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Re: Intervals enharmony question

From: Hans Åberg
Subject: Re: Intervals enharmony question
Date: Mon, 30 Apr 2018 20:50:41 +0200

> On 30 Apr 2018, at 20:15, Jacques Menu Muzhic <address@hidden> wrote:
> Going a bit further, I bumped into this case.
> Since the note at some interval from another one keeps its pitch name in its 
> different « variants », how about Db’s seconds?
> diminished second   Ebbb ???
> minor second        Ebb
> major second        Eb
> augemented second   E
> I’m sure no one ever uses triple flats though, must have missed something…

Use the two-dimensional keyboard layout below, extending them as necessary: Put 
in a chord which you know, and transpose it, or move from the one diagram to 
the other. A seven-note diatonic scale will always have all seven note names.

           ^ #
         . -> M
        / \
     b v   v m
where M (resp. m) is the major (resp. minor) second, and the
the sharp # (resp. flat b) raises (resp lower) with the interval
M - m, that is, the difference between the major and minor seconds.

Resulting key pattern, in a scale using names A B C D E F G:
      C#  D#  E#
    C   D   E   F#  G#  A#  B#
  Cb  Db  Eb  F   G   A   B
            Fb  Gb  Ab  Bb  C'
In terms of traditional interval names, writing
  P  pure
  M  major
  m  minor
  A  augmented
  D  diminished
plus numbers: 1st, 2nd, etc., this is
      A1  A2  A3
    P1  M2  M3  A4  A5  A6  A7
  D1  m2  m3  P4  P5  M6  M7  A8
    D2  D3  D4  D5  m6  m7  P8

>> Le 30 avr. 2018 à 15:50, Hans Åberg <address@hidden> a écrit :
>>> On 29 Apr 2018, at 22:17, Jacques Menu Muzhic <address@hidden> wrote:
>>> OK, now everything is clear, it’s precisely on jazz chords I’m working.
>> FYI, I recall the Mehegan books on jazz improvisation applying enharmonic 
>> equivalents freely. The Blatter books on instrumentation suggests applying 
>> them to simplify for harpists, which will save time and money. But 
>> orchestral instruments depart from Pythagorean tuning, not E12, so they are 
>> not equivalent, differing by a comma of about 20 cents.

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