Pianotech

Expand all | Collapse all

Well-Temperament

  • 1.  Well-Temperament

    Posted 06-07-2019 10:59
    Reference Thomas Young in Jorgenson's book, "Tuning" Nothing new under the Sun.

    ------------------------------
    Frank French, RPT
    Piano Technician
    Tuners Art
    frank@tunersart.com

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


  • 2.  RE: Well-Temperament

    Posted 06-07-2019 12:11
    What is the accepted meaning/definition/interpretation of well temperament?

    Did Bach use equal temperament and/or unequal temperament?


    "In 1850 the Bach-Gesellschaft was formed with the purpose of publishing the complete works of Johann Sebastian Bach (1685-1750) as part of the centenary celebration of Bach’s death. The collected works, without editorial additions, became known as the Bach-Gesellschaft-Ausgabe. After the formation of the Bach-Gesellschaft, during 1873, Philip Spitta (1841-1894) published his biography of Bach. In this biography Spitta wrote that Bach used equal temperament. In other words, by the late 19th century, it was assumed by one of the more important writers on Bach that Bach used equal temperament.

    During the 20th century, after the rediscovery of various kinds of historical temperaments, it became generally accepted that Bach did not use equal temperament. This theory was mainly based on the fact that Bach titled his collection of 24 preludes and fugues of 1722 as ‘Das wohltemperirte Clavier’, traditionally translated as the ‘Well-Tempered Clavier’. Based on the title, it was assumed during the 20th century that an unequal temperament was implied – equating the term ‘well-tempered’ with the notion of some form of unequal temperament.

    But, are we sure that it was Bach’s intention to use an unequal temperament for his 24 preludes and fugues? The German word for ‘wohl-temperiert’ is synonymous with ‘gut-temperiert’ which in turn translates directly to ‘good tempered’. Does a ‘good temperament’ necessarily exclude equal temperament?"

    Source: ​http://huygens-fokker.org/docs/Kroesbergen_Bach_Temperament.pdf

    ------------------------------
    Roshan Kakiya
    ------------------------------



  • 3.  RE: Well-Temperament

    Posted 06-07-2019 13:20
    Roshan-
    Having been reading and tuning for some 40 years, I can tell you that there is just enough historical information to support a rather wide range of hypotheses about Bach's tuning practice. In fact it is about time for a new theory to acclaim itself and tell us why all others are wrong.
    Interestingly, so far it seems that all assume that Bach had a highly accurate sense of temperament, and that there was one and only one way he tuned his harpsichord. If the slightest historical evidence otherwise should appear, we may expect a new cottage industry which, by analysis of Bach's compositions, would discern exactly how he tuned his clavier is 1728 and how he changed the temperament by 1732.
    My opinion, perhaps wrong, is that anyone's authoritative answer is an educated guess at best.
    Mathematics is precise. The square root of 2 is the same everywhere, as many decimal places as you can calculate.
    Tuning is highly generalized. Fuzzy. A harpsichord goes out of tune when a door opens and lets in a cool breeze for 30 seconds, or when a spotlight shines on the open instrument. Most of the time, nobody notices and folks just keep playing.

    ------------------------------
    Ed Sutton
    ed440@me.com
    (980) 254-7413
    ------------------------------



  • 4.  RE: Well-Temperament

    Posted 06-07-2019 14:20
    One of the biggest arguments for Bach expecting key colour to come out of his 48 is the prelude in D major in Book II which accords with Schubarts description of the expected key characteristics in an unequal temperament. Rejoicing and fanfares and a bugle call or hunting horn is exactly how the piece starts.

    Best wishes

    David P

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





  • 5.  RE: Well-Temperament

    Posted 06-07-2019 16:03
    If "good" temperament is another term for "well" temperament and equal temperament is not a "well" temperament, does that mean equal temperament is a "bad"/"unwell" temperament?


    What was the meaning of "good" in the world of tuning during Bach's time?

    Was a "good" temperament a temperament that made all keys usable?
    Was a "good" temperament a temperament that made key colours available?
    Was a "good" temperament a temperament that made all keys usable and also made key colours available?


    Is making all keys usable the only condition that must be satisfied to create a "well" temperament? If the answer is yes, equal temperament is a "well" temperament. If the answer is no, equal temperament is an "unwell" temperament because the opposite of "well" is "unwell".

