FAQ - Scale Construction - auto

How do I make my own scales?
This is pretty easy to do in FTS.

If familiar with the notation, you can just enter the scale you want to use in cents or ratios notation.

If using cents, be sure to add the word cents after each entry, like this:

  235.419 cents 453.56 cents 704.786 cents 927.453 cents 2/1 

Also be sure to include the   2/1  at the end of the scale if you want it to repeat at the octave. FTS can make non octave scales too, so if you leave out the 2/1 then that scale will repeat at the interval of   927.453 cents  - or whatever the last entry in the scale might be.

An alternative is to select   File | scale notation | Use SCALA convention: decimal points for cents  - you will probably want to do this if you do much scale constrcution as it makes it faster to enter scales in cents notation. If the number has a decimal point, such as 386.0 it is understood as a value in cents. Without a decimal point 386 gets read as 386/1.

The example scale would then be

  235.419 453.56 704.786 927.453 2/1 

For an introduction to these two notations see [cents_and_ratios.htm cents and ratios].

Another shortcut for cents notation is to prefix a number with an apostrophe, so '386 means 386 cents

To enter your scale in Hertz - see [More_scales.htm#Special_notations Special notations ] . That section also has yet another shortcut method for entering values in cents.

If you need more space to enter your scale, there's a special window for entering large scales:   Bs | Scale and Arpeggio as Text  (click on the   T...  button after the scale play button).

To save your scales, use   File | Save As | Files of Type |    SCALA Scales (*.scl) . You'll also find buttons to save and open scales in the   Scale / Arpeggio as Text  window.

If you have a large scale, you will probably want to make arpeggios for it - to play subsets of the scale. You may want to make your own arpeggios list for it too possibly. See  [Seeds.htm#New_arpeggios  Make new Arpeggio ], and [Seeds.htm#edit_arp_drop_lists Editing the Arpeggio drop lists].

Another way to make the scale is to click and select notes from other scales, use   Bs | Scale... . Here you will find a drop list of several scales with useful pitches in them - select one of these and click to add some of its intervals to your scale, then select another to add more. When your scale is ready, then use the   Main win...  button below the keyboard picture to copy it into the main window. See also [Seeds.htm#New_scales <font color="#0000FF"> Make new Scale ], and [Seeds.htm#save_scale How to save your scale].

You can add notes from equal tempered scales from this window too, with any number of notes to an octave or non octave. Just type the number of notes you want per octave into the <font color="#FF8000">  Equal Steps  window. You can also [Seeds.htm#equal_divisions_of_non_octave make equal divisions of a non octave] here too.

If you are into meantone scales, then select <font color="#FF8000">  Mean Tone...  and you will get a dialog to enter the amount of the comma and the position of the wolf fifth. Then click <font color="#FF8000">  Apply , then click <font color="#FF8000">  Select All  in the <font color="#FF8000">  Scale...  window. See [Seeds.htm#new_meantone_scale New mean tone scale].

There are other scale construction options from <font color="#FF8000">  Bs | Scales Options... . See [More_scales.htm <font color="#0080FF">Scales ]

These are basically just a few common scale construction options, plus some others that I happen to have got involved in. For a thorough and complete scale construction program, use Manuel Op de Coul's SCALA.

See [More_scales.htm#SCALA_scales <font color="#400040">SCALA scales ] <font color="#400040">.

You can show scales from FTS in SCALA using <font color="#FF8000">  Bs | Scale Options | SCALA Scales | Show currrent scale in SCALA , e.g. to analyse them, and you can show SCALA scales in FTS using <font color="#FF8000">  File | @Smithy  in SCALA.

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How do I enter a scale in Hertz?
First, to show the scales in hertz notation go to <font color="#FF8000">  File | scale notation | Hertz 

Then to enter the scale in hertz use the same notation - all the notations you can use to show scales in FTS can also be used to input the scales. So, just follow the same pattern - add the word Hz after each entry like this:

<font color="#0080FF">  300 Hz 350 Hz 450 Hz 600 Hz 

There's a shortcut too - you can prefix the entire scale with a z:

<font color="#0080FF">  z 300 350 450 600 

See [More_scales.htm#Special_notations <font color="#400040">Special notations ].

