, and add extra default scales. For details see

LMD tags for Modename.htm

To use the button Make list of scales (LSC) of all SCL files in current folder , you need to download the SCALA scales archive which is from the SCALA download page. This is an archive of over 2000 scales.

Once you've downloaded it and unzipped it, use browse to find the folder with the SCALA .scl files, and click the Make list of scales (LSC) of all SCL files in current folder button.

This makes a file called SCALA Scales.lsc . It will be saved in the same folder as the .scl files.

Once more, to add the list to Scales box | More scales , tick File | Scales options | SCALA scales | Add LSC files to "More scales..." drop list on Save or Open before you make it.

You can then get to the new list of scales from the Scales drop list by clicking More Scales... , then SCALA Scales.. ..

This will show the complete list of SCALA scales in the FTS scales drop list, ready for use.

You can also open SCALA Scales.lsc using File | Open .

To use the button Show current scale in SCALA , you need to download the SCALA program .

Then use browse for scala app. to find the file scala.exe for the Location of SCALA application box.

Then click the button to run SCALA, and see the names of intervals, and other details. This is the output for the pygmie scale

Pygmie scale
  1:          8/7             231.174 septimal whole tone
  2:         21/16            470.781 narrow fourth
  3:          3/2             701.955 perfect fifth
  4:          7/4             968.826 harmonic seventh
  5:          2/1            1200.000 octave

The third column can show various things. The Show current scale in SCALA button sets it to show cents (you can override this - see later).

Now that you have the scale in SCALA, you can use any SCALA command with it.

For instance, try SH OW I NTERVALS to show all intervals between pairs of notes in the scale.

(you only need to type the letters in red: SH I )

Interval class, Number of incidences, Size:
  1:  3  8/7               231.174 cents  septimal whole tone
  1:  1  147/128           239.607 cents
  1:  1  7/6               266.871 cents  septimal minor third
  2:  1  64/49             462.348 cents
  2:  2  21/16             470.781 cents  narrow fourth
  2:  2  4/3               498.045 cents  perfect fourth
  3:  2  3/2               701.955 cents  perfect fifth
  3:  2  32/21             729.219 cents  wide fifth
  3:  1  49/32             737.652 cents
  4:  1  12/7              933.129 cents  septimal major sixth
  4:  1  256/147           960.393 cents
  4:  3  7/4               968.826 cents  harmonic seventh

The interval class is the number of notes that make up the interval.

To show them ordered according to size rather than interval class, use the /TOTAL switch:

SHOW /TOTAL INTERVALS

Try SHOW LOCATIONS to find where some of these intervals are:

Let's find out where the other perfect fifth is:

SHOW LOCATIONS 3/2

Locations of 3/2:
 3: 0 - 3
 3: 1 - 4  diff. -35.697
 3: 2 - 5  diff. -27.264
 3: 3 - 6  diff. -27.264
 3: 4 - 7
Total of 5

It's found the two exact ones, and also the three approximate ones.

0 - 3 means degrees 0 and 3, i.e. the first and fouth notes of the scale. So this is the obvious one, from the first note of the scale up to 3/2.

Where is the other one?

To find it, click the Make New Seed button in FTS, and tick show degrees , then play the notes with degrees 4 and 7 (p.c. keys '5' and '8')

Septimal minor third:

Locations of 7/6:
 1: 0 - 1  diff.  35.697
 1: 1 - 2  diff.  27.264
 1: 2 - 3  diff.  35.697
 1: 3 - 4
 1: 4 - 5  diff.  35.697
Total of 5

And so on...

Type EXIT or Ctrl+Z to exit the program when finished.

The complete list of SCALA commands is given in the file helpindx.htm in the same folder as the SCALA program.

How it works:

Show current scale in SCALA saves the currently selected scale as xxx.scl in the SCALA folder. It then makes a command file Show_xxx.cmd , and runs SCALA with this as its start up command file.

This is what Show_xxx.cmd is like when first saved:

! Show_Show_xxx.cmd
! Load and show scale xxx.scl
set attribute cents
load xxx.scl
show

This command file loads the file xxx.scl, and shows it in the same format as for the examples given.

However you can edit it to change these commands, and add any other commands you like to it.

For instance, if you want to show something else in the third column, replace the word "cents" by one of the other SCALA attributes in the line:

set attributes cents

Details:

FTS leaves Show_xxx.cmd as it is once made. So any editing you do to this file is preserved. To make it anew, delete the old version, then run Show current scale in SCALA again.

When you make SCALA Scales.lsc . FTS copies all the entries in the .SCL files verbatim, except that it needs to add 1 for the first note of the scale, and to add the word cents after all entries which have a decimal point in them.

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Search scales or modes list

File | Scales options | Search scales or modes list...

This is especially useful for the SCALA modes or scales, because of the large numbers of entries in the lists.

For instance, suppose you want to find the Dorian mode.

Set the Arpeggios or modes list to the default 12 tone list.

Choose All modes... from the list.

