William, I'd say your modesty is a tad too far forward ... again, lol. (I think it can pay sometimes to "wear a few tassels, and bob and weave a bit", lol.) I recall your effort to retune Althyria's theme into orchestral intonation, using VIPro's tuning files and a little bit of guidance and info from me. Alas (my fault) it turned out to be an impractically difficult and long-winded thing to attempt in VIPro for the fair sized orchestra required by Althyria. But then, as I recall, you chose to make a wonderfully engaging, energetic and enjoyable mockup of a 16th or 17th century dance piece by Michael Praetorius, using one of VIPro's preset tuning files to intone the whole piece in Just Intonation. You got that piece rocking! (So I hope you'll excuse me for not buying that "I haven't worked with alternative tunings in VIPro" comment lolol. I read "alternative" as meaning anything other than ET.)

Yes, Hermode tuning is indeed aimed at automatically modelling the various small but vital pitch adjustments that orchestral players - especially brass players - typically make in order to keep harmonies sounding pure, clean and stable. But unfortunately, the Hermode model is fundamentally compromised by being tied to ET root progressions, which kinda waters down if not pollutes the clever intonation trickery going on above. Hence it can't quite pull off the trick of flawlessly mimicking real orchestral intonation - unless the piece being played is simple and happens to stay very close to ET pitches, never modulating too far away.

I'm in no doubt that your long experience as a player in orchestras and bands is a huge reason why I find all your original compositions speak the language of orchestral music so very fluently - despite the indignity of their having to be mocked up in ET.

At this point I'd want to slip in a promotion for my Situater orchestral intonation subsystem for Logic, saying something like Situater really does it for real - no compromises. But ... since the brilliant, nice folks at Apple have so very kindly f****d up Logic's Environment really badly to the point where Situater stands no chance of working at all, I'll not mention it. Aahh, these are the breaks.

I don't think Macker appreciates the major advances in harmonic thinking that equal temperament gives us as composers, which is why so many great musicians, at least in the Western world, embraced it and still do. ET allows musicians to employ modulation; modulation being one of the most important aspects of long-form works, at least up through the 20th century and for some composers, including current practice.

Without the ET tuning system that allows for all 12 major and minor keys to remain in tune, achieved by tuning 1/2 steps so that each semi-tone is 1.05946 (12th root of 2), times the frequency of the previous tone, moving from one tonal plane to another, whether through cadentially prepared modulation, abrupt modulation, or any other method, would have been impossible. The theory of Western tonal and modal harmony is based on the idea that modulation to either close or distant keys is an approach to composition that is highly valuable, adding to the complexity and dramatic aspects of music. None of the great symphonies of Mahler, Mozart, Beethoven, Brahms or Haydn could have been composed without the invention of equal temperament. Bach was so enthusiastic about this new tuning that he wrote the 48 preludes and fugues, all in different keys,--a feat that would have not been possible before ET. Additionally, the use of secondary dominants is a technique composers from the baroque period to jazz and pop musicians have used consistently. A progression like G7-C7-F7-Bb7-Eb7 etc could never have been used prior to ET, the earlier tuning systems would have made that impossible. A chain of secondary dominants is another example of the flexibility of ET that allows for modulation and moving tonal centers around to create drama, tension and interest.

Imagine inviting a singer over to your house in the year 1522. You're all ready to rehearse your new song that you just finished. But the talented singer is having difficulty with the range of several of the notes, they're just too low to get the effect and mood desired. The composer cannot simply transpose the piece to a higher key, or tonal plane, the keyboard instrument will go out of tune. This situation is what prompted musicians to seek a tuning system that had more flexibility, and in doing so allowed for modulation to become a well-utilized technique that most of us now take for granted.