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How do I convert a ratio to cents?
<font color="#FF8000">  File | scale notation | Calculator 

Set the <font color="#FF8000">  Expression  to <font color="#0080FF">  Ratios or Decimal 

Set the <font color="#FF8000">  Value  to <font color="#0080FF">  cents 

Type in a ratio here and you will see its value in cents.

Alterntively, use the javascript applet in the [cents_and_ratios.htm <font color="#400040">Cents and Ratios ] <font color="#400040"> page. (You are welcome to add this applet and the others in this help to your own web pages too BTW).

Use <font color="#FF8000">  File | scale notation | Cents  to show all the scales in cents.

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How do I convert cents to a ratio
Here, the thing is that the cents value will only approximate the ratio - maybe very accurately or maybe less so. So there will be a whole range of ratio values you could convert it to, depending on how close to the cents value you want them to be.

The web page in this help: [ratios_with_factors.htm <font color="#400040">Find all the best ratios for a scale in cents ] <font color="#400040"> shows all the approximating ratios found. (this uses javascript, which menas the calculations are slower, okay for small quotient ratios.).

In FTS, you can use the calculator again:

Set the <font color="#FF8000">  Expression  to <font color="#0080FF">  Cents 

Set the <font color="#FF8000">  Value  to <font color="#0080FF">  Same as scale 

Then from <font color="#FF8000">  Ratios Options 

enter the desired <font color="#FF8000">  Tolerance in cents to use for approximate ratios 

- say <font color="#0080FF">  20  cents by way of example.

You also want to select <font color="#FF8000">  File | scale notation | Cents or small ratios 

Now enter a value in cents, say, <font color="#0080FF">  300 . You will see the <font color="#FF8000">  Value  field show <font color="#0080FF">  6/5~ . The ~ indicates that it is an approxmate value.

Reduce the tolerance to say 10 cents, and this will show <font color="#0080FF">  19/16~ 

That uses the nineteenth harmonic, which is rather rare. Maybe one is interested in a ratio involving smaller prime factors. To do this, enter, say, 2 3 5 7 in the <font color="#FF8000">  Ratios Options | Factors to use for approximate ratios  - and now it will show <font color="#0080FF">  32/27~  - the pythagorean minor third, which is closer to equal tempered one than the just minor third. Set the tolerance to 2 cents, and you find <font color="#0080FF">  25/21~ . Set it to 1 cent, and now there are no ratios to find within range so it just shows 300 cents.

Actually there are closer approximations - there always are, but they will involve truly enormous quotients. You can go a little higher using the <font color="#FF8000">  Max quotient for Approximate ratios  box - but this slows down the calculation - and the next one is too high for this anyway for this one. If interested in ratios with really large quotients, I have a tiny MSDOS program to find those - let me know if you want it (I may port it to a windows app. at some point).

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How do I show the scale in various notations, such as hertz,. as cents values or the nearest ratios?
Use <font color="#FF8000">  File | scale notation  <font color="#400040"> and simply change the selection there to the notation you want to use.

Also, note that you can use the [ratios_with_factors.htm <font color="#400040">Find all the best ratios for a scale in cents ] <font color="#400040"> applet to convert an entire scale to / from hertz, ratios, cents and n-et notation.

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How do I look for a particular scale in the SCALA archive from FTS? (tutorial)
First you need to download the SCALA archive, and make the drop list of SCALA scales for FTS to use. See [FTS_and_SCALA.htm Setting FTS up for SCALA and vice versa].

Now go to <font color="#FF8000">  File | More Scales drop lists , or <font color="#FF8000">  Scales |  <font color="#0080FF">  More Scales drop lists  (look in the drop list of scales) and you should see an entry <font color="#0080FF">  SCALA Scales . Select that one. The scales drop list will then change to show all the scales in the SCALA archive. You can select any of them from the list.

If you don't see this entry yet, check that you have completed the instructions in [FTS_and_SCALA.htm Setting FTS up for SCALA and vice versa].

Now go to <font color="#FF8000">  Bs | Scales Options | Search Scales or arpeggios list .