    ------------------------------
    Roshan Kakiya
    ------------------------------



  • 6.  RE: Well-Temperament

    Posted 06-07-2019 16:43
    I believe "well-tempered" meant that the tuning had no "wolf" interval(s), i.e. could be used in all keys. It seems to basically be a descriptor for the condition of a particular instrument, like we might say "in tune." But of course one person's "wolf" could be a "strong third" for someone else. 
    Another term for this would be "circular temperament," i.e. it "circulates" around the circle of fifths.
    Thus equal temperament falls into the category of "well-tempered" and "circular" tunings.
    "Regular circulating temperaments" can be played in all keys and show some kind of mathematical/harmonic symmetry in their tempering patterns.
    Equal temperament could be seen as a regular circulating temperament.
    In the second half of the twentieth century, Owen Jorgensen invented the term "well-temperament," a noun which he used to categorize regular circulating temperaments organized such that the C-E third was the least tempered and the F#-A# third the most tempered, with the intermediate thirds progressing between. This temperament is taken to express appropriate "key color." 
    Thus, by the traditional Baroque meaning, equal temperament is "well."
    By the definition of Jorgensen and his followers, equal temperament is not a "well-temperament."
    Other scholars do not consider the term "well-temperament" a valid term. Not everyone holds Jorgensen in high esteem.
    Please recall that in the world, things that are not alike are not necessarily "opposite." Green and orange are not blue, but they are not "un-blue'' they just are not blue.
    History and musical instruments do not have the simple rationality of mathematics.
    If you want more answers you will need to undertake an extended study of tuning and temperament and form your own opinions

    ------------------------------
    Ed Sutton
    ed440@me.com
    (980) 254-7413
    ------------------------------



  • 7.  RE: Well-Temperament

    Registered Piano Technician
    Posted 06-08-2019 12:12
    As one of many students whose lives were changed and enriched by Owen Jorgensen, I will attempt to interpret what I understood him to say:

    I believe "well-tempered" meant that the tuning had no "wolf" interval(s), i.e. could be used in all keys.

    Correct!  There is discussion about exactly which temperament Bach had in mind, but key coloration was amply written about in the period, and seems part of the harmonic vocabulary in the preludes and fugues.

    In the second half of the twentieth century, Owen Jorgensen invented the term "well-temperament," a noun which he used to categorize regular circulating temperaments organized such that the C-E third was the least tempered and the F#-A# third the most tempered, with the intermediate thirds progressing between. This temperament is taken to express appropriate "key color." 
    Thus, by the traditional Baroque meaning, equal temperament is "well."
    By the definition of Jorgensen and his followers, equal temperament is not a "well-temperament."
    Other scholars do not consider the term "well-temperament" a valid term. Not everyone holds Jorgensen in high esteem.

    It's clear you never knew him, because everyone who did holds him in the highest esteem.  He was a supremely curious and modest man who tried to figure out the history of tuning and temperaments.  He thought the same musical archeological work he did from English sources (he read extensively, everything he could get his hands on, from American and British libraries and museums, pre-Internet) remained to be done from German and French sources.  He believed in the scientific method, proposed a theory, and made experiments (I can talk about the methodology I saw), knowing his work would be amplified in the future.  He would have been excited to learn of new discoveries in the field.
    What was the meaning of "good" in the world of tuning during Bach's time?

    Was a "good" temperament a temperament that made all keys usable?
    Was a "good" temperament a temperament that made key colours available?
    Was a "good" temperament a temperament that made all keys usable and also made key colours available?

    Jorgensen would have said "yes" to all three.


    Is making all keys usable the only condition that must be satisfied to create a "well" temperament? If the answer is yes, equal temperament is a "well" temperament. If the answer is no, equal temperament is an "unwell" temperament because the opposite of "well" is "unwell".

    I disagree:  equal temperament is a proper tuning for music conceived of in the mind of the composer without key coloration, as part of the musical expression.  

    Greetings to all,
    Linda Scott


    ------------------------------
    Linda Scott, RPT
    Portland, OR
    503-231-9732
    ------------------------------



  • 8.  RE: Well-Temperament

    Posted 06-08-2019 12:51
    Linda-
    I meant no criticism of Jorgensen as a person.
    I meant to point out that his work has received considerable criticism outside the circle of his followers.
    I use some of his offsets because I like the sound, but make no meta-claims about them.
    I don't believe the fate of the universe hinges on the width of Major Thirds, just our own enjoyment if we care about them.

    ------------------------------
    Ed Sutton
    ed440@me.com
    (980) 254-7413
    ------------------------------



  • 9.  RE: Well-Temperament

    Posted 06-08-2019 14:45
    I was not criticising equal temperament.

    I was only drawing attention to the impreciseness of the word "well".

    "Equal" and "unequal" are more precise words for describing temperaments, theoretically, because temperaments that are equal cannot be unequal and temperaments that are unequal cannot be equal. 

    Additionally, key colour can be expressed in terms of the varieties of any of the intervals of an unequal temperament.

    ------------------------------
    Roshan Kakiya
    ------------------------------



  • 10.  RE: Well-Temperament

    Posted 06-08-2019 18:13
    "Thus, by the traditional Baroque meaning, equal temperament is 'well'."

    Does any individual who has adopted the Baroque meaning of "well", such as myself, deserve to be criticised for doing so?