There are some drawbacks to ET, one being the slight tuning adjustments to the octave and 5th that create new tensions in the harmonics and overtones of instruments. If we take a chord, for example, like an F# minor maj 7+11 (f#,a c#,e#, b#), each particular tone's harmonics will create dissonances that a "pure" tuning system (one that follows exactly the division of the octave into its natural, Pythagorian order) will not produce. But this is also the beauty of the compromise, the ability to compose music in any key where each type of chord, regardless of its root, will be equal in terms of its tuning, consonance and dissonance, taking into consideration of course the subjectivity of say, how a d7#9 "feels" relative to an F7#9 or a B-flat7#9.

Direct experience through the daily practice of music, either as a player, composer, singer or conductor, teaches us things about music that no theoretical knowledge or "book knowledge" can give us. This doesn't mean that books are not highly useful, but rather that any art is comprised of theory and practice. One cannot replace the other. It's through direct experience that composers refine their techniques, their language, style, form and content. I know musicians that choose to work in non-Western tuning systems--which is fine if that's what you want to do. But for myself, ET still has great untapped potential to realize new music. And of course ET doesn't mean we cannot bend notes or use 1/4 tones, because we can, just as blues and rock guitarists have been doing for a very long time. MIDI tuning commands like pitch bend or other assigned control changes (CC) allow us to raise or lower the pitch of any note from 1 to 99 cents, which is more than adequate to experiment with tuning if we choose to. Keep in mind that a quarter tone has a span of 50 cents, so changing the MIDI tuning of a tone by 25 cents gives us an 1/8 tone--and we can go even smaller when desired. That's quite a bit of flexibility!

Knowledge of any art requires the practice of that art, theory alone won't do. It would be like one claiming to be an expert on the taste of dark chocolate merely by studying the ingredients carefully and comparing all the various brands of dark chocolate without ever having actually tasted dark chocolate. So much for intellectualizing that which can only be gained experientially!

Jerry

JSG, I disagree. You go your way and I'll go mine.

And you presume I'm just a theorist? Lolol. Dude, life tip: don't presume; you clearly suck at it and showing off your ignorance rudely like that just reveals a lot of bad stuff about you.

Toodle-pip.

VEP Feature Request

Been thinking more about the VIPro tuning files thing, and how Synchron Player could perhaps be helped in that regard. Then had a spanking idea! (Though VSL might already be way ahead of me, lol.) What I describe here goes far beyond the functionality needed simply to play the fujara library live with authentic intonation.

How about, for VEP 8 or 9, a centralised intonation feature (western orchestral and perhaps some other schemas too) in VEP's metaframe that operates on all Synchron Players and VIPro Players in all instances - maybe even on Kontakt, synths and perhaps other sample players too (given that they provide suitable pitch control access)?

This would involve one or more banks of 12-note "casts". Each cast specifies the precise pitch class to be used for each of the 12 keyboard note classes whenever played live or in playback. The pitch class specification includes the note name and whether a syntonic comma up or down should be applied; also whether or not that note should be ET if needed, for example, to prevent the orchestra momentarily straying too far away from the limited useful range of piano pitch classes, in a piano concerto. Any cast in the bank can be selected at any time. The current cast can be transposed up or down by 5ths, up to, say ±10 5ths. Cast selection or transposition can be done manually, remotely or by automation, in realtime speed. Editing, saving, copying and pasting casts are possible.

Without resorting to an exotic keyboard with more than 12 keys per octave (perhaps along the lines of, say, that designed by Nicola Vicentino in the 16th century), as far as I know there is today no other way of using a MIDI keyboard to play live with complex intonation, such as the European orchestral schema. In short, what I've outlined here is more than just a novelty. It's a further (and long overdue) innovatory step in the digital music revolution.

This is basically what my Situater orchestral intonation subsystem does in Logic. I've always intended it to be a non-profit, open-source thing and always wanted the DAW makers to copy or adapt it in their own ways for their DAWs. But stupidly, up until now I hadn't realised that VEPro too is superbly capable of embodying its own Situater-like feature!

I know you don't comment, one way or the other, on possible future products or new features, VSL, and of course I'm fine with that.