Enter your search term in the <font color="#FF8000">  words to find  field. E.g. if you want to find temperaments, enter <font color="#0000A0">  temperament  here.

Now, maybe you decide that list is too long for your current purposes, and you want to refine it to ones with the word <font color="#0000A0">  well temperament . Just repeat the search, this time with the word well. Each time you search the main window scales drop list in its current form after the previous searches - i.e. it is a search   within   the previous results.

That gives a more managable list. Now maybe you want to save it - to do so just use <font color="#FF8000">  File | Save As | Files of type |  <font color="#0080FF">  Lists of scales (*.lsc)  and enter the name you want to use, e.g. " <font color="#0080FF">  Well temperaments from the SCALA archive  ".

To get back to your new drop list of scales at any time, go to <font color="#FF8000">  File | More Scales drop lists  and you will see your new drop list there - or at least you will if you have this check box selected (which is the standard setting) - select it if necessary before you make the drop list of scales:

<font color="#FF8000"> ''' Bs | Scales Options | SCALA Scales | Make / remake scales / modes drop lists ...  <font color="#0000FF">  (Alt + Shift + 6)  <font color="#FF8000">  | Add scales drop lists to the More Scales drop list whenever they are saved or opened '''

To get back to the original SCALA scales drop list again ready for a new search, you need to re-open it using e.g. <font color="#FF8000">  File | More Scales drop lists , and select <font color="#0080FF">  SCALA Scales  again.

You can search for several words in one go - if you had searched for <font color="#0080FF">  well temperament  in the first place it would have had the same effect.

For more about this see [more_scales.htm#Search_scales_or_modes_list Search scales or Arpeggios].

Tip:
If you plan to do a number of searches, it can be useful to use <font color="#FF8000">  Bs | Arpeggio...  as that makes a copy of the main window scales list. Then in that window, unselect the <font color="#FF8000">  Sync scale with m. w. 

Now you can do searches in the main window and whenever you have refined the list to a small number of scales, you can then get back to the big list again by using the <font color="#FF8000">  Main win <-...  button in your <font color="#FF8000"> ''' Arpeggio..  . window - which is faster than going to <font color="#FF8000">  File | More Scales drop lists  and then selecting <font color="#0080FF">  SCALA Scales ''' again from the drop list.

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Why is a distinction made between arpeggios and scales - why not just have scales?
If you only have scales, then you will find that you have many ways of retuning the same scale, e.g. a major scale. You will then have to provide separate tunings for each one - e.g. a Quarter Comma Meantone major scale on C with the wolf at G# to Eb etc. This is impractical as there are hundreds of twelve tone tuning systems, and hundreds of arpeggios listed for each, each of which could start on any of the twelve notes of the tuning (except of course in twelve equal where all positions will sound identical).

So basically the reason is to reduce the size of the lists. It is also frequently useful to work with arpeggios if you are making a scale by selecting notes from a larger scale. A composer or musician may want to make a particular master scale - which only needs to be done once. Then he or she can make a drop list of arpeggios to select notes from this scale to use for particular movements or sections in a composition, or sections of an improvisation and so on.

The arpeggios get used in an even more general fashion in the fractal tunes, as you can make arpeggios that change direction, go below the 1/1 at times, or maybe go up to the octave or second octave then down to the fifth before the next repeat. This complex interaction of arpeggios and seeds sometimes helps to create some fascinating fractal sound worlds.

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Why call them Arpeggios? Mode sounds much better.
Yes indeed, and these are usually referred to as Modes in tuning circles so this is entirely understandable.

A mode in this sense is any selection of notes from a larger master scale. They can ascend and descend by different routes too, as in Indian or Arabic modes..

However, in FTS I use <font color="#FF8000">  Arpeggio  even more generally than this, since they can change direction mid course, or have repeating notes, or even have negative values too to go below the 1/1 of the master scale - all of which can be useful in fractal tunes. This is perhaps a little too general to be able to call them modes in the tuning sense.

