Exactly. What I get.

Root note appears as an option for Arabic, Pure Major...

If I choose Pure Major and select C, D or A as root note, what happens ?

---------------------------------

On my way to that video... Thank you, Bill.

++++++++++((

Mmmm....not related to my question.
He simply detunes a couple of tones.

My question is about the cents increments/decrements applied to each note when choosing Pure Major and then selecting a different root note.

No. Root note for those tunings that support it determine which notes get altered by how much. The previous generation documentation was more descriptive.

Thank you all.

I understand I was right ..

...which notes get altered by how much....starting from the root.

Pure Major..
Root A then A+0, A#+11.73, B+3.93, C+15.64, C#-13.69, E-1.96, etc...
Root D then D+0, D#+11.73.....G-1.96, G#-17.49, A+1.96...

😀 😀 😀 😀

[quotePost id=117362]

I understand I was right ..

Great!

Please help us all learn about this and explain the process you used to determine those exact values. That would be much appreciated.
[/quotePost]

https://music.stackexchange.com/questions/7986/why-is-just-intonation-impractical

Scroll down for a while...around mid page.

Or once there search for...

However, in just intonation

The table is built substracting the values of the intervals each scale has.

You know equal temperament have 100 cents for each semitone, 1200 for the octave. So a second such as CD has 200 cents and a third suchs as CE has 400.

But pure major uses realtionships such as 9/8, 5/4, 4/3, 3/2, 5/3 to get the same intervals.

And to calculate the cents there you go by

LogX/LogY=Cents/1200.

[quotePost id=117364]

...and 'just intonation which is NOT available on the Montage/Modx at all.

Why did you say 'Pure Major'? That appears to have NOTHING to do with the values you posted or the table in the article/forum.

[/quotePost]

So the microtuning option offering Pure Major and then a Root note to choose is not related to getting a Scale tuned to Just intonation starting on the choosen note as root ?

If not, then that would not agree with the table provided by Jason...which actually matches my thoughts.

I think the obscurities in the microtuning documentation are on purpose in this hardware because diddling with the supposed exactness of FM can reveal some inaccuracies that might otherwise be unexpected.

Done.
Thank you
So long...

😀 😀 😀 😀

I don't see an FM conspiracy here.

The affect of any microtuning settings is "open source" in the sense that there are "pure" waveforms (FM and AWM2) that are easily measured by a software or hardware based tuner. It takes about 15 minutes to run through 12 chromatic piano keys and jot down the result. Not that you should have to self-document -- but there's no way to hide the response.

Arabic 1 had a few surprises for me. I started by mapping out Equal Temp. so I had a "baseline".

Then I started with C3 (MIDI note) using the Arabic 1 microtuning and root note of "C". The tuning was identical, for the root note, to the equal temp. note. Same for C#3 (with C# root note), D3 (with D root), E3 (with E root), F3 (with F root), F#3 (with F# root), G3 (with G root), G#3 (with G# root), A3 (with A root), B3 (with B root). Almost all notes aligned with the equal temp. pitch for a given root note. However, D# and A# were significantly different than the equal temp. pitch.

This, by the way, isn't a universal relationship (of the root note pitch). It's just how it works out for Arabic 1. Of course, the relationship of the various notes above the root note are of interest and really more of the meat of micro tuning. However, I am only detailing the root note since that's the focus of the question.

One could make a chart of each micro tuning and map out the various keys (root notes) with frequencies on each piano key pressed. I'm not planning on doing it - but the tools are there for the willing.

I return to say that if my question goes "What pitch should I hear after tuning 470 using equal temperament scale and playing MIDI 57 (next low A from middle C, A2 for Yamaha, A3 for Roland) the answer should be: you will hear 235 Hz.

The answer cannot be that it is undocumented.
Of course it is not, but you are surely aware it goes 2^([+/-]steps/12).

The answer cannot be get a pitch tuner and measure it. Even so and going measuring it to find a discrepancy to what I thought it should be, there is no correlation to what is meant if undocumented.

The answer cannot be go trying and discover many things.

I perfectly know what I am after, indeed.

I couldn't report s glitch or an issue then as I don't know the exact meaning of a switch.

Bill, but of course you can build a Pure Major scale as soon as you are allowed to adjust in 1 cent increments any note. Quite another thing is not knowing what amounts of corrections go on each as you walk the scale from the choosen root

Anyway, many thanks.

Everything the very best.

😀 😀 😀 😀

Just knew BadMister retired. Congratulations.

@Bill:

Regarding:

'just intonation which is NOT available on the Montage/Modx at all.

FYI "pure" and "just" are synonymous intonation systems.