    ------------------------------
    Roshan Kakiya
    ------------------------------



  • 11.  RE: Well-Temperament

    Posted 06-08-2019 19:33
    " Does any individual who has adopted the Baroque meaning of "well", such as myself, deserve to be criticised for doing so?  "

    Yes. Actually.

    Equal Temperament is not a well temperament because it's not well at all. It's blind. Disabled from expressing contrasts of pure vs impure, clean vs dirty, solid vs liquid, certain vs uncertain and a whole lot else of expression. It has debased our music and not rewarded the sensitive musician for listening. As a result many musicians don't listen. They only transform black spots on paper into notes in time.

    I have said to my wife that if she needs (or wants) to awaken me out of a coma all she has to do is to play me a recording of Lang Lang playing the Raindrop prelude. I'll then awaken in a foul mood. Such musicians know nothing about the palette of sounds available to the instrument and music and have transformed it into mere entertainment.

    As for colour tuning being unsuitable for playing music not written to express colour - with all due respect a total misconception. 

    For years I have been demonstrating on my YouTube channel and elsewhere music by Debussy, Fauré, Berg, Prokofiev performed on an instrument tuned to Kellner temperament. It does no damage to the music, and in some cases so much the reverse that one wonders if the tuning of the day really was the Equal Temperament that we hear now.

    This afternoon we just presented a programme of harpsichord, all in Meantone and Kirnberger III, followed by the inaugural recital on an 1819 Beethoven model Broadwood grand tuned to Kellner. The programme was not entirely what you might expect:
    Keyboard Sonata in C minor - Giovanni Battista Pescetti (1704 - 1766)
    I Allegro ma non presto
    II Moderato
    III Presto
    Gargoyle no.2 op. 29 - Lowell Liebermann (b. 1961)
    Sonata in C major - Joseph Haydn (1732-1809)
    I Allegro con brio
    II Adagio
    III Finale - Allegro
    Sonata in A major, movement III Rondo 'Alla Turca' - Wolfgang Amadeus Mozart ((1765 - 1791)
    Mozart - Rondo 'Alla Turka'

    The Lowell Liebermann Gargoyle was extraordinarily good on this instrument tuned as it was and the whole programme was presented by it in a manner that a modern Steinway could only dream of.

    So often music is presented on "historic" instruments leaving one thinking "great music but shame about the instrument". Not at all what the audience experienced this afternoon.

    And that tuning does transfer successfully onto a modern piano too.

    Here's the first ever concert for which I tuned Kellner

    This was many years ago. I've refined the tuning technique since then.

    Another one from this time

    Perhaps it's no surprise that the instrument needed hammers re-felting after that.


    Here's another - Prolofiev 8 

    Equal temperament is a tuning rewarding no-one for listening that has transformed music into muzak and is hotel foyer tuning for hotel foyer pianos which have debased the concert platform, recordings, performers and audiences for far too long.

    Its ubiquity is not justified by its capability, rather incapability. 

    Whilst suitable for hotel foyer muzak other tunings can express the work of the masters as well and quite possibly arguably better. Whilst it might be suitable for 20th century music other tunings can be used with such music with no damage to the experience.

    Best wishes

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





  • 12.  RE: Well-Temperament

    Registered Piano Technician
    Posted 06-08-2019 22:37
    David, please. Your evangelism for unequal temperaments is fine and few on this forum seem to have much of a problem with it, but this hyperventilation of spleen over ET is just over the top and does your thesis no good.You've perused this forum enough to know that it is only you who uses such vituperative language, this is a technical forum, railing over and over about something that does not agree with your palette is tedious and parochial. 
    By the way, musical expression is by no means wholly dependent on tuning, good musicianship employs  a large and nuanced set of devices from articulation, tempo, pulse, to dynamics as well you know. 
    So please, take up your political cause in relevant journals, write a piece for Keyboard magazine, take your plaint to the world of musicians. We here know your position, your foul and snobbish language is only disruptive and does not advance your theoretical arguments. 
    Well-tempered indeed!

    ------------------------------
    Steven Rosenthal
    Honolulu HI
    808-521-7129
    ------------------------------



  • 13.  RE: Well-Temperament

    Posted 06-09-2019 06:44
    Dear Steven

    ;-) Please forgive me. It's simply that in Britain, and indeed there are some similar feelings on the continent, there's a sentiment that classical repertoire and piano music in particular has run its course. Senior professors of music have become despondent - as notably Chopin did according to Prof Jonathan Bellman when his favourite tuner died . . . but the good news is that upon experiencing an instrument I maintain one such professor has been reinvigorated saying that with such tuning she's able to evoke from the instruments sounds that she's been trying to reach for all her life and had not thought the instrument capable. She now realises it's the tuning and not the instrument, and that technicians have been out of touch with the music and the musical effect of what they've been doing. The trade of piano manufacturing and maintenance has been too out of touch with musical sound production, and the division of labour between tuning and playing has gone too far.

