Discussion: View Thread

the meaning of setting the temperament

  • 1.  the meaning of setting the temperament

    Registered Piano Technician
    Posted 10-19-2014 15:26
    This message has been cross posted to the following Discussions: Pianotech and CAUT .
    -------------------------------------------
    My esteemed colleagues

    I am in the process of writing a short article for music teachers about setting a temperament, and I want to accurately describe what the term "setting a temperament" means and where it came from. I have an idea, but I want to get some input from you guys. (I don't need information on how to set a temperament. That I know).   


    -------------------------------------------
    Willem "Wim" Blees, RPT
    Mililani, HI 96789
    -------------------------------------------


  • 2.  RE: the meaning of setting the temperament

    Member
    Posted 10-19-2014 17:12
    The meaning of the word comes from the verb "temper". As you know, the math of the physics of the string make it impossible to tune twelve perfect fifths and still have a perfect octave, so the need to narrow the fifths was called "tempering" the fifths. The "temperament" is the pattern of "tempering" that you use to accomplish the truing of the octave.

    --
    | || ||| || ||| || ||| || ||| || ||| || ||| || |||
    jason's cell 425 830 1561





  • 3.  RE: the meaning of setting the temperament

    Registered Piano Technician
    Posted 10-20-2014 03:30
    Don't organs and harpsichords also need tempering?

    Maria G. Pollock
    Registered Piano Technician
    773 307 5207

    The best way to get things done is do them.




  • 4.  RE: the meaning of setting the temperament

    Registered Piano Technician
    Posted 10-20-2014 03:40
    Maria

    Organs don't. Harpsichords do need to be tuned with a temperament.

    -------------------------------------------
    Willem "Wim" Blees, RPT
    Mililani, HI 96789
    -------------------------------------------




  • 5.  RE: the meaning of setting the temperament

    Registered Piano Technician
    Posted 10-20-2014 05:05

    Organs don't follow the same protocol as piano temperaments, but their tunings are indeed tempered. Ask any organ tuner.
    -------------------------------------------
    Tom Servinsky
    -------------------------------------------




  • 6.  RE: the meaning of setting the temperament

    Posted 10-20-2014 08:17
    Tempering is simply the spacing of notes. Actually all 88 piano keys are tempered. The temperament as most tuners know it is the spacing of the notes in an octave. As you know, modern tuning is called equal temperament based on the 12th root of 2. A mathematical equation to equally space the notes. Organs indeed are tempered with the same formula. 

    Pianos however have harmonics that are out of tune, referred to as inharmonicity, Out of tune harmonics are often referred to
    as partials (part of the whole).

    This inharmonicity causes a deviation of the actual fundamental pitch from being a perfect match to the mathematical formula for equal temperament.

    For instance of A4 is vibrating at 440 cycles per second, the partial created by the string being divided by 2 (the second partial) will likely vibrate faster than 880. It might be 880.1 or 880.2 but it could be anywhere. So to tune A5 we might need to tune it to 880.2 to have it sound, or be in tune. These are call coincidental partials. I explain to customers (who are interested) that this is simplifying tuning an octave in what tuners call a 2:1 ration for an octave. We can also match other partials like 4:2, 6:3 etc.

    And I explain that the same thing goes on with every interval we tune.

    And figuring out this puzzle is different in every piano, which is what makes tuning so much fun for me!.








































    Don't organs and harpsichords also need tempering?

    Maria G. Pollock
    Registered Piano Technician
    773 307 5207

    The best way to get things done is do them.


















  • 7.  RE: the meaning of setting the temperament

    Posted 10-20-2014 08:55


    -------------------------------------------
    William Hocherl
    Altoona PA
    814-943-0759
    -------------------------------------------




  • 8.  RE: the meaning of setting the temperament

    Registered Piano Technician
    Posted 10-22-2014 08:42
    So, slightly OT, but teaching this today. Why do some intervallic beat speeds progress, thirds and sixths , if others , fifths and fourths come to mind, remain relatively constant in ET? A good question from my students. I know my usual answer, but would like  the forum to weigh in with current thinking.
    TYIA

    David

    -------------------------------------------
    David Brown
    Dallas TX
    214-288-9413
    -------------------------------------------

    -------------------------------------------


































    Don't organs and harpsichords also need tempering?