Source: https://au.yamaha.com/en/support/greatstart/school-resources/article/ensemble_learning/intonation.html

8. Harmonic series tuning - "just" intonation
When dealing with chordal sonorities, performers need to understand how notes, or “overtones”, within the harmonic series above a given “fundamental” note vary in pitch from notes in an “equally tempered” tuning system, like piano. In simple terms, tuning according to the harmonic series is known as “just” or “pure” intonation (JI), and is one of the widely used professional models for tuning sonorities on instruments capable of fine pitch adjustment. When applying the professional standard of JI, the note A 440 as tonic in an A major chord is a different pitch to that same written note A as the third of an F major chord (which in JI is approx. 13 cents flat), and is different again as the lowered 7th in a B7 chord (which in JI is approx. 32 cents flat).

... not the only source, but cherry-picked one from Yamaha.

Therefore, the "Pure" systems are these available on Montage/MODX.

I get it - and empathize. That's why I stated: "not that you should have to self-document".

You've documented equal temperament as an example of the kind of documentation you want. So that's covered. If Yamaha were to document one other micro tuning system - which would you prefer they document?

[quotePost id=117375]I get it - and empathize. That's why I stated: "not that you should have to self-document".

You've documented equal temperament as an example of the kind of documentation you want. So that's covered. If Yamaha were to document one other micro tuning system - which would you prefer they document?
[/quotePost]

Thanks, Jason.

As a potential buyer I would like to know what I am to expect from any feature offered.

Historical tunings and scales are there, well known and you are already offering a great pack with Montage.

Say scale tune FGMANDRW offered ?
Explanation: this scale adds 13 cents to the third (once root is fixed) and removes 25 from the fifth (from the same root, of course). Purpose: to have great fourths.

You can always say go and find what Pure major scale is, understand it and come back to use it, but once is offered I find it necessary to ascertain what you do as it is implemented so the user makes it clear we are actually talking about mass but
not in pounds and kilos respectively.

Just found a glitch in my software.
It allows Pure Major and after selecting the root, any from C to B, A is always found to have no cents added or removed. A is fixed.

So I was curious about the Yamaha proceedings in this regard.

... not that this is an answer, but an interesting bookmark for representing intonation and perhaps something to compare.

http://www.microtonal-synthesis.com/GS_XG.html

Where it's easiest to look at the Roland chart since it gives all notes in terms of cent adjustments.

Line 44:	0	12	4	16	-16	-2	-10	2	14	-16	-4	-12

	Line 45:	0	-29	-16	16	-16	-2	-10	2	14	-16	-4	-12

Line 44 is pure major, line 45 is pure minor. Not all notes may agree from this source with Yamaha's implementation. However, the full link has interesting "recipes" for various micro tunings.

Note: These charts are all assuming a root note of "C" since "C" is always "0".

And equal temperament is the 0 for all 12 notes.

... btw: since all other systems are "standard" - my answer for the systems to document would be the arabic ones. I guess I could take a stab at an Arabic one and see if I can match it to one of the 7 Maqam families that have non-12-tone notes in them. Not that this is necessarily the pool of the "Arabic" microtunings - but it's a start.

Just (major) intonation (Pure Major in Micro Tuning) seems to use (for freq ratio between root and given chromatic notes relative to the root):

Root-lets call root C for this, but can really start on any note. It's the 1/1 interval (=1, same note)
C# 25/24
D 9/8
D# 6/5
E 5/4
F 4/3
F# 25/18
G 3/2
G# 25/16
A 5/3
A# 9/5
B 15/8
C (oct above root) 2/1

Where frequency of root (C in this case and happens to be 264.0 Hz for middle C - this is a software measured value which could have some amount of error) this is the 1/1 ratio. And calculating the frequency for each note would be to multiply the root frequency by the ratio next to the note. So for F#:

264.0 * (25/18) = 366.666(repeating) Hz

... any you may wonder why for a root note of C that "C" is 264.0 Hz. This is because the tuning is adjusted such that the math works out as above AND A4=440Hz. Because our instrument is tuned to A=440 in [UTILITY] for the tone generator global settings. This still holds true for Pure Major Micro Tuning. So, we check (for that A above middle C) ...

264.0 * (5/3) = 440.0 (on the nose).

This means that for most, if not all, of the Micro Tuning systems that adjusting the root note will not change the pitch of A4. And since most if not all systems have perfect octaves - that means none of the "A" notes will be altered by changing the root note. Other notes, however, should generally move around.

That is it, Jason. Congratulations.

And to easily input the cents necessary (#C), should you go for a custom scale, it goes

#C=Log(Rate)/Log(2)*1200

So 4/3 getting F means 498.0449, or 1.96 below Equal temperament, as stated in my first post (D with root A)

😀 😀 😀 😀

And once you realize A is kept constant regardless of the root, actually being offered as a feature to choose and start building the Pure Majo from, it goes without saying that it is wrongly implemented in the software I was using.

Had the system not provided the corrections applied to every single note so as to get the scale we were looking for, as Roland does in you example, no one would ever be able to report the issue.