Tutorials:How use FTS to compose microtonally (verbose)

Intro and motiviation
Tune Smithy is used for retuning music composed using other software such as your composition software or sequencer. By using Tune Smithy and composition software for ordinary twelve tone type composition, it is possible to compose in any tuning by suitably retuning the score.

A few simple examples of what you will be able to do
To take a few simple examples. Suppose you want to compose in seven equal - or a seven tone Thai tuning - one with seven equally spaced semitones to an octave. Then one way to do that is to play the notes from the white keys C D E F G A B C. The black keys can just be ignored. You compose using a normal twelve tone score in your composition software, but the composition when played is in a Thai tuning.

Or you could compose in the Javelan gamelan scales, again on a conventional score, by retuning it with the Pelog scale (which is seven tones to an octave) on the white keys and the Slendro (five tones to an octave) on the black keys.

Of course you can also compose directly in any of the twelve tone temperaments such as Pythagorean twelve tone, quarter comma meantone, Werckmeister III or whatever it is you like to use.

But you can go further than this, there is no need to retune octaves of the score to pitches an octave apart. You can use streteched octaves. Or you could play in the Bohlen Pierce scale repeating at 3/1.

You can even compose in scales such as the overtone / undertone series, or the Lambdoma (or tonality diamond) which don't repeat at all. All you have to do is to decide how to map the pitches to the score.

For instance one common way to handle a non octave scale or one with many notes to an octave is to play successive pitches of the scale from successive white keys - or from all the keys in succession. This you can do as well.

Any key on the score can be retuned to an pitch you desire. The rest is up to your imagination and inspiration.

This tutorial will introduce those ideas by example
This tutorial will introduce those ideas, by example. A short composition is presented for some of the main techniques. By the time you have gone through this page you should be able to retune your pieces to any tuning you desire.

One advantage of the method presented here is that a keyboard player can play your pieces on sight directly from your score. All that is needed is a suitably tuned keyboard, which indeed you could tune in FTS itself.

Tune Smithy needs to be used in conjunction with your composition software or sequencer
Tune Smithy is NOT suitable for composing directly, it is only useful for retuning compositions which you prepare in other software. But because it can retune the midi notes played by other software in real time, then the integration of FTS with your composing software feels seamless once you have it all set up.

You may discover the window in FTS. This can be useful to keep an eye on what is happening while the retuning is in progress and you can even play notes if you click on the window - but it is NOT intended for composing directly. It only shows a limited number of notes, and is very limited in the editing capabilities and the display capabilities. Perhaps some of the ideas used there could be useful for someone planning a truly microtonal notation software (such as the nudge to pitch and alternative score layouts) but I have no plans to develop one myself. It is just too much work. Give me a team of ten programmers and a few years and it might be a different story :-).

find the Composition retuning task
Find the Composition Retuning task http://robertinventor.com/software/tunesmithy/images/tasks_composition_retuning.png in your Tasks folder on your desktop.

This task is the best one to use as it sets FTS up to play each midi In channel on a different FTS part which is what you normally want for notation software retuning.

Just click (or double click) on the icon to start up FTS already configured for composition retuning.

Alternatively - set up your desktop shortcut to do Composition retuning
Do you intend to use FTS mainly for composition retuning? If so you may want to set up the desktop shortcut to start up the Composition Retuning task.

To do that, start up FTS, change to the Composition Retuning task in the menu, then in the File menu use. Then from then on the desktop shortcut will start up FTS suitably configured for composiiton retuning.

Connect your composition software or sequencer to FTS
To get the music from the composition software or sequencer to FTS, you need to use a virtual midi cable.

In brief, you need to select one of the virtual cable devices in the menu of your composition software, and select the same device in the  menu in FTS.

Now, all notes played in your composition software will be played through FTS.

Choose an Out device in FTS and configure FTS to work with it
In FTS, you need to choose an appropriate Out device to actually play the notes. After you select a device in the menu, run the  to test your output device capabilities and set up FTS appropriately to work with it.

Detailed instructions and trouble shooting
For detailed instructions and trouble shooting see virtual midi cable.