    Here's what the senior professor wrote to me the other day after her visit:
    " Such a revelation, and it all helped to make sense of the path I have been pursuing in my playing and teaching for many years. This has developed to now being almost entirely a matter of tuning, by touch, so that the music gradually emerges, from monochrome  to a palette of colours. Everything seems to follow logically from the "tuning."  I always thought it was a matter of adjusting the playing, - it never occurred to me that it was a matter of the actual tuning, so that was an extraordinary  discovery for me.
    I, too, have felt very alone in my way of working, knowing that my approach was diametrically opposed to that of all my colleagues, and that they could not begin to understand."

    On account of the impending collapse of music in the regions in which I inhabit, it's appropriate to be rather more than monochrome in my delivery of the message, and rather more than retiring in its volume.

    Whilst love me or hate me in my delivery - apologies for being snobbish about hotel foyer pianos and the muzak that is played on them and foul in referring to them thereto - the OP asked and invited response to the question " Does any individual who has adopted the Baroque meaning of "well", such as myself, deserve to be criticised for doing so?" and in doing so the manner of my answer included a hidden sense of humour which is difficult to perceive in the format of black and white on a computer screen through the abstract symbols which are words. "Baroque" was very much over-the top and the discussion a matter of ultimate meaning to the extension to the inescapability of the absurd and to which a response in the spirit of the Baroque appeared appropriate.

    However, whilst my delivery autistic in manner is worthy of your admonition, the content is another matter. The extent to which I have proved by experience and long experiment demonstrated by recordings from the very beginnings of those experiments that music not intended for chromatic performance in the true sense of the word isn't damaged by chromatic tuning.

    The myth which has been expressed by an author in this thread is well dispelled - and the point of the recordings quoted above demonstrates the need to do so. The persistence of the myth is a significant burden to music and the WikiPedia article on the Chromatic Scale is wholly blind to the meaning of Chromatic. "Chromatic" is not simply the going up of the scale in steps. Chromatic means colour and this word has no meaning in modern music. The meaning and the music has become impoverished in its demise.

    Wittgenstein remarked that the last barrier to humanity was in the overcoming of the limitations of language. At the end of our tuning hammers is a tool to overcome the current limitations of the musical language.

    By the way, what Roshan has done is extraordinary as he's demonstrated an assumption and something wrong with my analysis of harmonics and beats. By shifting semitones slightly, he's achieved a calming effect on the beats apparently approaching the effectiveness of Kellner unequal tuning. I had assumed that many of the beats come from the 9th Harmonic - but that is nearer to a tone than a semitone. Accordingly were he to have shifted relationships between tones I'd have expected the 9th Harmonic to be affected, but not the result of shifting semitones.

    With Baroque and unequally tempered wishes,

    David P


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





  • 14.  RE: Well-Temperament

    Registered Piano Technician
    Posted 06-09-2019 19:44
    David, none of which is an excuse for bad manners. Please remember where you are and stay on topic.

    ------------------------------
    Steven Rosenthal
    Honolulu HI
    808-521-7129
    ------------------------------



  • 15.  RE: Well-Temperament

    Posted 06-09-2019 20:24
    Dear Steven

    I'm so sorry but was not actually very much aware of anything that I might have said in my post could be interpreted as "foul language" nor "bad manners" other than answering the question posed and being objective in disproving the myth that "colour tuning" is unsuitable for 20th century works not intended for it, backed up by sufficient examples demonstrating the assertion. Whilst expressing such opinion in a forthright manner the manner of delivery appeared to me to be relatively objective in the face of the evidence rather than objectionable, other than in particular to Lang Lang in his interpretation of Chopin's Raindrop prelude.

    The assertion that colour tuning can be used for composition not written to invoke it was taken to the ultimate extreme yesterday with the piece "Gargoyle" by Liebermann on an instrument not only tuned to a chromatic tuning, but two centuries outdated  https://www.youtube.com/watch?v=sKxpJdvgoCQ  . See 9:50 .  At 28:16 you'll find the Mendelssohn Songs without Words No 2. and at 29:20 you'll find a significant change of musical colour that adds so much to the music, totally lost in modern performance with hotel-foyer tuning. 

    In specific answer to the question raised, a "well temperament" within the meaning of the Baroque cannot include "equal temperament"  because such tuning does not and cannot express the colour which we can hear being exploited by composers who wrote for it, who included Bach himself writing the 2nd Book Prelude in D major fairly and squarely within the context of Schubart's documentation of the key characteristics expected from the use of the key "The key of triumph, of Hallejuahs, of war-cries, of victory-rejoicing." opening as it does with a trumpet fanfare or hunting horn motif. For those not using the slider in Youtube videos here's what Mendelssohn had to say about the use of key colour https://youtu.be/sKxpJdvgoCQ?t=1758 . Hearing this, I don't think he'd have considered equal temperament a "well temperament" at all. 

