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Which temperament is the best for controlling inharmonicity?

  • 1.  Which temperament is the best for controlling inharmonicity?

    Posted 03-14-2019 18:10
    Is the solution a particular width of equal temperament?

    Is the solution a particular unequal temperament?

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    Roshan Kakiya
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  • 2.  RE: Which temperament is the best for controlling inharmonicity?

    Posted 03-14-2019 19:34
    Is the solution a particular unequal temperament?

    I forgot to mention that the lady who came to visit me told me that she hated Vallotti - too insipid, smooth - and for me too near Equal Temperament to tweak my ear at all.

    Best wishes

    David P

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    David Pinnegar, B.Sc., A.R.C.S.
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    +44 1342 850594





  • 3.  RE: Which temperament is the best for controlling inharmonicity?

    Registered Piano Technician
    Posted 03-15-2019 09:24
    I feel like you're asking the best way to cut a pizza to control its salt content. I think the real answer to the question is that there's not one answer that works for all pianos, and it will be whatever combination of stretch and slight deviations from equal temperament result in minimizing the beat rates of various slow beating intervals, which is what the piano tuner works out on site.

    On using historical un-equal temperaments to control inharmonicity: Maybe by cutting the pizza into 12 less-boring un-equal pieces you can distract people from noticing its saltines but you're not "controlling" the salt.

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    Anthony Willey, RPT
    Willey Piano Tuning
    Easy Piano Tuner
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  • 4.  RE: Which temperament is the best for controlling inharmonicity?

    Posted 03-15-2019 09:51
    But in using UT you're adding in the olives, anchovies and juicy peppers and enabling one to do away with salt.  Better for high blood pressure. 

    Best wishes 

    David P 


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    David Pinnegar, B.Sc., A.R.C.S.
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    +44 1342 850594






  • 5.  RE: Which temperament is the best for controlling inharmonicity?

    Posted 03-15-2019 11:07
    David-
    Would you be so kind as to tell us, in a very simple, physical-mechanical way how you tune "harmonic" octaves in the middle of the piano?
    Do you use an electronic device which gives frequencies of, say, A3=220Hz and A4=440hz, and you tune those notes to the electronic device without comparing the strings of A3 with the strings of A4?
    I am very simple, and need a very basic explanation to understand.
    Thank you.

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    Ed Sutton
    ed440@me.com
    (980) 254-7413
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  • 6.  RE: Which temperament is the best for controlling inharmonicity?

    Registered Piano Technician
    Posted 03-15-2019 14:30
    RE: "...enabling one to do away with salt"

    The point is you can't take salt out of an already-cooked pizza any more than you can remove inharmonicity from an already-built piano. Without major deconstruction anyway.

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    Anthony Willey, RPT
    Willey Piano Tuning
    Easy Piano Tuner
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  • 7.  RE: Which temperament is the best for controlling inharmonicity?

    Registered Piano Technician
    Posted 03-15-2019 15:00
    Yes, the salt is in the constituent parts. Cooked or not.

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    Steven Rosenthal
    Honolulu HI
    808-521-7129
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  • 8.  RE: Which temperament is the best for controlling inharmonicity?

    Posted 03-15-2019 15:10
    Does inharmonicity only need to be controlled to such an extent that it seems as if it has been removed, even though it has not been removed?

    If the answer to the question above is yes, do different temperaments facilitate the controlling of inharmonicity to different extents?

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    Roshan Kakiya
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  • 9.  RE: Which temperament is the best for controlling inharmonicity?

    Registered Piano Technician
    Posted 03-15-2019 15:58
    If there was a way of redistributing the salt (or much if it) into say the crust, and then serving it only to people who don't eat crust (or who like a really salty crust), you would would have a situation somewhat analogous to well temperament which shifts some of the "salt" into the lesser used intervals...IMHO.

    Yes, there is no way to "control inharmonicity" (as I see it) as it is a result of the materials and techniques of modern piano making. Neither is it "bad" (except in extreme cases with poor scaling) since it is what gives the piano it's truly unique voice. 

    If the piano owner is a simple player (home keys virtually all the time), a good UT makes much sense as it enhances the parts of the piano most (or completely) used by that player. It also makes sense for a sophisticated player who KNOWS where the salt is a grabs a bite of it every now and then for a specific purpose. 

    At least that's my take on it. I like the illustration Anthony.

    Pwg

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    Peter Grey
    Stratham NH
    603-686-2395
    pianodoctor57@gmail.com
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  • 10.  RE: Which temperament is the best for controlling inharmonicity?