Motivation
This is an easy starting point for composers who are used to writing music in the twelve tone system. You use a score which is familiar in all respects, except that it uses some other historical or modern tuning instead of the usual twelve equal. This will give a gentle introduction to what you can do with FTS and your composition software

This example uses quarter comma meantone piece - a tuning in vogue in the period leading up to Bach's time. Many of the major thirds are pure just intonation 5/4s, while one in three of the major thirds are sharp, and one of the fifths is very sharp. It has other interesting intervals that one may want to use in ones composition. You can find information about this tuning at Joe Monzo's Quarter Comma Meantone page. Or wikipedia entry about Quarter comma meantone

Whether you plan to write in it in a conventional fashion or explore its hidden exotic intervals, it would be nice to be able to hear the notes in quartet comma meantone while you are working on the piece :-).

Well, FTS can help you with that. The software notation program or sequencer you use almost certainly plays its notes via midi, and FTS can play midi notes retuned in any way you like. So all you need to do is set your notation program to use FTS to play the midi notes, and set FTS to use the desired tuning, and you will hear all the notes tuned as intended.

How to do it
This is the easiest of the examples. All you need to do in FTS is to select quarter comma meantone as your scale. You can leave the other options at their standard settings.

That's it done. You will now hear your composition in quarter comma meantone. Any controllers, instrument changes and so on should be handled by FTS automatically.

Leave the at, and leave  at the standard setting of. The black keys then play the in-between notes of the scale.

You can alternatively choose Play in Scale - and set to of. For this one it doesn't matter which you choose, but the approach is more flexible when you get to tunings with several tunings available for each accidental.

Trouble shooting (brief)
If this doesn't work, you need to check that everything is connected up properly - or find out how far the notes are getting and what happens to them.

first check that you can play notes in FTS. Show the PC keyboard player - or click the play scale button and make sure that you hear the notes tuned as intended.

Check that you have the virtual midi cable set up properly.

To check that the notes get as far as FTS, and see what happens to them, go to which is in the  drop menu. This will show you each note as it is received from Midi In, along with other details such as which channel it was recieved from, and what note FTS retuned it to.

To find out where the notes go next after FTS, go to - which you can find in the Out menu which will show each note which FTS plays via Midi Out.

If you still don't hear anything, then go to in FTS - and make sure everything looks okay there - and that the device selected isn't muted or set to zero volume. If unsure if you have the right device selected, there may be more devices available from Options | Properties in that window.

Check also that the In device is open in FTS - look at the menu. If it isn't, then select.

If this still hasn't sorted out the issue, then go to the more detailed Retune Compositions with FTS Check List

12 tone example - Andante in QC meantone
Here is an example, my [[Media:andante_in_c_major.mid | Andante in Quarter comma meantone]] for flute and harpsichord

This score is conventional, except for the instruction to retune to QC meantone - other tunings of this piece can be tried as well. I've put the instruction into the Lyric line for the NWC score.

[[Media:andante_in_c_major_source.rly Midi Relaying]] file to set up FTS appropriately.

Here is a [[Media:andante_in_c_major.nwc | NWC file]] for retuning.

The NWC files here are saved scores from Noteworthy Composer. You can also use the free NoteWorthy Player to play them - in the player, you can select the Midi Out device from Tools | Options | Midi.

Here is a midi file which you can open if you have Finale, Sibelius or one of the other notation programs - most should be able to read midi files: [[Media:andante_in_c_major_source.mid|andante_in_c_major_source.mid]]

This piece plays on two instruments simultaneously
You don't have to do any configuring of FTS to make this happen. So long as you run the Out Device Capabilities Wizard, and have set up everything as described here, then FTS should do it all automatically.

I assigned the flute to one staff in NWC, and the harpsichord to the other one, and made sure that they played on different midi channels in NWC - channel 1 for the flute and channel 2 for harpsichord.

There is no need for you as user to know how it is all done. But if you want to know the details of how it has achieved this, you can see it from in the Out menu.

What is a NWC file and why do you use this format for your scores?
It's the save format for NoteWorthy Composer, the program I use for all my compositions.

What I like about NWC is it's design philosophy. I find score entry very fast. Also unlike hte other programs I've tried, it makes it very simple to set bar lines wherever you like. You just type the tab key whenever you want a bar line. That's great if one likes to work with continually varying metres. Where it does fall a bit behind the likes of Finale and Sibelius is in the score output. Particularly its low resolution scores for images for web pages don't work very well - for some reason the lines tend to vary in width - which is why the scores here are closer to printer resolution. It's printed scores aren't too bad. There's a NWC to Lilypond converter for the next version of NWC still in beta which may help.

I will use it for these examples as my compositions are already in this format. If you know an easy way to convert these scores to Finale, Sibelius etc., let me know, or if you want to provide the files and upload them here that would be great.

Associating tunings with your scores for future reference
You need some way to know which tunings to use for which of your scores.