    Best wishes

    David P 

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





  • 16.  RE: Well-Temperament

    Posted 06-10-2019 03:41
    "The development of equal temperament enabled the 12 major and minor keys to be established. This was the most significant thing to happen to the tonality of Baroque music."

    Source: https://www.bbc.com/bitesize/guides/z8tsh39/revision/3

    Is this information or misinformation?

    The source is BBC Bitesize which is a revision tool for students studying for their GCSEs.



    "Johann Sebastian Bach’s 'The Well-Tempered Clavier' was an early set of works which demonstrated the full range of equal temperament."

    Source: https://www.bbc.com/teach/class-clips-video/equal-temperament/zhhtscw

    Is this information or misinformation?

    The source is BBC Teach.

    ------------------------------
    Roshan Kakiya
    ------------------------------



  • 17.  RE: Well-Temperament

    Posted 06-10-2019 04:55
    Dear Roshan

    Thanks so much for pointing me to this. If ever I seem a little spicy in expression of opinion it's precisely because of misconceptions spread by such rubbish. And it really is rubbish, superstition of no substance. The "experts" have been seen to be promoting the Emperor's New Clothes for well over a century.

    Equal temperament was certainly not the development that "enabled exploration of all the major and minor keys" and the recordings of the Chopin 24 Preludes, in Kellner unequal temperament, are here to prove it - 

    Perhaps hearing the colour change to which I've pointed out in the Mendelsohn Song Without Words, the chords changing shape, the delight of the surpise, the milestone in the journey of the story of the piece, might be enough to explain the real new excitement that we can restore to classical music and the piano in particular. www.youtu.be/sKxpJdvgoCQ?t=1758 

    Best wishes

    David P

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





  • 18.  RE: Well-Temperament

    Posted 06-10-2019 05:50
    Is there any solid evidence which conclusively proves that Bach thought a "Well-Tempered Clavier" can be achieved by using equal temperament?


    Is there any solid evidence which conclusively proves that Bach thought a "Well-Tempered Clavier" cannot be achieved by using equal temperament?

    ------------------------------
    Roshan Kakiya
    ------------------------------



  • 19.  RE: Well-Temperament

    Posted 06-10-2019 08:31
    As far as I know the squiggle on the top of Bach's 48, I believe misread and misinterpreted by Lehman, is a potential liklihood of evidence towards an unequal and against an equal temperament.

    It was subsequently a matter of "debate" between from memory Mersenne and Kirnberger, a pupil of Bach, in which Bach's family took up Kirnberger's side.

    Kellner's temperament is based on Kirnberger's 1779 III temperament and Bach's music sounds good with both. There is debate as to how far that temperament was known or disseminated at the time and a very dirty quagmire greets further speculation in such directions.

    The fact that the family held for Kirnberger against the proponent of equal temperament is for me indicative. Speculation beyond that hasn't been necessarily helpful but doing the experiment of applying the music to such tuning allows the music to be its own witness statement. Such experiment has not been very wide reaching beyond the confines of the few deemed "eccentrics" mad enough to have achieved it. Ed Foote is legendary and Enid Katahn a heroine.

    Best wishes

    David P

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





  • 20.  RE: Well-Temperament

    Posted 06-10-2019 08:44
    David,

    "As far as I know the squiggle on the top of Bach's 48 . . . is a potential likelihood of evidence . . . against an equal temperament."

    Is there any solid evidence that can conclusively prove or conclusively disprove this assumption?

    ------------------------------
    Roshan Kakiya
    ------------------------------



  • 21.  RE: Well-Temperament

    Registered Piano Technician
    Posted 06-10-2019 11:35
    There is a HUGE difference between mathematical equal temperament and the ability to play equally in all keys. One is a noun, the other a verb (in essence). Bach did not tune ET anywhere near what we today know as ET. 

    Historians and scientists commonly make mistakes in their interpretations when they are looking at evidence through a "modern" looking glass.  

    Pwg

    ------------------------------
    Peter Grey
    Stratham NH
    603-686-2395
    pianodoctor57@gmail.com
    ------------------------------



  • 22.  RE: Well-Temperament

    Posted 06-10-2019 11:56
    Is a piano that has been tuned to an approximation of equal temperament a "well-tempered piano"?

    ------------------------------
    Roshan Kakiya
    ------------------------------



  • 23.  RE: Well-Temperament

    Posted 06-10-2019 14:17
    With respect in my opinion and experience of alternatives, equal temperament or an approximation thereto is not a well temperament as it does not express the music well ;-)

    My experience is that a good unequal temperament or "well temperament" can substitute for equal temperament being able to work for music not composed for it, but that equal temperament is inadequate to work for music composed with liklihood of chromatic exploration and exploitation.