@Jerry Gerber said:

I don't think Macker appreciates the major advances in harmonic thinking that equal temperament gives us as composers, which is why so many great musicians, at least in the Western world, embraced it and still do. ET allows musicians to employ modulation; modulation being one of the most important aspects of long-form works, at least up through the 20th century and for some composers, including current practice.

Without the ET tuning system that allows for all 12 major and minor keys to remain in tune, achieved by tuning 1/2 steps so that each semi-tone is 1.05946 (12th root of 2), times the frequency of the previous tone, moving from one tonal plane to another, whether through cadentially prepared modulation, abrupt modulation, or any other method, would have been impossible.  The theory of Western tonal and modal harmony is based on the idea that modulation to either close or distant keys is an approach to composition that is highly valuable, adding to the complexity and dramatic aspects of music.  None of the great symphonies of Mahler, Mozart, Beethoven, Brahms or Haydn could have been composed without the invention of equal temperament.  Bach was so enthusiastic about this new tuning that he wrote the 48 preludes and fugues, all in different keys,--a feat that would have not been possible before ET. Additionally, the use of secondary dominants is a technique composers from the baroque period to jazz and pop musicians have used consistently.  A progression like G7-C7-F7-Bb7-Eb7 etc could never have been used prior to ET, the earlier tuning systems would have made that impossible.   A chain of secondary dominants is another example of the flexibility of ET that allows for modulation and moving tonal centers around to create drama, tension and interest.  

Imagine inviting a singer over to your house in the year 1522.  You're all ready to rehearse your new song that you just finished.  But the talented singer is having difficulty with the range of several of the notes, they're just too low to get the effect and mood desired.  The composer cannot simply transpose the piece to a higher key, or tonal plane, the keyboard instrument will go out of tune.  This situation is what prompted musicians to seek a tuning system that had more flexibility, and in doing so allowed for modulation to become a well-utilized technique that most of us now take for granted.

There are some drawbacks to ET, one being the slight tuning adjustments to the octave and 5th that create new tensions in the harmonics and overtones of instruments.  If we take a chord, for example, like an F# minor maj 7+11 (f#,a c#,e#, b#), each particular tone's harmonics will create dissonances that a "pure" tuning system (one that follows exactly the division of the octave into its natural, Pythagorian order) will not produce.  But this is also the beauty of the compromise, the ability to compose music in any key where each type of chord, regardless of its root, will be equal in terms of its tuning, consonance and dissonance, taking into consideration of course the subjectivity of say, how a d7#9 "feels" relative to an F7#9 or a B-flat7#9.

Direct experience through the daily practice of music, either as a player, composer, singer or conductor, teaches us things about music that no theoretical knowledge or "book knowledge" can give us.  This doesn't mean that books are not highly useful, but rather that any art is comprised of theory and practice.  One cannot replace the other.  It's through direct experience that composers refine their techniques, their language, style, form and content.  I know musicians that choose to work in non-Western tuning systems--which is fine if that's what you want to do.  But for myself, ET still has great untapped potential to realize new music.  And of course ET doesn't mean we cannot bend notes or use 1/4 tones, because we can, just as blues and rock guitarists have been doing for a very long time.  MIDI tuning commands like pitch bend or other assigned control changes (CC) allow us to raise or lower the pitch of any note from 1 to 99 cents, which is more than adequate to experiment with tuning if we choose to. Keep in mind that a quarter tone has a span of 50 cents, so changing the MIDI tuning of a tone by 25 cents gives us an 1/8 tone--and we can go even smaller when desired.  That's quite a bit of flexibility!

Knowledge of any art requires the practice of that art, theory alone won't do. It would be like one claiming to be an expert on the taste of dark chocolate merely by studying the ingredients carefully and comparing all the various brands of dark chocolate without ever having actually tasted dark chocolate.  So much for intellectualizing that which can only be gained experientially!