Add a note to the score
If there is just a little information needed, such as the desired scale and arpeggio, with everything else at the standard settings in FTS - it may be enough to just to add a note to your score. To be sure you use the same tuning every time, paste the scale itself from FTS into the score. Then whenever you work on that piece again in the future, do the standard settings again in FTS (if nec.) and copy and paste the scale back into FTS. If necessary do the same with the arpeggio, or anything else you need to keep for a particular score. This is a possibility when there isn't too much information needed to set up FTS appropriately

In these examples, I put the scale - the ratios / cents values - into the lyric line, together with any other retuning instructions that may be needed for a particular piece - that is my usual habit with NWC. If you don't want it to be visible - just put it in an non printing text field somewhere on the score for your own future reference.

Save a project with the same name as the score
If you have a lot of complicated settings to keep for the score, you may want to save a from Tune Smithy. To make sure that you can always see which project goes with which of the saved scores, save the project with the same name as the score and in the same folder. Whenever you open that score, open its same named project, and you have FTS all set up ready to play the score.

The project saves everything, all your Tune Smithy settings including details such as what notation to use to show the scales and notes in FTS, and also the window positions, skins etc. So, it may be more than you need for short or straightforward pieces, but this method is very useful for large complex projects. In fact, the skins can be useful to distinguish between different projects if you have several open at once, and it is often useful to set up all the windows particularly relevant to the project, and use the Help | Show the current windows at start of session (F4) option in FTS to show them all whenever you open that project in the future..

Save a midi relay file with same name as the score
The next option is to save a  Midi Relaying file from FTS, again using the same file name. That is the best method if all you want to save are the settings that affect midi relaying. This saves all your controller settings in FTS and so on, but not things such as notations to use, window positions and skins etc.

Save a Retuning Info file with same name as the score
If you just want to save the minimum information needed to tune it, save as a   Retuning Info  file

The Retuning Info  file saves your current scale and arpeggio and also the midi relaying settings for   In | Options ,  ''' Kbd. Options ,   Kbd regions  ,   Scales For Parts  , and   Scales to Morph To '''. So it saves the settings most relevant for retuning - but doesn't save the choice of controllers etc.

Saving your score for use in the Retuning Midi Player
It is possible to bypass the use of virtual cables by using the Tune Smithy retuning midi player (which you will find in your Tune Smithy Tasks folder)

Save your piece from the notation software as a midi file - best in Midi format 0. Just save it as it does normally, as a twelve equal midi file,

Then save a   Retuning Info  file from FTS using File | Save As | Files of type |    Retuning Info (*.RTN). Be sure to save it with the same file name as the midi clip (also in the same folder), so that the retuning midi player can find it.

Now whenever you play that clip in the retuning midi player it will be played in the desired tuning, You need to have Tasks | Retuning midi player | Read tuning info file if present  selected for this to work (it is the standard setting)..

The idea is that it is like a tune that you can play back in different ways, but always with the desired tuning. So - a sort of a way of extending the capabilities of standard midi just a bit by making it possible to set the preferred tuning for a midi file using another file of the same name with tuning info.

[midi_relaying.htm#top top], [midi_relaying.htm#retune_score start of section]

Scales with other numbers of notes per octave - scordatura scores
Now, that's just a start, because one may want to explore scales with other numbers of notes to an octave, maybe more than twelve for instance. Also one may be interested possibly in nonoctave scales too - ones that repeat at other intervals instead of the octave

This brings up new issues - if you just select any scale in FTS, and then use it to retune a conventional score, depending on the number of notes in the scale, individual notes in the score may no longer sound anywhere near the written pitch.

An example may help. Suppose you have a scale in FTS with distinctions of # and b such as say a 17 or 19 note scale. As that is too many notes to fit in a 12 tone octave on the score, you might set the scale to be played from successive notes in the score, like this:

Score:        C  C# D Eb E  F  F#

Played in FTS: C C# Db D D# Eb E

In this case the note E on the score plays a D#, and the F# on the score plays an E. So the notes you hear are nowhere near the expected pitches for a twelve tone score.

Generally, depending on the number of notes to retune, it is likely that the octave on the score will no longer play an octave in FTS.

This is potentially confusing for a composer on first encounter - but you can get used to it. You can get used to the pitches played by the notes on the score, and the relationships between the notes, and where the chords are in the new retuned score. In fact, some find it refreshing, something that leads one to new avenues of exploration.

