Re: Virtual pitch

In article <TbIfi.974$YS.740@trnddc03>, "Steve Latham"
<llatham@xxxxxxxxxxx> wrote:

But every source I've ever seen has said that the
Pythagorean diatonic scale is formed from a stack of P5ths.

What sources?

Actually, my high school physics text said that.

The Harvard concise dictionary of music says it too. Cf.
http://en.wikipedia.org/wiki/Pythagorean_tuning

No, that's *tuning*, not the scale. And scale here refers to, not a *tuning
scale* but a scale scale, like a Major scale.

They seem to be used synonymously in this context. The Harvard dictionary
says the Pythagorean scale wholly derived from pure fifths. In reality, it
means using the partials 2 and 3. In the
Wikipedia, Pythagorean scale redirects to the link above.

Pythagorean comma is derived from stacking 5ths, but the Greek genera, 
Modes, and Major and Minor scales were not.

The major Just intonation is derived by assuming: partials 2, 3, 5, octave
transposition and inversion (which gives p1 = 1, p8 = 2, p5 = 3/2, p4 =
4/3, M3 = 5/4), and that the major chord 4:5:6 should be correct at p1, p4
and p5 (giving the other intervals of the diatonic scale). I wrote some
axiomatization of this before.

Hans Aberg
.

Relevant Pages

  • Re: Two Schemes for Just Intonation
    ... I got this table for a twelve note scale from above, ... There is more than one way to construct a Just Intonation. ... By using E53 one can get intuition of the sizes of JI in relation to ... Intonation supports any number of notes per octave. ...
    (rec.music.theory)
  • Re: Virtual pitch
    ... which gives the chord p1:M3:p5 = ... gives the diatonic scale. ... thinker out there maybe this will be included in the future as a tone. ... They are, but none of them involves partials higher than 5, if it is Just. ...
    (rec.music.theory)
  • Re: Helmholtz and OTS
    ... p1, p4, p5, gives the rest of the diatonic scale. ... which had clearly emerged by around 1520-1525, where major and minor thirds ... references to ratios of 7. ... The idea I presented is that the choice of the partials 2, 3, 5 ...
    (rec.music.theory)
  • Re: Question about the meaning of "alt." chords
    ... it is between the 11th and the 12th partials that the 1st instance of the min 2nd interval appears. ... And supposedly the Western scale systemreally evolved out of various people's practices of combining tetrachords and tunings of tetrachords. ... 12TET, in particular, rounds off the above chords so that they are all much more useful. ... But I still believe that all people, in all cultures, experience combinations of pitched tones in essentially the same way *on some level*, and that this experience has its roots in the freq ratios found in the harmonic overtone series. ...
    (rec.music.theory)
  • Re: Virtual pitch
    ... gives the diatonic scale. ... Then the minor chord appears in two positions of ... they evolved towards accepting the old dissonances as consonances. ... They are, but none of them involves partials higher than 5, if it is Just. ...
    (rec.music.theory)