The arpeggios or modes list will now show the complete list of all the SCALA 12 tone modes, re-sorted according to number of notes, and numbers of smallest intervals.

Now go to File | Scales options | Search Scales or modes list..

Under What to search , choose Mode / arpeggio descriptions .

Enter Dorian in the words to find, and click Search Now .

There are 5 entries: pentatonic Dorian, chromatic Dorian, Chromatic Dorian inverse, Greek Dorian , Medieval Dorian (ecclesiastical).

You'll see other names listed, separated by commas - these are other names for the same mode. Gr. stands for Greek, and Med. for Medieval (ecclesiastical).

To show them all at once, so that you can compare them, select each in turn from the arpeggio / modes drop down list, and click the Arpeggio... button for each.

Medieval Dorian (ecclesiastical) is the common one.

You can use the same idea to search the SCALA archive of over 2000 scales.

Make the file SCALA scales.lsc as described in the previous section.

Under What to search , choose Scale descriptions .

Then search for whatever you are interested in.

N.B. Since the SCALA archive is continually evolving, your results will depend on the release date of the version you are searching. These results are for the most recent release at the time of writing this (May 2000).

Go to Scales drop down list | More Scales...

and you will see these scales:

Bagpipe scales : result of search for:

bagpipe

Most equal superparticular scales : result of search for:

superparticular

followed by search for:

most

Idiophones : result of search for:

idiophone xylophone marimba

Gamelans - 4 and 5 notes

Gamelans - 6 or more notes

result of search for:

gamelan slendro pelog

This gave 110 scales.

followed by search of the definitinos for:

cent

There are several modern Pelog / Slendro scales using ratios, but all the traditional ones in the archive are measured in cents.

This gave 63 scales

The scales were ordered according to the number of notes using File | Scales options | Sort Scales or Modes list.

A few that remain are modern, but were left in.

If you do want to remove these, to have only traditional gamelan scales, each line in the file corresponds to an entry in the list, so it is just a matter of finding the ones you want to leave out, and deleting the relevant lines.

There are a three gamelans, one with nine and two with eleven notes, which span just under, or just over two octaves, and so obviously fitted in the 5 note list. The one with 9 notes - Gender wayang from Pliatan, South Bali (Slendro) - needed to have 4 added at the second octave to make it into a suitable scale for FTS, since when playing along in FTS, you won't be limited to the compass of the original gamelan. The Tuning of chalung from Tasikmalaya. "slendroid" has detuned octaves and ends with 2413.980 cents 2776.930 cents - one extra note beyond the second octave. To make into a playable scale for FTS, the extra note was left out. FTS will repeat it at the detuned second octave, and you can double octave shift voices using Arpeggio shift from the Channels drop down list above the third column. To shift up by one octave only, choose Arp. degree shift, and shift by 5 notes. The Gamelan selunding from Kengetan, South Bali (Pelog) . has one extra note in the third octave, 202/47 which was removed. For each of these, the original is also left in, with an arpeggio that lets you play the notes of the gamelan only.

Then it was a matter of dividing it into two files, according to the numbers of notes, and copying the line:

@index.lsc@ Index to lists of scales

to the head of the second one, and placing a '+' sign in front of the first scale after that, to mark it as the one to be shown when the file is opened.

The line:

~all *pelog.lmd*

was added before the first of the 7 note scales, to associate them all with the modes file pelog.lmd.

and:

~all *:*

after the last of them to reset to the default list of modes for the last gamelan in the list, which has more than 7 notes.

For all the details of how the LSC files work see: List of scales format

The Canright scales in this list are from On Piano Retuning , Pentatonics I Have Known , and Superparticular Pentatonics , and are useful to have at hand when reading those articles. They were typed by hand, using the LSC format.

If you enter several words, it looks for entries containing any of them. For instance

Slendro Pelog : show all entries with the words Slendro or Pelog .

If you have several words, and want to find entries that include them all, search for each one in turn.

For instance, to find scales with all the intervals of the Pygmie scale, search the scale definitions for each one in turn.

The scale definitions and mode / arpeggio definitions are the ones you see in the Intervals , and Note numbers boxes.

The excludes option works like this:

a b c ... !z !y !x ... : all entries with any of a, b, c and with none of x, y, z.

Example:

Slendro !Pelog : show all entries with the word Slendro, and without Pelog.

!z !y !x,... : any entries with none of x, y, z (i.e. no positive terms is taken to mean select from all entries)

Example:

search scale definitions for:

!3/2 : all scales lacking a perfect fifth.

Searches are for tokens, i.e. sequences of characters separated by white space.

If all the tokens you have entered to search for are alphanumeric, the search treats any non alphanumeric characters in the descriptions such as *:@~ etc as separators, i.e., equivalent to white space.

However if any of your tokens includes a non alphanumeric character such as &*@ etc, it treats it as a non separator for the search, i.e. as part of whatever word it is in.