Jerry

This is totally specious and incorrect.  The reason Bach loved ET was because on an organ or a harpsichord he could play and compose with a lot of modulations. That has nothing whatever to do with orchestral or ensemble playing by musicians that instantly and intuitively alter their tuning based upon just LISTENING.  jsg - they don't adhere to ET when modulating from the key of C major to f sharp minor! Do you actually think that?   What they do is listen as they are playing and adjust the tuning instantly - if they are good musicians - based upon a tuning that sounds "right."  It is  not based upon ET of a previous key,  even remotely. So this comment is entirely wrong and based upon a keyboard player - jsg - who is used to fixed tunings, and making a sweeping statement about all tunings - which has nothing to do with the reality of playing instruments other than keyboards or harps, celesta or vibes, etc. in an orchestra or ensemble. If it's a piano concerto, that is a different matter, because then the players are forced to tune to the ET piano.        

@William said:

This is totally specious and incorrect.  The reason Bach loved ET was because on an organ or a harpsichord he could play and compose with a lot of modulations. That has nothing whatever to do with orchestral or ensemble playing by musicians that instantly and intuitively alter their tuning based upon just LISTENING.  jsg - they don't adhere to ET when modulating from the key of C major to f sharp minor! Do you actually think that?   What they do is listen as they are playing and adjust the tuning instantly - if they are good musicians - based upon a tuning that sounds "right."  It is  not based upon ET of a previous key,  even remotely. So this comment is entirely wrong and based upon a keyboard player - jsg - who is used to fixed tunings, and making a sweeping statement about all tunings - which has nothing to do with the reality of playing instruments other than keyboards or harps, celesta or vibes, etc. in an orchestra or ensemble. If it's a piano concerto, that is a different matter, because then the players are forced to tune to the ET piano.        

You're right, I stand corrected.   Of course string players and singers are constantly adjusting their pitch, that's a given, I didn't imply that they don't.  As a pianist, I do not have the luxury of intoning while playing, the tuning is fixed.  The facts about ET being tuned as it is (the 12th root of 2, 1.05946 times the frequency of the previous note) is accurate and what I said about modulations hold true.  Where I was wrong was in forgetting that ET and well-tempered are not the same.  They're close, but different.  Here's a link about that from a piano tuner.  Thanks for pointing out my error William.

https://www.math.uwaterloo.ca/~mrubinst/tuning/tuning.html

Jerry

Actually though the Well-Tempered Clavier is so famous,  I'd never looked at it from the standpoint of a composer of a time before equal temperament tuning  necessarily being limited in modulating by the extreme out-of-tune results of going into a new key with the various intervals that sound good in another key.  One can see how Bach with his enthusiasm as both player and composer would appreciate it.   

@William said:

This is totally specious and incorrect.  The reason Bach loved ET was because on an organ or a harpsichord he could play and compose with a lot of modulations. That has nothing whatever to do with orchestral or ensemble playing by musicians that instantly and intuitively alter their tuning based upon just LISTENING.  jsg - they don't adhere to ET when modulating from the key of C major to f sharp minor! Do you actually think that?   What they do is listen as they are playing and adjust the tuning instantly - if they are good musicians - based upon a tuning that sounds "right."  It is  not based upon ET of a previous key,  even remotely. So this comment is entirely wrong and based upon a keyboard player - jsg - who is used to fixed tunings, and making a sweeping statement about all tunings - which has nothing to do with the reality of playing instruments other than keyboards or harps, celesta or vibes, etc. in an orchestra or ensemble. If it's a piano concerto, that is a different matter, because then the players are forced to tune to the ET piano.        

This is fascinating and if I understood what William is saying correctly it might have answered a question I had for a long time.

Did I understand correctly that since a string instrument has no fixed tuning, (except the G D A E of the open violin strings etc.,.), so that they can choose any 'temperament' they want, and end up choosing the one that is natural to the ear? In that case does a string player always play the natural harmonic scale i.e., simple ratios? if not what scale does the ear naturally "fall" into? Are all instruments other than piano not fixed tuning?

And what happens in a piano concerto? Do the rest of the orchestra make automatic slight adjustments to match the piano tuning?