    Maria G. Pollock
    Registered Piano Technician
    773 307 5207

    The best way to get things done is do them.























  • 9.  RE: the meaning of setting the temperament

    Registered Piano Technician
    Posted 10-22-2014 13:43
    It's a result of inharmonicity and stretch in response. The fifths are wider than "calculated," hence they approach beatless (or wide, depending on how much you stretch). Al Sanderson said 4ths tend to have the same beat rate throughout, which is another result of stretching: a lower 4th/upper 5th will have the 4th beating faster if the 4:2 octave is wide. So the 4ths tend to remain the same while the 5ths are slower, but this will depend on how much you stretch.

    The really wide (or narrow), 5th partial based intervals (M3, M6, m3, m6) will progress in beat rate more or less as predicted by calculation. By calculation I mean what the beat rates would be without inharmonicity or stretch. In the case of these intervals, the stretch of the upper note more or less cancels out the inharmonicity effect of the lower note. At least that is how I picture it.
    Regards,
    Fred Sturm
    "Since everything is in our heads, we had better not lose them." Coco Chanel






  • 10.  RE: the meaning of setting the temperament

    Posted 10-23-2014 03:47
    There's another way of looking at this beat-rate increase/decrease. Where middle 'A' is 440Hz, the 8ve. above should be 880Hz and the 8ve. above that 1760Hz. This is the simplistic view-point. Likewise, in the downward direction the 'A' below middle 'A' will be 220Hz and the one below that = 110Hz. Plotted on a graph you can see a curve. All the notes of a piano should follow this curve. Therefore any intervals will be subject to it as well. I find that 10ths., which are stretchable to my hand, show this curve in a conveniently audible fashion. But 17ths. are even more audible - if less convenient. Is this a good illustration for your students, David?   Michael (UK)

    -------------------------------------------
    Michael Gamble
    semi retired
    Brighton
    01273813612
    -------------------------------------------




  • 11.  RE: the meaning of setting the temperament

    Posted 10-24-2014 17:05
    Michael,
    this is an excellent picture of what is temperament. The clearest I've heard in so many years, I would adopt it in the next course, if you allow me.
    Best regards,
    Luigi


    -------------------------------------------
    Luigi Lamacchia
    i
    Bari
    -------------------------------------------




  • 12.  RE: the meaning of setting the temperament

    Posted 10-25-2014 04:49
    Of course, please do, Luigi. I am very flattered by your answer! If this simplistic illustration helps your students in the understanding of E.T. - at least it's something tangible.   Michael (UK)

    -------------------------------------------
    Michael Gamble
    semi retired
    Brighton
    01273813612
    -------------------------------------------




  • 13.  RE: the meaning of setting the temperament

    Posted 10-24-2014 01:59
    The only difference between tuning a pipe organ and tuning a stringed instrument is that varying the pitch of a pipe has no effect whatever on the adjacent pipes - unlike a piano which does.... The largest organ I tuned was a 5 manual at Doncaster Parish Church. That took three days. It still does!   Michael (UK)

    -------------------------------------------
    Michael Gamble
    semi retired
    Brighton
    01273813612
    -------------------------------------------




  • 14.  RE: the meaning of setting the temperament

    Registered Piano Technician
    Posted 10-21-2014 09:54
    Organs need tempering as well. I know because I tuned and played organ. I asked the question to see if everybody understands the difference between the musical comma and inharmonicity.

    Maria G Pollock RPT
    773 307 5207




  • 15.  RE: the meaning of setting the temperament

    Posted 10-20-2014 15:23
    Hello,

    Not only are fifths and octaves incompatible, but so are thirds and octaves and thirds and fifths. By incompatible I mean, for example, that if you tune three pure contiguous thirds and then listen to the resulting octave, you have a very unmusical, narrow octave. Setting the temperament is the process of reconciling these incompatibilities in such a way that the instrument is musical. 