So for instance, to search for any of the tokens: 2 3 4 5, exact match, and with ' / ' as a non separator, you just need to add " //// " as an extra token

2 3 4 5 ////

That will find any scales with 3, 4, or 5 as entries, but will ignore entries like 3/2 or 5/4, etc. Since the search is for " //// ", this will also ignore any entries consisting of just a single ' / ' (which is used in some of the descriptions of the scales in the SCALA archive).

One can search within previous results, for instance, search for 3/2, followed by 5/4, followed by 7/6 to find all the scales that include all these intervals

To further customise the search, you can prefix any of *, ~ or #

* = any ending, ~ = any beginning, # = exact match.

Use *~ to search for any beginning as well as any ending.

The exact match tick box ONLY affects tokens without prefixes.

exact match is equivalent to #

exact match unticked is equivalent to *

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Sort scales or modes list

Sorts any of the scales. or modes / arpeggios.

Choose which list to sort .

The scale definitions and mode / arpeggio definitions are the ones you see in the Intervals , and Note numbers boxes.

Choose the Sort Method . For instance, by the number of notes.

Then click Sort Now .

Details:

The lists are sorted by making a sort token for each entry, then sorting those alphanumerically.

Look at the Result sort tokens list to see the tokens.

This list can give you useful information about the results of the searches, so will be described here in some detail.

If you click on an entry in the Result sort tokens list, the corresponding scale will be selected in the main window.

A typical entry might be

n___17_ 22

That means, it had 17 notes, and was the 22nd entry in the list before sorting.

Other sort methods are

i = smallest steps first

typical entry:

i___1.01364____5___1.05350___12_ 22

This means it had 5 intervals of size 1.01364 and 12 of size 1.05350, and was the 22nd entry before sorting.

t = most superparticular intervals first.

typical entry:

t___31_ 22

That means, it had 31 superparticular intervals.

a = alphanumeric ordering of the entries.

typical entry:

a_Arabic_17-tone_Pythagorean_(M) 22

s = largest superparticular intervals first - looks for any intervals between any pairs of notes in the scale.

typical entry:

s___3.0____7___4.0___11___9.0___13_ 22

The numbers shown are the denominators.

So it had 7 3/2 s, 11 4/3 s, and 13 9/8 s

If you look at it in SCALA, you will see that it has 16 3/2 s - all except one of the fifths is pure. However the ' s ' search is only for intervals within the scale, and doesn't take account of the octave repeat.

To search beyond the octave, add an o before the s

The o only applies to entries after it.

Search: os

typical entry:

s___3.0___16___4.0___16___9.0___15_ 22

Use k if you want to switch the o option off again.

Reverse sort

You can use ' - ' to reverse sort. This works by subtracting all the numbers from 1000 (for ' a ', it replaces A by Z , B by Y , and so on, and ' 0 ' by ' 9 ', ' 1 ' by ' 8 ' and so on, so it reverse sorts within letters, or numbers, but keeps the numbers before the letters). It applies to all tokens that follow, until a ' + ' is encountered.

So for example -ni+a will sort by most notes first, then by largest steps first, but then because of the +a , will sort alphabetically rather than in the reversed alphabetic order.

One will most often use the alphabetical sort for the descriptions.

To sort the descriptions alphabetically, choose " Scale descriptions for the what to search box.

Since the idea of a number of notes doesn't make sense for the description, those options are always applied to the definitions of whichever list is being sorted by descriptions.

typical entry:

n__983_i_998.98636__995_998.94650__988_a_Arabic_17-tone_Pythagorean_(M) 22

The intervals, and numbers of notes have all been subtracted from 1000. For instance, the 983 is 1000-17 for the number of notes.

You can use ' ~ ' to apply what follows to the second half of the next token only.

For instance: o~-s will apply the ' - ' to the second half of the ' s ' token only, replacing an entry like s___3.0___16 with s___3.0__984

typical entry:

s___3.0__984___4.0__984___9.0__985_ 22

This o~-s is a useful option because it shows the scales with the largest superparticular intervals first, and amongst ones with the same largest superparticular interval, the ones with most instances of it first.

Combine it with ' t ' as: o-t+~-s and you have the scales with the most superparticular intervals first, then of those, the ones with the largest ones first, and amongst those, the ones with most of the largest ones first.

For the options ' s ' and ' i ', which produce lists of several numbers, you can use ' < ' or ' > ' to change the order in which they are shown.

The default is ' < '

For instance: >i to show scales with smallest maximum size of step first

typical entry:

i___1.05350___12___1.01364____5_ 22

You can search the mode / arpeggio list in the same way.

Some of the modes lists, the ones linked to the original list of scales, were sorted using:

n~-i

typical entry:

n____7_i___1.00__998___2.00__995_ 9

This shows least numbers of notes first, smallest steps first, and amongst those, the ones with most of the smallest steps first.

This one had 7 notes, 2 one note steps, and 5 two note steps. In fact, it was the diatonic major scale, steps 2 2 1 2 2 2 1.

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