I am a physicist and should really know this better but thanks for clarifying. I have Helmholtz's 'Sensations of tone' where he spends a whole chapter on various tuning systems. But have never read it LOL

Anand

@agitato said:

This is fascinating and if I understood what William is saying correctly it might have answered a question I had for a long time.

Did I understand correctly that since a string instrument has no fixed tuning, (except the G D A E of the open violin strings etc.,.), so that they can choose any 'temperament' they want, and end up choosing the one that is natural to the ear? In that case does a string player always play the natural harmonic scale i.e., simple ratios? if not what scale does the ear naturally "fall" into? Are all instruments other than piano not fixed tuning?

And what happens in a piano concerto? Do the rest of the orchestra make automatic slight adjustments to match the piano tuning?

I am a physicist and should really know this better but thanks for clarifying. I have Helmholtz's 'Sensations of tone' where he spends a whole chapter on various tuning systems. But have never read it LOL

Anand

Yes, string players and singers can intone while performing, meaning they can make slight adjustments to their pitch in real time.  In doing so they gain a fluidity when moving around different key areas that instruments like piano, organ and harpsichord don't have. 

With the Vienna Instrument Pro player, we can "humanize" the attacks of every instruments by creating "random" pitch maps that can detune the attacks of notes slightly, or even not-so-slightly.  Though this is not quite the same as what live players can do, it certainly helps to create at least some sense of fluidity of pitch.

Even the exact pitch of A4 is not universal although A4=440hz is pretty standard.  With our virtual orchestras, we can change that as well if so desired. But some orchestras tune to 441 or 442 or even 432.  It is said that Leonard Bernstein wanted his orchestras tuned to 442.

As a keyboardist I am partial to equal temperament because of the flexibility it allows with modulation, distant keys and polychords, particularly double mediant poly chords.   Then again, as a pianist I am stuck with it unless I instruct my piano tuner to change temperaments but I don't really have a need to do that.

[Edited 24th April]

Anand, in Helmholtz's famous book his big topic is Just Intonation (JI). Like Euler, Helmholtz was fascinated by - one might even say infatuated with - the small integer ratios of JI, and was convinced that orchestras do, or should, use this intonation. It turns out he was only partly correct about orchestral intonation.

In fact European orchestral music has long been based on Pythagorean Intonation (PI), except - typically - where brass instruments play harmonies polyphonically, in which case some of the brass players make small tuning adjustments (a syntonic comma up or down) to render the harmony cleanly in JI. A crude rule of thumb is: PI for melody, JI for harmony.

PI can readily yield attractive melodies, but typically (in some instruments) produces harsh and unstable sounds in polyphonic harmony. JI can too easily be less than attractive and even ugly in melody, but typically produces clear and stable sounds in polyphonic harmony. ET can typically be too vague, foggy and bland to be attractive in melody (although some great masters have written beautiful harmonically-entwined melodies for ET), and is typically about as harsh and unstable as PI in polyphonic harmony.

Strings have the advantage of vibrato (and tremolo), which can allow large string ensembles to ignore the need for pitch adjustments away from PI for clean harmony in JI. However, in small string ensembles, especially quartets, pitch adjustments typically have a very important role in the rendition and may require much planning and rehearsal. Using ET sample libraries to write a string quartet can too easily result in an appalling mess of bad tuning that would be impossible for adept string players to sort out in their rendition, if the writer blithely attempts to imitate the great masters in modulating far and wide, but without having the ear and skills of a great master. Alas, for all too many would-be composers today, such have the platitudinous temptations of ET's triteness and banality become.

In India and the Middle East there are various traditional scales that combine PI and JI in ways that can yield very attractive and distinctive melodies (hence my interest in traditional fujara intonation). Many if not most of these cases, however, never involve anything like the complexities of typical European orchestral polyphony, and hence some may be very difficult if not impossible to embody in European orchestral works.

Traditional European staff notation always assumes PI, and conventionally leaves as implicit any adjustments of pitch for the sake of clean JI harmony to be made during rendition.