    Were your TV or computer screen be confined to black and white you would not consider it a "well" device at all whereas colour screens can serve well even for black and white.

    Equal temperament is a genre unto itself.

    There is actually an important reason for using a well temperament rather than a pseudo equal temperament. Whereas equal temperament gives the piano a glistening conflict of harmonics with scale notes, so a shimmering characteristic in which nothing is still, your pseudo equal calms that down. When we have a well designed well temperament giving variations between keys then depending on the key we can choose what is still and what is glistening. Sunshine and shade rather than constant grey skies.

    Best wishes

    David P

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





  • 24.  RE: Well-Temperament

    Posted 06-10-2019 16:08
    I think "well temperament" needs to have a standard definition.

    I have proposed a simple, clear standard definition and I have also shown how it can be modified to account for equal and unequal temperaments:

    "Well Temperament: A temperament that makes every key usable.

    Equal Well Temperament: A temperament that makes every key usable and has identical semitones throughout.

    Unequal Well Temperament: A temperament that makes every key usable and does not have identical semitones throughout."

    https://my.ptg.org/communities/community-home/digestviewer/viewthread?MessageKey=da22d3bf-9ef3-4b7d-acbf-fdaa773c281c&CommunityKey=6265a40b-9fd2-4152-a628-bd7c7d770cbf

    ------------------------------
    Roshan Kakiya
    ------------------------------



  • 25.  RE: Well-Temperament

    Posted 06-10-2019 16:39
    The definition is standard among all who understand the term -  https://en.wikipedia.org/wiki/Well_temperament 

    "Well temperament means a mathematical-acoustic and musical-practical organisation of the tone system within the twelve steps of an octave, with the goal of impeccable performance in all tonalities, based on the natural-harmonic tone system [i.e., extended just intonation], while striving to keep the diatonic intervals as pure as possible. This temperament acts, while tied to given pitch ratios, as a thriftily tempered smoothing and extension of the meantone, as unequally beating half tones and as equally beating [i.e., equal] temperament.

    Equal temperament is not based on the natural-harmonic tone system.

    Best wishes

    David P

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





  • 26.  RE: Well-Temperament

    Registered Piano Technician
    Posted 06-10-2019 17:55
    Aren't both Well and Equal temperaments defined by deviations from pure intervals?

    ------------------------------
    Steven Rosenthal
    Honolulu HI
    808-521-7129
    ------------------------------



  • 27.  RE: Well-Temperament

    Posted 06-10-2019 18:05
    Definition of equal temperament:

    "An equal temperament is a musical temperament, or a system of tuning, in which the frequency interval between every pair of adjacent notes has the same ratio."

    Source: https://en.m.wikipedia.org/wiki/Equal_temperament


    In this case, equal temperament has not been defined in terms of deviations from pure intervals.

    ------------------------------
    Roshan Kakiya
    ------------------------------



  • 28.  RE: Well-Temperament

    Registered Piano Technician
    Posted 06-10-2019 19:16
    Roshan, upon further thought I arrived at that too. I guess it is the methodology of aural tuning that derives ET based upon pure intervals. Yet I wonder if that's a distinction without a difference. There are mathematical definitions of Well temperaments also.

    Here's another definition of ET:
    "Modification of the intervals of just intonation in the tuning of instruments of fixed intonation to permit harmonic modulation. It allows one to modulate to or play in any of the 12 major or 12 minor keys."

    ------------------------------
    Steven Rosenthal
    Honolulu HI
    808-521-7129
    ------------------------------



  • 29.  RE: Well-Temperament

    Registered Piano Technician
    Posted 06-10-2019 22:16
    ET1/2STEP = (8800 + INHARMONICITY) cents/ 88 ?


  • 30.  RE: Well-Temperament

    Posted 06-11-2019 04:37
    12 tones to the pure octave equal temperament:

    Semitone = 1200 × log2(2)1/12 = 1200 × 1/12 × log2(2) = 1200 × 1/12 × 1 = 1200 × 1/12 = 100 cents.


    19 tones to the pure twelfth equal temperament:

    Semitone = 1200 × log2(3)1/19 = 1200 × 1/19 × log2(3) = 100.10 cents.


    7 tones to the pure fifth equal temperament:

    Semitone = 1200 × log2(3/2)1/7 = 1200 × 1/7 × log2(3/2) = 100.28 cents.

    ------------------------------
    Roshan Kakiya
    ------------------------------



  • 31.  RE: Well-Temperament

    Registered Piano Technician
    Posted 06-11-2019 07:49
    I think "well temperament" needs to have a standard definition.