    Posted 03-15-2019 16:34
    How would an unequal temperament that is symmetrical around the circle of fifths affect the overall inharmonicity of a piano?

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    Roshan Kakiya
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  • 11.  RE: Which temperament is the best for controlling inharmonicity?

    Posted 03-15-2019 18:35
    Peter's description is spot on.

    A UT doesn't control the inharmonicity, if bringig together many perfect intervals it simply makes it irrelevant. 

    If the UT has a number of perfect fifths arranged so that there are some perfect thirds too, then there will be a lot of mathematical concordance in the vibrations produced. That harmonises. If the central three octaves in which most harmonic activity is set up are tuned without stretch, then the fundamental of many of the scale notes will interrelate in exact mathematical accordance. By doing this, the inharmonic partials are sent all over the place, not reinforcing each other. So then the harmonicity of the scale overcomes the inharmonicity of the strings making the inharmonicity irrelevant.

    Best wishes

    David P
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    David Pinnegar, B.Sc., A.R.C.S.
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    +44 1342 850594





  • 12.  RE: Which temperament is the best for controlling inharmonicity?

    Registered Piano Technician
    Posted 03-15-2019 20:18
    "A UT doesn't control the inharmonicity, if bringig together many perfect intervals it simply makes it irrelevant."

    It's funny that we don't seem to have enough common language to discuss these issues without misunderstandings. I believe in maintaining the beat rates of the mathematical models when tuning actual pianos, ignoring inharmonicity to the extent such is possible. Not sure if you are saying a similar thing.

    "If the UT has a number of perfect fifths arranged so that there are some perfect thirds too, then there will be a lot of mathematical concordance in the vibrations produced. That harmonises.

    That is true. But we differ I think on whether temperament should or should not be considered a zero sum game. In UT's the concordances in some keys are the direct result of making discordances in other keys. In my world, professional pianists are working on spinets, play in all keys and are accustomed to a nice pure 12th ET. Just like UT's, pure 12th ET plays a zero-sum game because the concordances of the 5ths, octaves, and 12ths come at the expense of tempered M3rds just like in pure octave ET, but this is a solution with a solid history. As long as there have been modern pianos, there has been stretch; pure 12th ET stretches in quantity about the same as traditional stretch; the difference is that the stretch is carefully controlled to be uniform through more than just the middle 3 octaves, one might claim it is uniform through the whole scale. When combined with high precision tuning technique, and after a good bit of practice at it, the effect can be heard by many laymen as a very, very good tuning. You continue to mention the shimmer of ET, but I hear purity and coherence and consonance in every single key with the modern ET's 

    "If the central three octaves in which most harmonic activity is set up are tuned without stretch, then the fundamental of many of the scale notes will interrelate in exact mathematical accordance."

    I don't see the way in which this statement could be true. If one tunes the upper note of an interval to sharp partials, then the intervals as measured at the fundamentals will be wide to the mathematical model and will not "interrelate in exact mathematical accordance". Really wish we could reconcile this language; it would be worth the effort.

    "By doing this, the inharmonic partials are sent all over the place, not reinforcing each other. So then the harmonicity of the scale overcomes the inharmonicity of the strings making the inharmonicity irrelevant."

    This sounds to me to be a description of chaos, not coherence, dissonance not consonance, and this could be readily heard as such.

    You know, you and I share an interest in Pianoteq. Maybe we should share some short demonstrations of the effects about which we speak, recorded with Pianoteq. We could even develop MIDI files to be played with each of our preferred settings in A-B fashion.









  • 13.  RE: Which temperament is the best for controlling inharmonicity?

    Registered Piano Technician
    Posted 03-15-2019 20:59
    Kent, I think the language problems can be resolved as long as apples=oranges, models=experiential reality, and music is restricted to foreshortened keyboards in specified keys.

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    Steven Rosenthal
    Honolulu HI
    808-521-7129
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  • 14.  RE: Which temperament is the best for controlling inharmonicity?

    Posted 03-16-2019 06:19
    Yes - language is a problem. Perfect thirds are in my language perfect mathematical 5/4 thirds to which brass players are accustomed playing on harmonics, particularly horn players. Sweet and beatless and it's these that give brass groups and barber-shop quartets their tight sound.