A piano concerto can sometimes turn out to be a battle ground in which the orchestral musicians do as little as possible to compromise their intonation for the sake of the piano, such that the pianist is sometimes left to sound embarrassingly out of tune. I guess it can depend very much on whether the the pianist shows himself or herself to be the orchestra's respectful and grateful guest, rather than arrogantly presuming to be its master.

It's horses for courses, isn't it. I use a_lot of non-ET pitch in myriad ways, but...

AFAIC, correcting such an instrument with its own intonation to 12tET is egregious and deadly. A good library implementation gives us the real notes of it (NB., I have yet to bring this flute out to check). Conversely an exotic intonation in VI Pro for certain instruments gets to be pretty dodgy (nothing is really 12tET on earth; ie., you're retuning things you'd have to do work so as to actually know where the thing sits in the continuum of pitch).

For the Synchron line we'd likely be reintoning more than the isolated instrument part; so I will use pitch bend in the pb lane in the DAW as though pre-fader approach. I would tend to look at some JI if I'm building the section from parts, looking for simpler concords than ET does in a harmony (one major point of that implementation was to get those concords in this key and now the next key, a change of matrix = a new JI set), but re-intoning the whole section as recorded does not seem to be best practice IME. I don't think the same implementation of scala/tun suits Synchron in the same way. I also use special instruments from different vendors for their intonation.

One thing I used recently had gestures or 'licks' that are genuine idiom in a shakuhachi "In D" which turned out to be D Dorian, so using this you better be pretty much wanting those intervals, as the discrete tones reflect this reality. The Wiki on Fujara indicates ornamention usually occurs in Mixolydian; It's called an *overtone flute*, ie., any diatonic anything is derived from its specific physicality. If the fundamental is G, F is the 7th harmonic, which is ~31¢ flatter than ET, and I doubt finding the natural seventh took a whole lot of doing. So if the goal there is to create a more-or-less ET 7th that's compromised by nature and not such a great idea.

So I checked it out. Yeah, the F per G is not an ET m7 and the B per E isn't sharp like ET either. I'm hearing harmonic intervals like 7:4, 5:4.

Civilization 3, many thanks for your interesting remarks on this topic. It's good to know you're another intrepid adventurer who sometimes seeks interest and enjoyment beyond the claustrophobia-inducing confines of the almost total ET monopoly in the sample libraries industry.

In my Situater I also rely on Pitchbend to produce the precise intonations I want, when playing live or in playback. Situater always sends a 14-bit Pitchbend message as an "escort" for each and every MIDI Note-On for all instruments that I wish to re-intone. At present I have 48 "Escort Kits" in Situater, each kit being able to accommodate 16 independent monophonic channels, giving me a maximum of 768 monophonic instrument channels that can all be intoned automatically in realtime by Situater, according to what note each instrument plays at any moment. Actual Pitchbend values come from lookup tables embedded in Situater, and are selected automatically according to any 12-note preset "Cast" I select or transpose on Situater's main user panel (manually, remotely or by automation).

Situater's accuracy of pitch of course depends partly on the accuracy with which samples have been tuned to ET by the sample library's maker. Thus far, I'm happy to report that all of my VSL orchestral libraries are very satisfactory in that regard. But I have discovered substantial non-linearity in Kontakt's Pitchbend response curve, and have had to construct a correction mechanism in Situater just for Kontakt libraries.

In fact VSL-Fujara's "greatest gift" is not denied to me if I can discover - with confidence - at least one of the fujara's authentic intonation schemas, then I can set it up as a preset cast in Situater. My first desire was to play fujara solo, from a keyboard, in at least one of its authentic intonations, simply for the pleasure of imagining myself on a hillside in the Slovakian mountains with only sheep and dogs for company! But more than that, I'd love to explore and invent melodies and melodic figures in authentic fujara intonation that also might, perhaps, become useful in orchestral settings. But this doesn't help other VSL-fujara owners - hence the theme of lamentation with which I started this thread.