    I have proposed a simple, clear standard definition and I have also shown how it can be modified to account for equal and unequal temperaments:

    "Well Temperament: A temperament that makes every key usable.

    Equal Well Temperament: A temperament that makes every key usable and has identical semitones throughout.

    Unequal Well Temperament: A temperament that makes every key usable and does not have identical semitones throughout."


    Roshan,

    Personally, I actually like your proposed definitions, however I would suggest insertion of one qualifying expression in EWT as follows: 

    Equal Well Temperament: A temperament that makes every key usable and has virtually identical semitones throughout.

    Reason: It is actually impossible to achieve total equality in these intervals from a mathematical standpoint. However we can come close enough so that what slight variations do exist in practice  become musically irrelevant (in context). 

    Pwg

    ------------------------------
    Peter Grey
    Stratham NH
    603-686-2395
    pianodoctor57@gmail.com
    ------------------------------



  • 32.  RE: Well-Temperament

    Posted 06-11-2019 08:11
    Peter,

    It is theoretically possible to have identical semitones throughout an equal temperament. The definition that I have proposed for Equal Well Temperament is the theoretical definition. For example, every semitone, theoretically, has a size of 100 cents in 12 tones to the pure octave equal temperament.

    I like your modification because it accounts for the variations that occur in practice.


    Theoretical definition of Equal Well Temperament:

    A temperament that makes every key usable and has identical semitones throughout.


    Practical definition of Equal Well Temperament:

    A temperament that makes every key usable and has virtually identical semitones throughout.

    ------------------------------
    Roshan Kakiya
    ------------------------------



  • 33.  RE: Well-Temperament

    Registered Piano Technician
    Posted 06-11-2019 09:39
    "Theoretical/Mathematical Definition of Equal Well Temperament:

    A temperament that makes every key usable and has identical semitones
    throughout."

    Given that this is a forum for discussion of piano tuning topics, I
    need to point out that there is a well-established definition of equal
    temperament on the piano:

    Equal temperament is that temperament in which the beat rates of all
    like intervals progress smoothly across the chromatic scale.

    There is no ultimate authority when it comes to piano tuning theory.
    And piano tuning theory is not fully discussed in the wider world of
    music theory, probably because the field of piano tuning is small, and
    the problem of applying the theoretical mathematical temperaments to
    the inharmonicity-laden piano is a very challenging problem that is
    not widely understood.

    Even so, piano tuning theory exists among the piano tuning
    practitioners and is well-developed and should be recognized and
    respected for what it is, one of the great human endeavors.

    True, piano tuners do not always agree about what constitutes a good
    piano tuning. However, piano tuning organizations around the world
    have had some success establishing standards for piano tuning, no
    small feat!

    There is a great deal of material whose source is piano tuning
    practitioners, and this material is worthy of your study. You will not
    ever understand piano tuning theory just by studying general music
    tuning theory. Give us the credit due our endeavor.

    We have repeatedly suggested appropriate piano tuning theory sources.
    Do we need to list them yet again?




  • 34.  RE: Well-Temperament

    Registered Piano Technician
    Posted 06-11-2019 10:15
    Thanks, Kent, for your comments. It is interesting to me that a music based math has become a scientific measurement tool: that's where mathematicians and piano turners get into trouble. The cents system of acoustical measurement is well established. It is math based. It is our ruler in both senses of the word. There's no good reason why acoustical measurements have to necessarily be based on the 12-note division of an octave. I guess this is where history intrudes into the discussion. The fact that  pianos and piano tuning don't fit neatly into that measurement system confuses mathematicians and creates discussions like this one that really just rehash mathematical arguments of the 19th century. Rehashing history can be instructive, if not ponderous.

    I prefer equal temperament on pianos; others argue for more variety. I will not stand in the way. I believe in using unequal temperaments on harpsichords and fortepianos. But I find that the task of getting modern pianos to approximate an equal temperament is hard enough without complicating the task with unequal temperaments. Ultimately I feel that all piano tuning ends up unequal to some extent. And there's beauty in it and satisfaction in the work and the final result.

    Richard West








  • 35.  RE: Well-Temperament

    Posted 06-11-2019 16:09
    "  I believe in using unequal temperaments on harpsichords and fortepianos. But I find that the task of getting modern pianos to approximate an equal temperament is hard enough without complicating the task with unequal temperaments.   "

    Actually they are not difficult nor more complicated, just slightly different

    Best wishes

    David P

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





  • 36.  RE: Well-Temperament

    Registered Piano Technician
    Posted 06-12-2019 07:41
    I have been reading, mostly, but not necessarily following these threads. 

    Would someone please restate what I think I read in one of them some time ago?

    Is it that using some unequal temperaments eliminates the need for stretching, or is it that some users of unequal temperaments prefer not to stretch?

    Thanks.

