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Re: Musical notes...

Cross-posted to 3 groups.

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James Dow Allen <user4353@newsgrouper.org.invalid> posted:

> 
> Show of hands, please.  How many of you view rec.puzzles in a
> fixed-width font?  IIRC back in the 20th century, this newsgroup
> had an over-riding default to fixed-width (Courier) because many
> presentations relied on that.




https://rec.puzzles.narkive.com/

https://newsgrouper.org/rec.puzzles
https://csiph.com/group/rec.puzzles
       ------- BOth these sites let me switch easily between views.


> 
>  - - - - - - - - -
> 
> Music scales lead to interesting exercises in simple arithmetic.
> Nothing new in this post, but it might be a starting point for those who've
> never thought about the arithmetic of music intervals.
> 
> In the following diagram white keys on the piano are shown as AAA, BBB, etc.
> Black keys are shown as ,,, or mmm.  The keys C major and A minor use
> only white keys, but for ease of comparison we look at the key of C minor
> where three black keys (E♭, A♭ and B♭) are used.
> 
>      CCC  ,,,  DDD  mmm  EEE  FFF  ,,,  GGG  mmm  AAA  mmm  BBB  CCC
>       24  ...   27  28.8  30   32  ...   36  38.4  40  43.2  45   48
>                         "3rd" "4th"    "5th"     "6th"     "7th"
> 
> Starting with C = 24 arbitrarily, the other white keys are simple integers:
> Initially 24, 27, 30.  The numbers need to be sort of logarithmic,
> so the whole step difference increases from 3 to 4: 32, 36, 40.
> (The step from 30 to 32 is just a half step: There's no black key in between.)
> Finally, the difference is 5 (40, 45) with the final 45, 48 another
> half-step.
> 
> If you ever forget the simple rational numbers which define the Just Scale,
> the above explanation for (24, 27, 30, 32, 36, 40, 45, 48) should
> obviate the need for Google.  Unfortunately if you tune your piano
> to produce the Just Scale for C Major, it won't be Just in any other key.
> 
> The black keys shown above for C Minor have ratios to C=24 that may look
> uninviting (28.8/24 "minor 3rd", 38.4/24 "minor 6th", 43.2/24 "minor 7th")
> but multiply throughout by 25/24 and get nice numbers: 6/5, 8/5, 9/5.
> (In "principle."  Your instrument is very unlikely to be tuned this way.
> 6/5, 14/9, 16/9 is another solution for the black keys in C minor.)
> 
> The scales evolved, and some cultures used quite different scales.
> Etc., etc.
> 
> James

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Thread

Musical notes... David Entwistle <qnivq.ragjvfgyr@ogvagrearg.pbz> - 2026-05-27 08:20 +0000
  Re: Musical notes... James Dow Allen <user4353@newsgrouper.org.invalid> - 2026-05-27 12:58 +0000
    Re: Musical notes... David Entwistle <qnivq.ragjvfgyr@ogvagrearg.pbz> - 2026-05-27 18:06 +0000
      Re: Musical notes... David Entwistle <qnivq.ragjvfgyr@ogvagrearg.pbz> - 2026-05-28 10:15 +0000
  Re: Musical notes... ram@zedat.fu-berlin.de (Stefan Ram) - 2026-05-27 16:25 +0000
    Re: Musical notes... James Dow Allen <user4353@newsgrouper.org.invalid> - 2026-05-27 17:10 +0000
  Re: Musical notes... James Dow Allen <user4353@newsgrouper.org.invalid> - 2026-05-28 12:30 +0000
    Re: Musical notes... HenHanna@NewsGrouper <user4055@newsgrouper.org.invalid> - 2026-05-28 18:21 +0000
    Re: Musical notes... msb@vex.net (Mark Brader) - 2026-05-28 18:50 +0000
    Re: Musical notes... David Entwistle <qnivq.ragjvfgyr@ogvagrearg.pbz> - 2026-05-29 17:19 +0000
    Re: Musical notes... Charlie Roberts <croberts@gmail.com> - 2026-05-29 15:48 -0400
      Re: Musical notes... ram@zedat.fu-berlin.de (Stefan Ram) - 2026-05-29 20:59 +0000
        Re: Musical notes... James Dow Allen <user4353@newsgrouper.org.invalid> - 2026-05-30 12:07 +0000
          Re: Musical notes... James Dow Allen <user4353@newsgrouper.org.invalid> - 2026-05-30 12:25 +0000
            Re: Musical notes... James Dow Allen <user4353@newsgrouper.org.invalid> - 2026-05-30 12:33 +0000
            Re: Musical notes... ram@zedat.fu-berlin.de (Stefan Ram) - 2026-05-30 12:56 +0000
    Re: Musical notes... Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2026-05-29 22:38 +0100
      Re: Musical notes... David Entwistle <qnivq.ragjvfgyr@ogvagrearg.pbz> - 2026-05-30 06:38 +0000
    Re: Musical notes... Phil Carmody <pc+usenet@asdf.org> - 2026-06-05 16:41 +0300
      Re: Musical notes... James Dow Allen <user4353@newsgrouper.org.invalid> - 2026-06-05 14:54 +0000

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