    --
    Alan McCoy
    (509) 999-9512





  • 16.  RE: the meaning of setting the temperament

    Posted 10-21-2014 04:25
    This aspect is born out by what is known as 'The Circle of Fifths' If you start
     with A=440 and go round the tuning to perfect fifths, by the time you reach that A=440 again you will be out by what is known as the Pythagorian Interval. It is this interval which is cunningly distributed over the 13 semitones of the Octave which give the various Temperaments.   Michael (UK)
    -------------------------------------------
    Michael Gamble
    semi retired
    Brighton
    01273813612
    -------------------------------------------




  • 17.  RE: the meaning of setting the temperament

    Registered Piano Technician
    Posted 10-21-2014 10:22
    Although the relationship of fifths to the octave (12 fifths = more than an octave) tends to be what current piano tuners focus on, what is far more important for our keyboard scheme (12 notes in an octave) is the fact that three major thirds fall FAR short of an octave (and four minor thirds FAR beyond an octave). 

    The question of how large to make major thirds has been the basic problem over the centuries. They will always have an average width of an equal tempered third (if you have 12 keys per octave). Any third that is narrower than an equal tempered third will have to be compensated for by making another third wider. 

    The fifths are almost irrelevant in their sound, as the equal tempered fifth is barely noticeably narrow. But when you add them together, they affect the thirds a lot. If you decide to have pure (just) thirds, you will narrow the fifths enough to make them noticeably out of tune, and you will also be limited to eight major thirds (the other four will be far too wide to be usable).
    Regards,
    Fred Sturm
    "A mind is not a vessel to be filled, but a fire to be kindled." Plutarch









  • 18.  RE: the meaning of setting the temperament

    Posted 10-22-2014 07:21
    When tuning ET I use an 'invisible' tuning tool - the 17th. when outside the bearing area.Can't stretch it of course with one hand (not being Rachmaninoff!) but by playing through the piano chromatically, on completion, using the 17th. one can appreciate the gradual increase (going upwards or decrease going downwards} of the resultant beat-rate of the harmonics and then one can question any gross deviations! It's a great 'tool'. Better than the 10th. but not as convenient! - no good for UT of course!     Michael (UK)
    -------------------------------------------
    Michael Gamble
    semi retired
    Brighton
    01273813612
    -------------------------------------------




  • 19.  RE: the meaning of setting the temperament

    Registered Piano Technician
    Posted 10-21-2014 09:08
    I see the temperament as the distribution of the 12 chromatic notes within an octave.

    Ross W Duffin says in his book How Equal Temperament Ruined Harmony:

    "Temperament is a way of tuning the notes of the scale using intervals that have been modified (tempered) from their pure forms."

    -------------------------------------------
    Mario Igrec
    http://www.pianosinsideout.com
    -------------------------------------------




  • 20.  RE: the meaning of setting the temperament

    Registered Piano Technician
    Posted 10-21-2014 23:31
    Tuners employ a temperament octave. But the proper application of piano tuning techniques results in the entire compass of notes being tempered. This include octaves in pianos. The first step in tempering a piano is to decide how wide the octaves will be and then use your intervallic tuning/testing routines to subdivide the octaves into whatever intervallic tempering scheme you desire.

    -------------------------------------------
    Edward McMorrow
    Edmonds WA
    425-299-3431
    -------------------------------------------




  • 21.  RE: the meaning of setting the temperament

    Posted 10-22-2014 07:25
    The amount of octave stretching (which is being mentioned here) is dependent on the piano being tuned, its quality and its size. Some pianos just don't take to 8ve stretching at all.  Michael (UK)

    -------------------------------------------
    Michael Gamble
    semi retired
    Brighton
    01273813612
    -------------------------------------------