    ------------------------------
    Cindy Strehlow
    Urbana, IL
    ------------------------------



  • 37.  RE: Well-Temperament

    Posted 06-12-2019 08:04
    On stretching with unequal temperaments, yes - to some extent no stretching is required because there are important relationships between notes of the scale at the fundamental frequencies of 7 perfect fifths in Kellner or Kirnberger III, some near pure thirds too, these intervals become much more important in the music than the octave coincidence of 2nd partials.

    In addition, variable stretching takes the widest thirds too wide.

    This holds for the central three octaves. Tenor C upwards to Middle C upwards to Treble C upwards into that octave. Above that tune as you want. Below Tenor C, on good and well scaled pianos tune so that the unison and or quint harmonics falling in the middle octave or the tenor octave accord. 

    Because such tuning accords with the harmonics in harmony a more musical sound can be created by the pianist.

    Best wishes

    David P

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





  • 38.  RE: Well-Temperament

    Registered Piano Technician
    Posted 06-12-2019 09:16
    Cindy asked: Is it that using some unequal temperaments eliminates the need for stretching, or is it that some users of unequal temperaments prefer not to stretch?

    David replied: to some extent no stretching is required

    Richard adds: And therein is the crux of the problem. Unequal temperament was suited to non-inharmonic strings found in early keyboards with fewer keys and lower tension. The inharmonicity of heavy, higher tension wire creates problems as the unequal intervals are expanded from the one initial octave in the middle of the piano. 

    All the inharmonic upper partials demand some stretch in pianos. As David says, you can choose to minimize the stretch in the middle three octaves, but at some point you may have to over stretch to make up the difference. This is in contrast to current thinking in pure 12th "equal" temperament. The very first octave is expanded as much as possible, but within the limits of inharmonicity. The pure 12th is the current "hot" interval, in that it can be used to expand the tuning in a way that melts all the inharmonicity together to create a really "pure" sound, i.e., the octaves all sound very clean and the upper octaves sound neither sharp nor flat when playing arpeggios.

    Richard West







  • 39.  RE: Well-Temperament

    Registered Piano Technician
    Posted 06-07-2019 17:02
    The terms "well" or "good" are in contrast to what was otherwise commonly used, referred to as the "vulgar" (common) tuning. This was Pythagorean and only allowed playing in about 2/3 of the "available" keys...therefore it was not "good" nor "well" for playing in all keys. Bach wanted to became to play in all the keys, making all the harmonies available for musical expression. He was though, thoroughly familiar with the consistently accepted key coloration that results from centering clearest harmony around the key of C. 

    Therefore his tweaking of the temperament did not destroy that progressive key coloration, but rather "robbed Peter to pay Paul" and opened up the previously unavailable keys, albeit with a lot of dissonance in them, but at least they were now usable as opposed to unusable. They were by NO MEANS anywhere near EQUAL (but they were "good"). I believe an analysis of the music itself proves this.

    "Well temperament" is simply a term to describe the broad range of unequal temperament ideas that existed prior to the adoption of "equal temperament".  The term "equal temperament" is still slightly a misnomer since it is virtually impossible to consistently produce a TRULY EQUAL temperament also. I'm theory yes, in practice no.

    Pwg

    ------------------------------
    Peter Grey
    Stratham NH
    603-686-2395
    pianodoctor57@gmail.com
    ------------------------------



  • 40.  RE: Well-Temperament

    Posted 06-07-2019 17:12
    This sounds too Boolean for me.

    Wittgenstein I believe observed that the last barrier to humanity was the overcoming of the limitations of language

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





  • 41.  RE: Well-Temperament

    Registered Piano Technician
    Posted 06-07-2019 17:42
    Perhaps it is simply better to use the terms "equal" and  "unequal". 

    In the STRICTEST sense, TRUE equal temperament is simply impossible to achieve on an acoustic piano. However (in theory) it could be produced on an electronic keyboard that retains its pitch stability. 

    But we use the term ET because the best version of it is mighty close to EQUAL. "Close enough for jazz".

    Pwg

    ------------------------------
    Peter Grey
    Stratham NH
    603-686-2395
    pianodoctor57@gmail.com
    ------------------------------



  • 42.  RE: Well-Temperament

    Registered Piano Technician
    Posted 06-12-2019 00:37
    Music died the day that first rebellious 14th century monk sang a third instead of a fifth.  It's been all downhill since then.  And anyone who says differently is part of the conspiracy to kill music!  Which is already dead.  Because of pianos.  The end.

    ------------------------------
    Nicholas Litterski, RPT
    Austin TX
    512-573-8920
    ------------------------------



  • 43.  RE: Well-Temperament

    Posted 06-12-2019 09:20
    Nicholas...glad you are feeling open minded about things today <G>

    ------------------------------
    Jim Ialeggio
    grandpianosolutions.com
    Shirley, MA
    978 425-9026
    ------------------------------