Another reason for calling them arpeggios rather than modes is that there is some risk of confusion with modal music. The use here is similar enough to the tuning concept to be potentially confusing to newbies, e.g. for those who have a background in Irish or Scottish folk music, which still uses the ancient system of modes. Indeed, it could confuse players of Jazz too. In this context a mode is understood as a particular sequence of whole tone and semitone steps, rather than as a selection of notes from a larger scale. See this site: A Beginner's guide to Modal Harmony. Other sites: In search of the Wild Dulcimer (table of contents). For modes as used in Jazz, see. Jazz Modes.

I did originally call them modes in the interface, but changed to Arpeggio to help reduce confusion for newbie users.

Tuning specialists and those who are already familiar with this field can read Arpeggio in this help to mean Mode in nearly all the contexts in which it is used - except for a few cases where the fractal tunes are discussed. In those examples it may be used too generally to count as a mode, and is best understood as an <font color="#FF8000">  Arpeggio .

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I would like to use arpeggios which ascend one way and descend another way as in Indian or Arabic modes. Can FTS help with this?
Yes it can!

It is an easy matter to add such modes to FTS - you can use the melodic minor as a model for how it works. You can find this in the twelve tone scale arpeggio lists

For details, see How to Make New Arpeggios - that mainly focusses on how it is done interactively in FTS.

To summarise briefly, it's done like this:

0 2 3 5 7 9 11 12 " 0 2 3 5 7 8 10 12

where the numbers are scale degrees, the first half before the double quote is the ascending mode and the second half is the descending one. So this means that it will ascend 7 9 11 12 and descend 12 10 8 7.

Something to be aware of - your arpeggios will need to ascend and descend by the same number of white notes per "octave" of the midi keyboard layout - so if it has fewer notes ascending than it has descending or vice versa, just repeat some of the notes in oneof the directions. You would do it so that the others still align up like this:

0 2 3 5 7 9 11 12 "  0 2 3 3 7 8 10 12

(melodic minor with the fourth left out in the descending arpeggio - you just repeat the previous note at that point).

The melodic minor arpeggio is mainly included here for use in fractal tunes. It may not be so very useful for keyboard work in Western music, except for beginner keyboardists - as it is easily fingered. After all in Western music one has only twelve keys and a keyboard designed for the scale one is using, and only one such mode to learn. However it is possible that in Indian and Arabic music, these modes may be rather useful indeed. They would also be exceedingly useful for making fractal tunes too as you could make tunes that automatically follow the traditional modes.

If anyone is interested in compiling such a database in a form useful for performers of Indian or Arabic modes, please contact me. The only database I have is the one for Scala which ignores such differences between ascending and descending modes.

If you have the database already prepared in some particular notation system, or just prefer to use your own notation system to make it, no need to convert it by hand. Just let me know as it is normally a fairly trivial matter to program FTS to be able to read a new notation system too - at least if it is a notaton system that can be presented in text format.

You could just get FTS to read your database all in one go and make an arpeggios list from it. Just let me know how the notation system works - with a list of all the symbols used and what they mean - so I can program FTS to read it :-). Don't worry if it seems a little complex either and takes a while for people to learn - I don't need to learn it myself, only need to know what the rules are so I can program them, and then from then on FTS will be able to read it.

More information: for arabic modes, The Arabic Maqam World, Near Eastern Modes. For Indian modes, see The sound of India.

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[faq_scales.htm#why_scale What is a scale?]

Well in general use, the scale is pretty similar anyway. You talk about practicing arpeggios and scales. Then you say a piece is in say the key of D minor meaning that the home scale for the piece is the scale of D minor.

However, this doesn't tell us whether it is in twelve equal, or quarter comma meantone, or in Werckmeister III - the terminology ignores tuning distinctions.

In this field of the study of tuning systems, it is usual to use the word Scale to refer to the precise tuning used. Discussions, literature and other programs use the word in this sense, and that is how we will use it. There doesn't seem to be any reasonable alternative. We can reserve the word <font color="#0000FF">  key  for the other usage. Just keep in mind that scale here has aquired a new meaning - the particular precise tuning used, usually presented in cents or ratios notation.

In this notation, the home note of the scale gets called the 1/1, or 0 cents, whichever key it is in. You change the key by changing the pitch of the 1/1.

Tuning is too broad in its meaning nor it seems is there much risk of confusion. So far no-one seems to have got confused by the use of the word Scale in this sense to my knowledge.