    With a UT involving lots of perfect fifths tuning by perfect fifths means that the fundamental notes are tightly fitting between them ignoring harmonicity. Using an electronic tuner is a shortcut, but the 1st partial or 2nd harmonic, the octave, is rarely terribly out so one can get a good result with conventional means. It doesn't really have to be exact. 1/2 beat per second isn't going to matter because the sound of the piano dies away and I think that lots of decimal points in calculations sap away from really what we can hear and what matters. In essence, many harmonicity curves are reasonably flat in the central octaves anyway so it's not really a problem. But if there is a hint of stretch the one interval which can be disturbing is the Tenor C# to the Treble F - is that 3C# to 5F? So if tuning with any risk of inharmonicity stretching what you're doing, just don't be frightened to cheat and raise the bottom C# by a beat. One can very tied up trying to be really exact but the real world isn't always, and its the spirit of the tuning that works.

    Yes - Pianoteq is a most fantastic laboratory and I think one can use it as pointers as to what _might_ happen on a real instrument. It's really good but I still feel the effects are more pronounced on the real instrument. When tuning I often hear a higher presence of 5th harmonic on the real instrument than I seem to hear on Pianoteq, although it is there.

    It's the introduction of the 5th harmonic which really changed piano tone from the 1870s onwards, and gave the opportunity to instruments to impress by dazzle of shimmer with the smoothly progressing beating 3rds against the 5th harmonics. Before this onset of the modern period the 5th harmonic was much more suppressed, the 3rd harmonic being strong, and which gave a special accordance with the tuning systems with perfect 5ths. 

    So another way of looking at things with respect to UTs is that the systems using perfect fifths turn the clocks back to the former piano tonality. The 5th harmonic in the modern instrument is still there so in some keys it sings whilst in others it still shimmers, and so we're able to get the best of both worlds.

    In jazz and improvisation, being able to get another tone colour by modulation is found to be great fun. There are many musicians who simply don't know what they can achieve better with UT and resistance to it is often merely being frightened of what they don't know about. Once tried many are converted.

    In Pianoteq play around with the modern instruments in Well Temperament rather than equal. On an experiment recently with a good musician, the Pianoteq version of the Grotrian sounded better in ET but the tonality of most of the other modern instruments seemed nicer in Well Temperament or Kirnberger III, WT however giving more nuanced differences between keys.

    Best wishes

    David P

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    David Pinnegar, B.Sc., A.R.C.S.
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    +44 1342 850594





  • 15.  RE: Which temperament is the best for controlling inharmonicity?

    Registered Piano Technician
    Posted 03-15-2019 21:25
    When you talk about "perfect thirds" my music theory teaching memories scream in protest.

    If you mean "beatless thirds" like in meantone, my cello playing aural template of intervals, deeply ingrained since age 10, refuses to consider them musically acceptable, though some people like them. To have both perfect fifths and beatless thirds in a temperament requires some really gross interval deformations. Pythagoras would probably not have approved.

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    Susan Kline
    Philomath, Oregon
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  • 16.  RE: Which temperament is the best for controlling inharmonicity?

    Posted 03-16-2019 05:28
    Kent,

    "In UT's the concordances in some keys are the direct result of making discordances in other keys."

    What happens if an unequal temperament is very close to equal temperament?

    The effect that you have described would surely be minimised to the greatest extent.

    Those who favour equal temperament and those who favour unequal temperament could just meet in the middle to resolve their differences.

    Think of a venn diagram. One circle contains equal temperament. The other circle contains unequal temperament. Both circles overlap to form a common ground.

    A temperament that lies within this common ground is my well temperament.

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    Roshan Kakiya
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  • 17.  RE: Which temperament is the best for controlling inharmonicity?

    Registered Piano Technician
    Posted 03-16-2019 09:52
    A UT doesn't control the inharmonicity, if bringig together many perfect intervals it simply makes it irrelevant. 

    This is like saying that physics is irrelevant. This is not true.

    If the UT has a number of perfect fifths arranged so that there are some perfect thirds too, then there will be a lot of mathematical concordance in the vibrations produced. That harmonises. If the central three octaves in which most harmonic activity is set up are tuned without stretch, then the fundamental of many of the scale notes will interrelate in exact mathematical accordance. By doing this, the inharmonic partials are sent all over the place, not reinforcing each other. So then the harmonicity of the scale overcomes the inharmonicity of the strings making the inharmonicity irrelevant.