I'm somewhat puzzled by what you report as hearing in the fujara library. You say you've heard distinctly non-ET tuning, and yes I agree a few of Fujara's Long notes are a bit off from ET, as shown by my pitch table below. However, as the table also shows, I've not found many pitches that could be heard or regarded as conforming to standard PI, and none at all to the PI-plus-JI intonation schema that I've modelled to represent a hypothetical "traditional" fujara. I'd say this VSL library is more or less bog standard ET, except for a few odd deviations that don't appear to fit any intonation schema I'm aware of or can even postulate.

The 7th partial

As for the "septimal seventh" (i.e rendered by the 7th partial), I'm not hearing that interval anywhere between fujara's long notes (main factory preset), nor do my pitch measurements show anything close to a septimal seventh interval. Indeed I can hear the 7th partial in top G as played with artistic flourish and recorded in this library - but of course that's a case of timbre, not melodic interval. In which factory preset and articulation have you heard this septimal seventh as a melodic interval?

In traditional European intonation, as far as I know the only example of the 7th partial coming into play is in the German, French and Italian versions of the augmented sixth chord (formerly known as the Extreme Sharp Sixth); and even there, the true 7th partial is only evident (I've heard it and measured it) when that chord is played on various keyboard instruments tuned to a certain variety of Meantone Temperament (MT). In nominal PI, the augmented sixth interval is about two commas short of the full 7th partial ! However, as yet I'm completely in the dark about what, if any, use of the 7th partial is or has been made by adept fujara players at any time in history.

For my taste, whereas the augmented 6th chord in is fun to use in MT but also useful in PI, I avoid the septimal seventh above the tonic like the plague - it makes me wince and sets my teeth on edge; it's not something I'd ever want to get used to. Indeed in all modern concert grand pianofortes, the 7th partial is deliberately suppressed by the hammers striking each string group at a certain distance along the string such that the 7th partial cannot be audibly engendered in the strings.

Table of fujara pitches - theoretical and measured

The table below shows deviation (in cents) from ET, as follows. The 2nd column shows nominal PI tuning, and can also be ascribed to my model of a modern fujara. The 3rd column shows several JI deviations from ET tuning, as can be ascribed to my model of a traditional fujara (hence the column title "TF"). In note names specified for this 3rd column the minus sign denotes that the nominal PI pitch is lowered by a syntonic comma; also, F(7)5 denotes the septimal seventh produced by rendering the 7th partial when all holes are stopped. The 4th column shows VSL-fujara's pitch deviations from ET as measured by Melodyne 5 Studio, using 7.5 second note lengths separated by 0.5 sec.

(Notes: I've found Melodyne's pitch detection algorithm is accurate only to within about ±3 cents, so the measured deviations from nominal ET shown in the table may not be as much as Melodyne reports (or may be more). However, where the measurements suggest significant erroneous deviation from ET, I'd just say - hey, it's a freebie! Lol. In melody on its own, on a good day, deviations beyond about ±4 cents from nominal PI or JI can tend to get my attention when just listening. Since Melodyne got a bit confused about the pitch of top G, I've left it out of the table.)

        Note       PI      "TF"      VSL

• F5         –8                    –1
• F(7)5              –31       (–1)
• E5         +2                   –7
• E5–                 –20       (–7)
• Eb5       –12                  –5
• Eb5–               –33       (–5)
• D5         –2                   +1
• Db5       –16                 +1
• C5         –6                     0
• B4         +4                  +3
• B4–                 –18      (+3)
• A4            0                  –3
• G4          –4                   0
• F#4        +6                  –3
• F#4–                –16       (–3)
• F4           –8                  +2
• E4           +2                 +2
• D4           –2                  –3
• C4           –6                  +1
• B3           +4                  –6
• B3–                   –18      (–6)
• A3             0                    0
• G3           –4                   –3

My abject apologies to everyone for me getting far too nerdy here; I certainly didn't intend or want to get into techie details when starting this thread. I suggest that any further technical discussion on this instrument should be in a new thread in the Synchron forum.