Well, hopefully I've demystified the implementation for you. Like I said - if you have any other implemented preset Micro Tuning you want a breakdown of - I can do that. I'm not going to run through them all but I can handle doing one more.

BTW: A=440 is adjustable. And yes, the bad part is that this is a global setting so changing microtonal "centers" is not so easy. Obviously tone generator global setting changes between tunes is not practical. However, Part-level "Detune" is available for adjusting. So every part you want to adjust, you'll need to set the Detune to offset "A" by the amount desired.

I didn't say every feature is implemented in the most friendly way with high marks for elegance. That does go against a legacy of tradition where the knobs are there with little abstraction or "helpers".

I think this is a key area of growth (potential) for Yamaha. There are improvements around the edges but there is lots of legacy that I imagine Yamaha sees as being trampled over if they provide truly elegant solutions. If that's the case, I disagree and think much of the design and interface can be retained in an "advanced" level - but provide elegance in the UI and architecture so users have a choice if they want to. Certainly some of the "elegant way" additions may rightfully displace harder ways to do the same thing. There's not a reason to have a worse and better way for the exact same action. And power users would enjoy something more straight-forward if really no functionality is lost. Sorry about the soap-boxing, but I felt it may help to convey how exactly I'm (seemingly) on your side here.

No, no...

It is not a matter of demystifying anything.

I know many people finds those numbers and calculations a bit on the tough side, but not me.

Most probably a bag pipe is selected and played without even approaching the master tuning (475-485) and then even let's forget about mixolidyan or pure major ..

The thing was to know what Yamaha meant when offering a root and a Pure major.

And do it correctly, not as my software.

Then that's it. I was just wondering if you wanted me to go through Arabic 3 or some other tuning system. If Pure Major was it - then that's done.

[quotePost id=117382]Then that's it. I was just wondering if you wanted me to go through Arabic 3 or some other tuning system. If Pure Major was it - then that's done.
[/quotePost]

😀 😀 😀 😀

Thanks. See you...

BTW: for those reading, the formula for calculating cents may also be expressed:

Freq2/Freq1 (ratio of two frequencies) where Freq1 is the lower frequency of an interval and Freq2 is the higher frequency of an interval. You can determine the cents (c) between these two frequencies by:

c = 1200 * log10(Freq2/Freq1) / log10(2)
or
c = 1200 * 3.322038403 * log10(Freq2/Freq1)

I put this in terms of log10 because Mac's built-in calc has Log10 and not Log2.

Hi again...

After letting the whole Earth know my software is wrong when developing a Pure Major scale I am back to say it could have been myself the one to blame.

While I am still to receive a clarification from my software designer, I think perhaps might finally understood the reasoning for note A remaining unaltered as we change the root in the Pure Major scale.

Being accustomed to equal temperament we go easily through the octaves up and down, then we meet this other tuning without realising that while truly providing us with great beautiful sounds it turns it is only adequate for a short span of notes.

See bag pipes use some three drones (one of them two octaves below the master tuning, the others matching it) and then a chanter with just nine notes named for example Low G, A, B, C#, D, F#, High G, High A. The master tuning is set for A.

So I firstly discovered the steps Just intonation calls for when going Pure Major then went to stablish a root for the scale, 1/1, 25/24, 9/8, 6/5, 5/4, 4/3, 45/32, 3/2, 8/5, 5/3, 9/5, 15/8, 2/1.

Among the many things I heard to set a root was that a perfect fourth is not an overtone but an undertone so if one is planning to use that interval in the song while using the A scale then the trick is setting the root on D.

Well, it goes that as we are restricting the span of notes used, the master tuning will remain fixed. If we stablished that note as the root we apply the appropriate steps and that is it. Easy.

But let's change the root, say we want it on D.

I firstly started applying the steps as before, myself a new entry pretending to see A going altered. It is not so. No, it doesn't go like that.

As the master tune is A (MIDI 69) and the root has been moved to D, we first change the value of D starting from A by applying inversely the step or by dividing by it.

Once known the value of D we can start applying the calculation, knowing that A is still the very same A we first decided to tune our instrument to.

So the correct procedure is that while we can go changing the root, the master tuning A will always remain the origin as we simply apply firstly the ratio that Root/A calls for but always starting from A and never from the root, and from the computed data for the root we go building the other tones using the known relationships.

If they don't tell me this is so I don't know what else could I think of.

😀 😀 😀 😀

With Pure Major and root of D, A is 3/2. So D(Pure Major freq)=440/(3/2)=440*(2/3) = 293.333(repeating) Hz.

If you wanted D(root) as the equal temp value of D, then the difference is:

D(Equal Temp) as 293.6 - D(PM freq) as 293.333 = 0.2666(repeating). So we would either set the master A=440 tuning to A=440.3 (approx - or "higher" 440.2 value" or set the Part common detune to +0.3Hz. The master (tone generator, [UTILITY] ) tuning has higher resolution for reducing the error. And either technique could be used to move around the tuning of the "A" tuning which, in turn, would adjust the root note. Given the higher resolution of the tone generator tuning, it would be nice if the Performance would allow for an offset to that value in the increased resolution units of that parameter. In addition, for user feedback, it would nice if the significant digits were increased for the tone generator value given the resolution generates more significant digits than displayed in the "Hz" helper. Not that one couldn't derive this - but it's just (seemingly) an unnecessary handicap.

[quotePost id=117387]With Pure Major and root of D, A is 3/2. So D(Pure Major freq)=440/(3/2)=440*(2/3) = 293.333(repeating) Hz.

If you wanted D(root) as the equal temp value of D, then the difference is:

D(Equal Temp) as 293.6 - D(PM freq) as 293.333 = 0.2666(repeating). So we would either set the master A=440 tuning to A=440.3 or set the Part common detune to +0.3Hz. The master (tone generator, [UTILITY] ) tuning has higher resolution for reducing the error. And either technique could be used to move around the tuning of the "A" tuning which, in turn, would adjust the root note. Given the higher resolution of the tone generator tuning, it would be nice if the Performance would allow for an offset to that value in the increased resolution units of that parameter. In addition, for user feedback, it would nice if the significant digits were increased for the tone generator value given the resolution generates more significant digits than displayed in the "Hz" helper. Not that one couldn't derive this - but it's just (seemingly) an unnecessary handicap. [/quotePost]

Not wanting to match at all the frequency of the root to the one it would have under equal temperament (You say.."If you wanted D(root) as the equal temp value of D, then the difference is:...)

It is simply that we need the math to see the cents in D Pure Major, the cents in D Equal Tempered and then get the difference either to check the software doing it correctly or to set a Custom scale by telling the differences or deviations to apply from Equal temperament rounded to the nearest cent.

Let's tune 475 Hz and D...

So it goes Log10(475*2/3/(475*2^(-7/12)))/Log10(2)*1200= -1.9550 or -2 cents.

Thank you again, Jason.

Very nice of you.

And now time for me to enjoy playing that astounding bag pipe I made and the drums supporting it...