    Tuning the central three octaves with a clean 2:1 goal goes against what tuners have been doing for the past century. Most tuners stretch at least as far as to make the 4:2 octave clean. This leaves the 2:1 octave wide and helps the fifths to be slightly closer to pure at the 3:2 level, but leaves fourths moving a little fast. Most, if not all, piano tuners reject 2:1 octaves as sounding narrow/flat. Even though it may seem that going for the narrower octave would clean things up, it just makes the upper coincidental partials more noisy and jangly. It also contributes to eventually making the high treble sound flat and the low bass not flat enough. In short you can't ignore physics. Inharmonicity rules in pianos. That's not to say you can't play with mild UTs. But we aren't dealing with harpsichords or even fortepianos here. Inharmonic upper partials influence the final sound.

    Richard West





  • 18.  RE: Which temperament is the best for controlling inharmonicity?

    Registered Piano Technician
    Posted 03-16-2019 12:16
    Isn't it the case that inharmonicity varies inversely to tension?

    Thus, couldn't one reduce inharmonicity simply by raising the pitch?

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    Scott Cole, RPT
    rvpianotuner.com
    Talent, OR
    (541-601-9033
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  • 19.  RE: Which temperament is the best for controlling inharmonicity?

    Posted 03-16-2019 12:20
    Yes.
     When the strings are at their breaking points, the inharmonicity is zero!

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    Ed Sutton
    ed440@me.com
    (980) 254-7413
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  • 20.  RE: Which temperament is the best for controlling inharmonicity?

    Registered Piano Technician
    Posted 03-16-2019 12:48
    Interestingly, when I hiked my piano up to A-444hz (temporarily to see if it made any difference) I found that it sounded better (to me) and a number of weird things in many (not all) notes virtually disappeared. Those same anomalies came back when I brought it back down to 440hz.

    So yes, tension does affect inharmonicity. 

    Edit:  Inharmonicity is what creates the unique sound profile of the modern piano. If there was zero IH it would sound much more like an organ to our ears. The combination of: 1) inharmonic partials, 2) The number of audible partials, 3) The relative amplitudes of each partial all combine to create the sound that we refer to as the modern piano.  Keith Coop demonstrated and proved this in a class at Lancaster last summer. It was more than just interesting. 

    Play just one note (no 3rds or 5ths or whatever)...you are hearing the effect of inharmonicity. It's there due to the physical structure of the instrument.  Also, a freely vibrating string is different in its harmonic output than a bowed string.

    Pwg

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    Peter Grey
    Stratham NH
    603-686-2395
    pianodoctor57@gmail.com
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  • 21.  RE: Which temperament is the best for controlling inharmonicity?

    Posted 04-03-2019 07:44
    What I meant here is that if the 7th and 9th, especially the 9th partials are put either onto a scale note, or removed well away from it, their contribution either enhances harmony or becomes irrelevant. Likewise bringing the 5th harmonic nearer to unison with the scale note, or removing it well away. When the 2nd 3rd and 4th harmonics line up harmoniously and the 5th in some keys they can be so strong in chord combinations that they overpower inharmonic sounds.

    Put another way, a perfect fifth produces a sub-fundamental an octave down. When this occurs in a chord it reinforces. A 4th harmonic and a 5th harmonic produce a subfundamental two octaves down. When you play for instance a C below Tenor C, an E above Tenor C, in Kirnberger III or Kellner you'll have an extra resultant E above middle C, without playing the E, as the 5th harmonic and 2nd harmonic of the lower notes line up and reinforce. This tightness of tuning improves harmony and the extra rich reinforces harmonious content makes the inharmonic sounds irrelevant. It overpowers them.

    Linguistic descriptions are inadequate - we can only try to convey the idea of intention. It's only in the real experience that we can hear a reality difficult to describe in words. Even electronic recordings are not recreations of the reality of an instrument before our ears, however good that might be.

    Perhaps I'm describing techniques that in ET give a flat sound. In a UT it ceases to be flat as the key unlocks doors to soundscapes of different tonality.

    Best wishes

    David P

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    David Pinnegar BSc ARCS
    Curator and House Tuner - Hammerwood Park, East Grinstead, Sussex UK
    antespam@gmail.com

    Seminar 6th May 2019 - http://hammerwood.mistral.co.uk/tuning-seminar.pdf "The Importance of Tuning for Better Performance"
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  • 22.  RE: Which temperament is the best for controlling inharmonicity?

    Registered Piano Technician
    Posted 04-04-2019 11:05


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    David Love RPT
    www.davidlovepianos.com
    davidlovepianos@comcast.net
    415 407 8320
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