[CAUT] P-12ths was: Tuning a Steinway D and a Bosendorfer Imperial together

[Ronald Worth]

Ric,
 
 
Is this the crossroad between the sciences, acoustical physics and human auditory physiology?
Where are the piorities and goals in both fields? Where are the piano tuners' priorities?
 
Ok. Distribute the inharmonicity. Clearcut goal. Smoothest "fit", (progression of all the intervals) that the piano instrument's scale and design allow. In theory.
 
Non-fixed stringed (fretted) instruments can "bend" the pitch of the notes -  as if there is more "pleasure" to tailoring the pitch to the logarithmic hearing of humans. Fretted instruments are not "plagued" by an overabundance partials. It almost appears as if the fretted instruments can place their emphasis on the fundamental - or at least using no more than the second, and third partials to sound "pleasing". Yes, of course, these instruments have (far less) inharmoncity too.
 
The previous paragraph is hopeless towards approaching acoustical and physiological questions and inquiries with any analytical approach. The whole discussion is thwarthed by words such as "pleasure", "pleasing", "sounds good", etc., etc. As long as it is not clear what sounds invoke what physiological reactions (human emotions and/or feelings) and why, defining what sounds "good" is hopeless.
 
I believe the material sciences - still in their infancy - will one day be able to tailor the inharmonicity curves of (any solid-state, gas, liquid or plasma material) strings to that of the logarithimic hearing curves of humans. Tailoring any solid-state materials' inharmonicity to that of the logarithimic hearing of humans is the first step towards answering what sounds 'good'. We have a long way to go.
 
Ron
 
 
 
 
> Date: Tue, 14 Oct 2008 09:10:51 +0100> From: ricb at pianostemmer.no> To: caut at ptg.org> Subject: [CAUT] P-12ths was: Tuning a Steinway D and a Bosendorfer Imperial together> > David.,Fred> > Take the span of D3-A4 and tune them to a perfect 3:1 12th then measure > the 3rd partial of each, and split the difference into 19 semitones with > the 19th root of 3. Then do the same except take A3-A4 tune them to a > perfect 6:3 octave type... then measure the 3rd partial of each (to keep > on the same page) and split the difference into 12 semitones with the > root of two. Compare the A3-A4 area of both. The differences ARE > significant... tho small. They become more significant as you impose the > P-12th priority on the rest of the piano. So much so that you just cant > do it in the lower bass... really even on small consoles. The lower bass > gets too narrow... high if you will, and its sounds well... to use a > word I usually guard myself against.... bad.> > In the treble the end effect is that you end up with a very moderate > stretch and a significantly altered treble tuning curve. You can see > this clearly on a graphic of both types of curves. The octave priorities > most often use end up with the F5-F6 area a bit lower then the P-12th... > yet the highest range of the P-12th is lower. In a sense you can say > (and this is exactly what Jim Coleman commented back then...) that the > treble stretch is quite moderate...without sounding like it is. > (paraphrased but an accurate commentary)> > If you stop to think about what partials tests we use for the treble > this only makes sense. We use 6:3, graduate to 4:2 and then its rather > bingo what some folks choose for that highest octave. Especially the > last 5-6 notes. I see folks tuning C8 regularly way above the 35 cents > sharp limit a P-12th tuning usually imposes on it.> > The bass... well in the end you use 12th types instead of octave types. > And if you think about them... they fit "inharmonicity wise" right in > between the various octave types. This is why (I believe) Stoppers real > maths work on the subject support his claim and why Kent observes that > Stopper (or rather the P-12th scheme itself) deals with inharmonicity in > a unique way that yields a very nice tuning.> > That transition area in the bass where one needs to move from 6:3's to > something a bit wider. You can see this happening quite easy by just > cross checking 12th types. You can do this with octave types as well.. > but using 12th types seems to <<find>> that exact area where the stretch > needs to begin... and how much it ends up "stretching". Thats the > beauty of the thing as it is a computable curve that works with the > inharmonicity of every individual piano. You simply split an appropriate > 12th interval in the temperament area into 19 semitones using the 19th > root of 3, Tune the next 19 notes upwards in the treble to exact perfect > 12ths of the resultant <<temperemant>> area and then extend the perfect > 12th condition all the way up using those. (Actually you end up > creating an exponential like curve instead of the resulting linear curve > a strict calculation of 19 semitones with the 19th root of 3 yeilds for > the temperament area.. but thats another matter) In the bass.. you just > cross check at all times the 3:1, and 6:2.. on big pianos also the 9:3 > in the lower bass. Inharmonicity forces these to coincide at some > point...just wide of pure. And thats where the <<automatic stretch>> > kicks in.> > Those of use with Tunelab can do this easy. Take a blank tuning curve > and set all tuning partials to the 3rd partial except the lowest > octave.. which you set to the 6th but never really use and the top from > F6 upwards to the 1st as Tunelab wont allow the 3rd in that region and > you dont really need them anyways. Then set your tuning curve priorities > to 3:1 in the treble and 6:3 in the bass... sample your usual notes and > create the curve. Tune a middle area 12th range and the corresponding > 12th above to each note in this range directly to the ETD. Also tune the > corresponding octave below to each note in this middle range. That gives > you all but the lowest octave and the highest 12th tuned. Extend the > perfect 12th priority to the top area using the 12th region directly > below (their 3rds partials should be very close to right on if Tunelab > has calculated inharmonicity correct). For the bass you have an octave > already tuned... as a 6:3 octave type. I retune this area and the entire > base cross checking with 3:1, 6:2's and in the lower region with 9:3's > on big instruments. Tunelab Pocket makes doing this cross checking > extremely easy because of its partials switching button.> > Try it... compare closely both aurally, graphically and maths wise if > you can. I am sure you will see a very significant difference and Dr. > Coleman immediately noticed (and liked btw) back when he looked at > this. His P-5ths tuning also creates similar unique effects. Indeed... > all enforced tuning priorities will result in their own overall tone > colour. This is nothing new we discuss this kind of thing all the time. > It should surprise no one that the P-12th tuning handles inharmonicity > of real pianos differently then other tuning priorities..> > Cheers> RicB> > > > Richard:> > The difference between the 12th root of 2 and the 19th root of 3 is> 6.297037897993807971388553887547e-5 or> 0.00006297037897993807971388553887547. I can't tune that precisely but> maybe you can. :-)> > dp> > > David M. Porritt, RPT> dporritt at smu.edu> > 
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