Anyway whatever it's advantages or disadvantages for a composer, the result is easily playable by a keyboard player.

The keyboard player doesn't even need to learn what interval the "octave" on the score beforehand to sight read it. Just give him or her your original score as shown in the notation software, and then tune the keyboard identically to the way you tune your score in FTS. So for instance if the score shows an F#, the keyboard player plays the F# key on the keyboard - it will then get retuned by FTS to whatever pitch the composer wishes that key to play. In fact, the keyboard player doesn't even need to know any of the pitches in advance of pressing the keys to sight read such a score. All that is necessary is that the keyboard is tuned in advance to match the score (either by playing through FTS or by tuning it appropriately in advance by whatever method if acoustic).

This is like playing a string instrument with a scordatura tuning - i.e. with the strings retuned to some tuning other than the standard one. So for that reason, to coin a word, let's call this a scordatura score, a term most usually familiar to string players.

For those new to it, here is a bit on the historical context: See this Scottish fiddle tune (on-line). Another example of scordatura is Bach's cello suite number 5 (on-line), intended to be played on a 'cello with the high A string tuned down to G. The idea is that when you read the score (in its original form) the notes on the score for the G string indicate where to place the fingers, rather than the intended notes to hear. So a G as played for instance will be shown as an A on the score, an A will be shown as a B and so on.

A 'cello player can play such a piece from the Scordatura score on a suitably tuned 'cello, using the familiar hand / eye coordination. The A on the score would normally be played on the unstopped A string, so using their familiar hand eye coordination, they play it as such, but because the string is retuned to G, the note they hear is a G. Scordatura is also a feature of music written for the eighteenth century viola d'amore.

So lets call the score you make for retuning via FTS a scordatura keyboard score, since it tells the keyboard player where to place his or her fingers on the keyboard. It doesn't represent the actual pitches heard. This is a relatively new thing because it is only with software that keyboards could easily be retuned to any tuning like this

So, the advantage of a scordatura keyboard score is that it can be sight read by a keyboard player with no further training, using the same hand / eye coordination that they use for a conventional score. Scordatura keyboard scores are suitable for any keyboard instrument, and also other "fixed pitch" type instruments such as a harp, xylophone, accordion, or glockenspiel provided that they are capable of being tuned to the scale shown on the score. Players of these instruments have nothing new to learn to play your piece. They just need to retune their instrument or obtain or construct a suitably tuned instrument for the piece and they are all set to go.

It's not so easy for players of other instruments such as wind, voice, strings etc. to read such a score, so ideally one would want to be able to generate both types of score in one go. See [#keyboard_scordatura_and_other_microtonal_notation_systems Keyboard Scordatura and microtonal notation systems].

Anyway whatever the practicalities for performers, it is a good way also for a composer to get notes quickly on the paper and hear it as you compose in the desired tuning, because you can do it using the existing conventional composing packages with all the features they have. Also many composers work with a keyboard to hand to try out ideas - and for such composers the scordatura keyboard convention is a natural one to use. You can easily pick up your keyboard and try out a few ideas in the middle of composing the piece. To test ideas and variations on your score, just read from your score as you would normally do when testing a piece on keyboard, but be sure to use a keyboard retuned appropriately to match the score.

I think later when someone makes a truly microtonal notation software they will surely need to include the option to generate a scordatura score and to compose directly in it. But a truly microtonal software program would let you generate other types of scores as well for other instrumentalists automatically - unfortunately no such program exists yet anywhere in the world as far as I know. It is a fairly major software challenge, surely rather harder than a twelve tone notation software, and may well require some new ideas too to make it easy to program - but it's not an impossible one. (But beyond my current abilities as far as I can tell, FTS itself is more than enough work for me as it is, without trying to launch into a microtonal notation software program as well).

Let's hope one gets developed!

Meanwhile though, keyboard scordatura works well enough for the time being.

Let's look at some examples of these keyboard-scordatura type scores.

[#top top], [#retune_score start of section]

Scordatura example - Days end song
[days_end_song.htm Day's end song] for Oboe and Cor Anglais. (or [javascript:popup('days_end_song_new_win.htm') open in new window] ).

Midi clip (retuned): [e-cards/days_end_song.mid days_end_song.mid]

NWC score (for retuning): days_end_song.nwc

Midi source (for retuning): days_end_song_source.mid

Midi Relaying file to set FTS up to retune it: days_end_song_source.rly

Again, this is just an ordinary looking twelve tone score - apart from the lyric line which reads:

  White notes play 9/8 5/4 3/2 9/5 2/1 .

