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Single octave - Just intonation vs 12-tone equal temperament | by endolith
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Single octave - Just intonation vs 12-tone equal temperament

Same as flic.kr/p/6px5VQ but with equal temperament lines added graphically in Inkscape.

 

Names of some of these intervals:

 

1/1 (unison P1)

16/15 (minor second m2)

9/8 or 10/9 (major second M2)

7/6 (septimal minor third)

6/5 (minor third m3)

5/4 (major third M3)

4/3 (perfect fourth P4)

7/5 or 10/7 (tritone TT)

3/2 (perfect fifth P5)

8/5 (minor sixth m6)

5/3 (major sixth M6)

7/4 (harmonic seventh)

16/9 or 9/5 (minor seventh m7)

15/8 (major seventh M7)

2/1 (octave P8)

 

Many of the white lines have names, but you can't play them on a piano.

 

Horizontal axis is logarithmic. As you can see, these notes are not in any natural way equally spaced. Equal temperament is bogus.

 

Height of the white lines is just the numerator times the denominator, as circuitously described here, drawn so that low numbers are taller. This just shows the "smallness" of the ratio. I used log scaling of the vertical axis to make things look better, so I think this is actually identical to Tenney's harmonic distance measure. Please clarify if I'm wrong.

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Uploaded on December 31, 2009