24 tone uneaqual tuning.

[drewz]

I made this so I can play purer major 3rds and the lesser septimal tritone in all 12 key of the equal temperament system. here it is in cents 0 84.2 100. 184.2 200. 284.2 300. 384.2 400. 484.2 500. 584.2 600. 684.2 700. 784.2 800. 884.2 900. 984.2 1000. 1084.2 1100. 1184.2 1200. Has anyone done this before or has anything been written using this method? Again this is only intended for playing in the original 12 keys of equal temperament system. If Im correct this should be less of a compromise than the well temperament systems where only some keys sound in tune and others to a lesser extent unlike the tuning Im proposing in regards to the original 12 tones.

:the major 3rd interval of the original 12 notes can also be adjusted by 2 cents if desired

[synthifou]

I've personally never experimented with this sort of thing before, but I'm aware of the existence of other tuning systems.

I know of quarter tone compositions (24 notes), such as Wyschnegradsky etudes and others, and there are compositions that have been written specifically for 12TET equal temperament.  However, I'm a little confused as to what you are doing here (which may be derivative of my ignorance of the subject).  The 100n intervals are those that correspond to equal temperament, but what do the 84.2 +100n notes represent?  Are you just comparing an equal temperament to another system?

[hfmadopter]

Interesting but no I have not done this officially. I tend to just run a a couple cents sharp as I go up the trebble side of the middle intervals and a couple flat as I adjust into the bass. At each octave I allow a drift, if you will. And at that I have not decided if this is how I want to continue. Do you tune for pure unisons ? I notice in some old tapes of Horowitz that his piano seems to be tuned slightly off pure but yet the harmony is very good. That could be the old recordings just as well.. I'd love to speak with his tuner if he is still around !

[synthifou]

Neat,

I think I may be confusing equal temperament and just intonation, not exactly sure about all the minor variations.  It’d be nice to find a chart that compares the differences through cents/ratios to better understand their relationships. 

Hfmadopter, did you tune your instrument with ‘drift’ so that the more local notes played together sound more perceptibly in tune?  I heard that pure tuning or using exact equal spacing between steps and perfect unisons tend to sound more dissonant without tweaking some of the intervals.  It’s a subject I’ve been thinking about lately, actually, so I’m just wondering. 

[iansinclair]

Interesting but no I have not done this officially. I tend to just run a a couple cents sharp as I go up the trebble side of the middle intervals and a couple flat as I adjust into the bass. At each octave I allow a drift, if you will. And at that I have not decided if this is how I want to continue. Do you tune for pure unisons ? I notice in some old tapes of Horowitz that his piano seems to be tuned slightly off pure but yet the harmony is very good. That could be the old recordings just as well.. I'd love to speak with his tuner if he is still around !

Speaking from a vast and deep well of no knowledge about this at all -- I have a very good piano technician who does my tuning for me, thank you! -- you bring up something which I have always wondered about, and never gotten a decent answer to.  Maybe this is the time...

In principle, a pure massless and infinitely flexible string will have a definite fundamental frequency.  Further, it will also vibrate at exactly twice that frequency (second harmonic)(the octave) and three times the frequency (octave and a pure fifth) and four times and... and so on.  But... a piano string is neither massless nor infinitely flexible.  So -- is the frequency of the first harmonic (the octave) exactly twice the frequency of the fundamental?  Or is it slightly higher?  And if isn't exact, should (or does!) one tune the octave to an exact octave, or does one tune the octave to the actual frequency of the second harmonic?  Although the differences -- in theory at least -- should be small, wouldn't it make a difference to the brilliance and singing of the piano, particularly with the dampers raised?

This isn't a question of temperament -- that's a whole different subject -- but pure physics and acoustics.

Illumination, please!

[drewz]

The 100n intervals are those that correspond to equal temperament, but what do the 84.2 +100n notes represent?  Are you just comparing an equal temperament to another system?

84.2 is where you get the purer major 3rds and the additional lesser septimal tritone from. The major 3rd in this tuning is about -2.11 cents flat and the lst is +1.69 sharp which is perceptively unnoticeable. Like I said you can adjust the major 3rd by 2.11+ cents to approximate the just intonation's major 3rd which would raise the lst +3.8 cents sharp, but again it perceptively wouldn't make a difference anyway, as it is said that we could only here up to a 6 to 5 cent difference. I myself can somewhat barley tell the difference between a just intonated major 3rd and the ET major 3rd (except when playing the two 3rds together simultaneously its more noticeable) which has a difference of +13.69 cents. Its a difference I hear nonetheless.

[hfmadopter]

Neat,

I think I may be confusing equal temperament and just intonation, not exactly sure about all the minor variations.  It’d be nice to find a chart that compares the differences through cents/ratios to better understand their relationships.  

Hfmadopter, did you tune your instrument with ‘drift’ so that the more local notes played together sound more perceptibly in tune?  I heard that pure tuning or using exact equal spacing between steps and perfect unions tend to sound more dissonant without tweaking some of the intervals.  It’s a subject I've been thinking about lately, actually, so I’m just wondering.  

By drift ( not a technical term I realize !) I mean that as I move up in scale away from the center in octaves I let it go a bit sharp and down toward the bass is opposite. I'm following this pattern from the book Piano Servicing, Tuning and Rebuilding. In that book it's mostly ear tuning but it references electronic tuning.

I am not a professional tuner but have worked with one many years ago ( actually a couple different ones). If I get in real trouble I call him ! So far so good I'm relatively pleased with my outcome. Honestly I'm just getting to the stage I can hear beats with in a unison ( I used to only touch up my piano between professional tunings, I've moved beyond that). Otherwise I have to depend on electronics to get me in the ball park first. I can also tune octaves pretty well by ear but like to check electronically now and then there as well. I can tune thirds but I don't hear beats and maybe should not.. So to answer your question, I tune the octave and the octave above or below separately. I first span the octave with a single note, most often starting with A. My goal when done is a couple cents high above the middle and low below the middle register.

I guess that explains a whole lot of nothing but if I get everything even the piano is not as lively sounding to me. Like you, I would like to learn more !

[drewz]

I've personally never experimented with this sort of thing before, but I'm aware of the existence of other tuning systems.

I know of quarter tone compositions (24 notes), such as Wyschnegradsky etudes and others, and there are compositions that have been written specifically for 12TET equal temperament.  However, I'm a little confused as to what you are doing here (which may be derivative of my ignorance of the subject).  The 100n intervals are those that correspond to equal temperament, but what do the 84.2 +100n notes represent?  Are you just comparing an equal temperament to another system?

If I'm playing in C then the major 3rd would be 384.3 cent but i want to change to the key of C# then the major 3rd would be 484.2

[iumonito]

Pianists are not as familiar with this because often they do no longer tune their own instruments, but for harpsichordists, this is actually a question of taste and interpretation.

The acoustics of the piano will affect greatly what you do with temperament.  Experiment, by all means, but be suspicious of innovation.  It is often the case that what you have discovered (bravo!) is as old as the middle ages, or there is a good reason not to adopt it.

All that said, I am currently simmering thoughts about tuning practices at the time of Chopin, and on pianos like Chopin used.  Interesting.

Consider, for example, this:

https://www.pianostreet.com/smf/index.php?topic=39288.0