So now here is how one would listen to the score in FTS:

From the Midi Relaying view, click the   Standard Settings...  button (you don't have to do this for every piece you do, but if you have been playing a fractal tune or have modified some of the more way out settings, you need to do it).

Set the   Scale  to 9/8 5/4 3/2 7/4 2/1  as shown in the score. You can use the Scale & Arp as text button, or go to the More version of the main window to fine the scale text field.

Set the <font color="#ff8000">  Arpeggio  to <font color="#8080ff">  Follow scale .

Leave <font color="#ff8000"> ''' Play Arp. from  at the standard setting of <font color="#8080ff">  White notes '''.

One can also add a note to the score say what pitch to use for the 1/1 - I use the convention that if omitted, the 1/1 is concert pitch c. To set the pitch for the 1/1 of the scale in FTS, use the <font color="#ff8000">  Pitch...  window. The <font color="#ff8000">  Standard Settings...  button resets it to concert pitch middle c.

For those who are following this with NoteWorthy Composer (or the free Note Worthy Player),use days_end_song.nwc (for retuning to the scale). Relay from NWC to FTS, set up the scale as just described, and you should hear the same pitches played as you hear in the example midi clip. If using other notation software, then start with days_end_song_source.mid.

Note, as this scale is five tone, then the A of the score actually plays a note an octave above the C. In fact, the scale is the normal just intonation pentatonic scale apart from the 7/4 (Bb in C major), which transforms it into a scale with four successive whole tones and including the 1/1 5/4 3/2 7/4 dominant seventh. I could have used alternatively 9/5 or 16/9 (original version had a 9/5 here). The 7/4 gives the most harmonious chords. The 9/5 gives a fairly strongly beating 25/18 between the 5/4 and the 9/5 of the dominant seventh chord.

Here for comparision are all the same files, for the original version of the same piece with the more vibrant ( beating) 9/5s:

[days_end_song_orig.htm Day's end song_orig] for Oboe and Cor Anglais. (or [javascript:popup('Day's end song_orig_new_win.htm') open in new window] ).

Midi clip (retuned): [e-cards/days_end_song_orig.mid days_end_song_orig.mid]

NWC score (for retuning): days_end_song_orig.nwc

Midi source (for retuning): days_end_song_source_orig.mid

Midi Relaying file to set FTS up to retune it: days_end_song_orig_source.rly

In use, this method of composing is pretty much like writing any ordinary twelve tone score. After editing the score, you click the play button in your notation software, and because everything is being relayed via FTS, you hear it with the correct re-mapped pitches. This method lets you hitch into all the facilities of your existing sequencer / notation software. .

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Octave padding example - Hexany recorder trio
When working with scales of six or less notes, sometimes it is nice to be able to show octaves of the scale as conventional octaves in the score. This is also easy to do when working scordatura-keyboard fashion - add a duplicate note to the scale to make it into a seven note scale with a repeating note.

This method may also make it a somewhat easier score for players of other (non keyboard type) instruments to use.

Here is an example with the scale padded out to an octave: my [hexany_recorder_trio.htm Hexany Recorder Trio] (or [javascript:popup('hexany_recorder_trio_new_win.htm') open in new window] )

Midi clip (retuned): [e-cards/hexany_recorder_trio.mid hexany_recorder_trio.mid].

NWC score (for retuning): hexany_recorder_trio.nwc.

Midi source (for retuning):[hexany_recorder_trio_source.mid hexany_recorder_trio_source.mid]

Midi Relaying file to set FTS up to retune it: hexany_recorder_trio_source.rly

To retune, set the <font color="#ff8000">Scale to <font color="#8080ff"> 8/7 6/5 48/35 8/5 12/7 12/7 2/1  as shown in the score. Set the <font color="#ff8000">  Arpeggio  to <font color="#8080ff">  Follow scale . Leave <font color="#ff8000"> ''' Play Arp. from  at the standard setting of <font color="#8080ff">  White notes '''.

I wanted to try playing along with on recorder using alternative fingerings to play in the hexany tuning. Since I wanted to read it on the recorder, this was easier if the octaves on the score corresponded to what I know as octaves, e.g. all the Cs plays 1/1 and octaves above / below that, the D of score plays the 8/7 etc. Anyway this is the kind of thing one can experiment with and see what one finds easiest.

I did this retuned midi clip in NWC - just played it all the way through in one take retuned in FTS - you can do this because of the way NWC respects all the dynamics, tempi and flow directions in the score. You can also save it to a twelve equal midi file in NWC and play that in FTS using the retuning midi player.

