How to find exact numbers (in cents or ratios) for the different temperaments -- "Pure Major" etc.

[AndAllForOne]

Hi,

According to the Px-5S manual (and also the 350 manual, and maybe the rest of the Px's) there are 17 different temperaments available as options.

 

This is interesting to me because I've been playing in Partch's version of "Just Intonation" for decades on other instruments, and it would be nice to be able to mach that on the keyboard.

 

But the devil is in the details. I'll need to know exactly what changes have been made, at each chromatic step, to be sure.

 

For instance, the "Pure Major" option might use traditional just intonation, but probably not (I've seen different definitions of it, and I don't know what Casio's is) -- so won't know unless I get a list of the 12 steps and either the ratios used by Casio, or the cents values away from Equal Temperament they use.

 

So, anybody know -- is this information available anywhere, or is there a good person to ask in Casio?

 

Thanks

 

 

 

[Hugh O Kelly]

The fact is that all tuning is out of tune.

So lets be clever.

Lets tune all 3rds perfectly

Playing in C is great .C to E sounds perfect.

But E the third is the minor 3rd in C# minor which is now out

lets say I'm playing in Ab(The 3rd between Ab and C is now out)

So with mean tone in some keys it sounds in tune but in other keys its way off

 

Meantone temperament

From Wikipedia, the free encyclopedia

 

 

Meantone temperament is a musical temperament, which is a system of musical tuning. In general, a meantone is constructed the same way as Pythagorean tuning, as a stack ofperfect fifths, but in meantone, each fifth is narrow compared to the ratio 2^7/12:1 used in 12 equal temperament. The meantone temperament:

• generates all non-octave intervals from a stack of tempered perfect fifths; and
• by choosing an appropriate size for major and minor thirds, tempers the syntonic comma to unison.

Quarter-comma meantone is the best known type of meantone temperament, and the term meantone temperament is often used to refer to it specifically.

 

The main thing is you understand is that all tuning is a compromise 

( if we lived on a planet that revolved around in 360 days we would have perfect tuning)

 

Meantone tunings R Size of the fifth in octaves Fraction of a (syntonic) comma 9/4 31/53 1/315 (nearly Pythagorean Tuning) 2/1 7/12 1/11 (1/12 Pythagorean comma) 9/5 32/55 1/6 7/4 25/43 1/5 5/3 18/31 1/4 8/5 29/50 2/7 3/2 11/19 1/3 Equal temperaments[edit]

Neither the just fifth nor the quarter-comma meantone fifth is a rational fraction of the octave, but several tunings exist which approximate the fifth by such an interval; these are a subset of the equal temperaments ("N-ET"), in which the octave is divided into some number (N) of equally wide intervals.

Equal temperaments useful as meantone tunings include (in order of increasing generator width) 19-ET, 50-ET, 31-ET, 43-ET, and 55-ET. The farther the tuning gets away from quarter-comma meantone, however, the less related^[2] the tuning is to harmonic timbres, which can be overcome by tempering the timbre to match the tuning.^[3]

 

 

[Hugh O Kelly]

Coming up are lots of pages from a good book that if you hang on in there you will get a better understanding of tuning.

 

To read ,just read the attached thumbnails

[Hugh O Kelly]

one of many pages

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[Choppin]

@AndAll4One

 

There is actually tuning data in midi messages.  I can't remember the details, but you can find the cents are represented within 2 bytes of 7 bits.  This may be only retrievable through sysex messages, and it may only be transmitted when the frequency or actual tuning is changed.  You could probably look up general information about midi tuning and sysex messages and find what I'm sorta recalling.

 

A viable test might be to assign a slider on the Px-5s to fine tuning pitch change.  Set a temperament and move the slider and monitor what comes back on a Midi Ox display.  The changes may be tuned to the temperament so you would actually see what the values are between adjustments of the slider.  In theory, the difference between the values returned by the relative position of the slider would tell you the tuning of the temperament. 

 

I'm not near a keyboard now, so this is just an idea.

[AndAllForOne]

There is actually tuning data in midi messages.

[snip] 

Set a temperament and move the slider and monitor what comes back on a Midi Ox display. 

[snip]

I'm not near a keyboard now, so this is just an idea.

 

Good idea, that's the kind of thing I was hoping for (if Casio hasn't actually published a spec of the cents values).

 

I use Logic on a Mac, so Midi OX isn't available to me, but I might be able to rig up something inside Logic. Or find a Mac equivalent to Midi Ox.

 

Thanks.

 

And @Hugh O'Kelly:

I appreciate that you're trying to help me, but I was more looking for a way to get the specific numbers, like how Choppin suggested. I've actually had a fair amount of experience with alternative tunings, so that sort of background wasn't what I was after. 

 

A2F1

[Joe Muscara]

 

I use Logic on a Mac, so Midi OX isn't available to me, but I might be able to rig up something inside Logic. Or find a Mac equivalent to Midi Ox.

 

I use this. It's great.

 

http://www.snoize.com/MIDIMonitor/

[Hugh O Kelly]

Tuning is something that most of us would think we know about

but not many know that all tuning is out and don't get it.

For those who don't know the pages I included should show some light.

[wombatguy]

Im not sure about the particual instrument your using but i hope this helps!

 

One note value change in "Coarse Tuning" would apply to one change in a semitone steps (one key up or down on the piano).

"Fine Tune" parameters usually applies to one-cent step changes in a pitch.  One-cent is 1/100th of a semitone step.

[kero binso]

Almost 10 years later, I have the same question.  Did Casio ever publish definitions for its scales, in cents?

 

e.g. meantone probably means 1/4 comma meantone, but i read Mozart preferred 1/6 comma meantone so I’d like to confirm which it is.

 

e.g. Bayati is a whole family of scales, I’d like to know which is included here. 
 

thanks to anyone reading this!