Hi,

so finally I get to the point where I dare share an abstraction.

As the topic implies, [temperament] does basically the same thing as [mtof], only that it will let you switch between 137 different tunings. I also gave it a gui that will show you what tuning you are in and what the deviations from equal temperament (in cent) are for each pitch class. (Unfortunately, this makes it take up quite some space on the canvas - but I suppose you could just turn off the graph-on-parent. Maybe I'll find a way to control that conveniently via a tgl button?)
The temperaments.txt file needs to be in the same folder as the abstraction.

This is the page where I found the cent deviations.
http://www.instrument-tuner.com/temperaments.html

It must be said that this can never be "truly" historically accurate, since midi notes work with enharmonic equivalence (i.e., e-flat is exactly the same pitch as d-sharp), and historical tunings often or always don't (I have to read up on the details myself...). So, you would probably need seventeen different pitch classes per octave - and midi note numbers provide us with only twelve.

If you look at the tables on the above website, you might notice that the deviation for A is always zero - that is because one needs some kind of reference tone to build the temperament on. However, this needn't necessarily be A; so the third inlet in my abstraction lets you set that too (integer midi note nrs). At this point, though, this reference tone must always be an equal-tempered one - another historical inaccuracy. I will probably rebuild the mechanism a little so this inlet will accept Hz input instead, thus allowing you to set the reference pitch to, e.g., 415 Hz.

But I suppose these are rather marginal issues, since who would want to use pd as a "period instrument" anyway? So, I hope this will be useful for somebody's creative messing around, even if it is not "historically sound".

Have fun, if possible; and if you do, I'd be happy to know.
Cheers!

EDIT: Just noticed that I wrote VIII/2013 into the abstraction. I meant July, of course. Big deal.
Plus, the above webpage actually states that "the values are relative to the keynote C", not A as I assumed from the figures. I will have to do some thinking so as to be able to say whether this makes any sense.

http://www.pdpatchrepo.info/hurleur/temperament.zip

from glancing at it I think what they mean is that the scale is built from c as the root of the scale but the midi note a will be unchanged? also, because some scales were based around overtones it's completely valid to have only 7 notes in tune, since songs that used them were modal. many of these aren't modal e.g. Well temperament was used from the time of Bach until the late 19th/ early 20th century for keyboard instruments I believe, and certainly some keys sounded better than others within the system. In my opinion some keys in well temperament sound way better than equal temperament. That alone is a pretty good reason to use it in tonal music, especially if it's easy to modulate.

I wouldn't want to use pd as a period instrument, but there are many interesting experiments with "modern" music and tuning systems. (like Harry Partch)

thanks for this

I changed the tuning file and patch to be based around the root of the scale and C (while learning sh).
edit: fixed a small bug October 19th, 2021
temperament.zip

Hey sebfumaster,

cool that you actually took the time to go and improve my patching - I appreciate it!
However, I have to postpone taking a closer look at it, because I should actually be doing something else now - deadlines ...

Amazing! Thank you so much for your shared passion--I love the unfolding reciprocity of the open source community. This is exactly what I needed to find, and I very much appreciate the good work. I will definitely be learning a lot from this.