[#top top], [#retune_score start of section]

Example using accidentals - Graham Breed's blues scale
Let's take another example, this time my tune in [Graham_Breed_blues_scale.htm Graham Breed's blues scale] (or [javascript:popup('Graham_Breed_blues_scale_new_win.htm') open in new window] ),

Midi clip: [e-cards/Graham_Breed_blues_scale.mid Graham_Breed_blues_scale.mid].

NWC score (for retuning): Graham_Breed_blues_scale.nwc

Midi source (for retuning):[Graham_Breed_blues_scale_source.mid Graham_Breed_blues_scale_source.mid]

Midi Relaying file to set FTS up to retune it: Graham_Breed_blues_scale_source.rly

This is another one in a 12 tone scale like the Andante in Quarter Comma meantone - but a bit more exotic in its tuning.

To retune, set the <font color="#ff8000">Scale to 133.0 182.4 386.3 449.3 498.0 653.2 680.4 835.6 884.4 947.3 1151.2 1200.0

I just thought this is a good point to mention the two ways of playing such a piece.

One way is to leave it at the standard setting of <font color="#8080ff">Play in Arpeggio with <font color="#ff8000">Play Arp From as <font color="#8080ff">  WhiteKeys  and set the <font color="#ff8000">  Arpeggio  to <font color="#8080ff">  Diatonic . The black keys are then treated as accidentals of the arpeggio, and will play the in between notes. This is the standard setting for Midi relaying. It is somewhat more versatile when you want to change to another tuning with more than twelve notes, as the arpeggio will still play the white notes, even if the new tuning has too many accidentals for all the black keys - see [midi_in.htm#Playing_accidentals Playing fine shades of accidentals from the music keyboard].

Some prefer to set FTS to <font color="#8080ff">Play in scale, and play the scale from <font color="#8080ff">All keys.

Both approaches have the same effect for a twelve tone scale, so you can use either method with this one.

[#top top], [#retune_score start of section]

Non octave scale example - Jacky Ligon's golden meantone
You can use non octave scales with this scordatura-keyboard method too - there is no need for it to repeat at the octave. I chose one of Jacky Ligon's non octave scales for this example.

See my tune in [jacky_ligon_golden_meantone.htm Jacky Ligon's golden meantone non octave scale] (or [javascript:popup('jacky_ligon_golden_meantone_new_win.htm') open in new window] ),

Midi clip: [e-cards/Jacky_Ligon_golden_meantone.mid Jacky_Ligon_golden_meantone.mid].

NWC score (for retuning): Jacky_Ligon_golden_meantone.nwc

Midi source (for retuning):[Jacky_Ligon_golden_meantone_source.mid Jacky_Ligon_golden_meantone_source.mid]

Midi Relaying file to set FTS up to retune it: Jacky_Ligon_golden_meantone_source.rly

Successive "white keys" of the score this time play an eight note mode of Jacky Ligon's non octave golden meantone scale (the cents values for the scale are given on the score and so are the scale degrees for the mode).

To retune this score, leave it as <font color="#8080ff">Play in Arpeggio with <font color="#ff8000">Play Arp From as <font color="#8080ff">  WhiteKeys. Then just enter the <font color="#ff8000">Scale  and <font color="#ff8000">  Arpeggio  from the score in the main window, and relay in the normal way.

So set the <font color="#ff8000">Arpeggio to: 1 5 6 9 12 13 16

and the <font color="#ff8000">Scale to Jacky Ligon's Golden Mean non octave scale 75.120 121.546 196.666 318.212 393.332 439.758 514.878 636.424 711.544 757.971 833.090 954.637 1029.756 1076.183 1151.302 1272.849

This time the scale is non octave, and the mode repeats every 8 white keys. So c plays the 1/1, d' plays the first repeat of the scale, which is at 1272.849 cents, and so on.

So - a "very scordatura" score you might say.

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Other examples
For more info about these pieces, and a fair number of other pieces composed in the same way composed with NWC and FTS, see my on-line page: Tunes. You will find some other techniques there - particularly- the use of an extra line in the score to change the root key of a piece - as explained in the section [#tonic_shifts Tonic shifts and Tonic Drifts].

For mp3s of some of them: Robert Walker (mp3.com.au)

And that basically is it. Any questions, do please contact me!

[mailto:support@tunesmithy.co.uk support@tunesmithy.co.uk]

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