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Thread: Tempered and Untempered Intervals

  1. #1
    Apprentice, Piano
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    Tempered and Untempered Intervals

    Dear ALL,

    Would someone please tell me what those captioned intervals are?

    Thanks

  2. #2
    Lieutenant Commander, Concertmaster
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    Quote Originally Posted by grand choeur View Post
    Dear ALL,

    Would someone please tell me what those captioned intervals are?

    Thanks
    If you want, you can have a look here:

    http://pages.globetrotter.net/roule/temper.htm#_nr_340

    All the best,

    Torsten

  3. #3
    Captain of Water Music Thomas Dressler's Avatar
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    To make it simple, an untempered interval is one that is truly in tune. A tempered interval is one that is purposely not in tune.

    The reason we have tempered intervals is that in reality, notes do not function like they do on the keyboards we use in western music. C-sharp is NOT really the same note as D-flat. This is the very simple explanation of a very complex subject. In order to make the notes fit on our western (12 notes per octave) keyboard, intervals have to be tuned OUT OF TUNE on purpose.

    There are different ways of doing this, and equal temperament is only one, and it does not really work well for Baroque and earlier music. Generally, notes are tempered as follows: fifths are tuned slightly flat, thirds are tuned sharp.

  4. #4
    Captain of Water Music Thomas Dressler's Avatar
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    For more on the subject of temperament, check out this thread as well:

    http://www.magle.dk/music-forums/1429-temperament.html

  5. #5
    Commodore con Forza
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    Quote Originally Posted by Thomas Dressler View Post
    To make it simple, an untempered interval is one that is truly in tune. A tempered interval is one that is purposely not in tune.

    So maybe they should really be called untampered and tampered intervals.

    (Sorry, couldn't resist...)

  6. #6
    Captain of Water Music Thomas Dressler's Avatar
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    HAHA! I have to remember that one. . .

    A choir member recently gave me what appears to be a very good book on the subject of temperament. The title could be a little off-putting to some people, but it really seems to be worthwhile reading. It explains things pretty well and has a lot of interesting information.

    How Equal Temperament Ruined Harmony (and Why You Should Care) by Ross W. Duffin. W.W. Norton and Company, 2007.

  7. #7
    Admiral of Fugues Contratrombone64's Avatar
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    Johann Sebastian was a bit of a pioneer in this field ... brilliant mind, which shows in his music

  8. #8
    Commodore de Cavaille-Coll
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    Tampered and Distempered Intervals...

    Ok,

    Where Kirnberger III is known as Triple McCheeseburger...

    And where Chromatics is a rare blood disease...


    Giovanni

  9. #9
    Lieutenant Commander, Concertmaster
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    ' untempered ' intervals can also be decribed as ' just intonation '
    (the ratios of the frequencies of the notes are integers)
    To make a just scale that can play a song with 3 major chords:
    Dominant, Subdominant, and Tonic :
    for a triad (major chord) ratios = 3,4,5
    say.....c,e,g
    to get a progression:
    6, 8, 9
    6=3 since we are dealing with harmonic math
    likewise 8=4
    so we have c,e, (needed for progression)
    to make a simple progression in 4/4 :
    6*4=24=c
    6*8=48=C
    6*3=18=g
    6*8=48=C
    8*4=32=f
    8*8=64=F
    8*3=24=c
    8*8=64=F
    9*4=36=g
    9*8=72=G
    9*3=27=d
    9*8=72=G
    8*4=32=f
    8*8=64=f
    8*3=24=c
    8*8=64=F
    repeat
    note: multiply 'a' (20) by 11 to set ' a=440 '

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