Call me a "Zartist"

>Graham Breed wrote:
>> So, the melody C-D-Dbb-Cx-Dbb-Cx-Dbb-D is the same as C-D-C-D-C-D-C-D?
>> You don't hear the interval Dbb-Cx as a semitone?
>
>Question: can you _sing_ this progression... accurately? If so, you are a
true >lusus natur=E6.

Barbershop singers must then be superhuman, as most can and do sing way way
way more accurately than this.

>In the more usual timbres at least, the 7:6 interval beats too much to
>be consonant, affected as it is by the unison. The 7:5 is obscured by
>the fifth and fourth. There is a slightly stronger case for the 7:4, but
>note that the first partial of the lower tone beats with the fundamental
>of the upper tone (8:7).=20
>
>The 7:4 forms dissonant intervals with the consonances of the senario,
>whereas 8:5 does not (at least not with 6:5 & 4:3).=20

This is all Greek to me. All of the septimal intervals are used in
Barbershop singing, and I've got some Barbershop that sounds like glass.
Exposure to it has been known to cause paradigm shifts.

>Your phrase "vanishing of the syntonic comma" is unfortunate. This comma
>does vanish in the 22-tone equal, but at a value (218 cents) that leads
>to excruciatingly dissonant 'major thirds' (436 cents)

This third is only 1 cent off the 9/7, which is only dissonant if you use it
like, or expect to hear a 5/4. Speaking of which, the 7th 22TET degree
offers a 5/4 far better than 12 or 19 tone. Only 4 cents off.

>minor thirds (273 cents)

The 7/6 is the 7th superparticular, one of the most consonant intervals
known to man. The 22TET, 6 cent deviation is very significant, however.

>major sixths (927 cents) and minor sixths (764 cents)

Inversions of the above.=20

>as soon as one modulates more than a few keys. But even if one remains
>within the same key, many intervals within the tonal fabric become
>dissonant so long as fifths of 709 cents are preserved.

We're talking about equal temperament?

>To those who treasure each new whining, commatic dissonance like the
goose's >golden egg, and hate consonance with a passion, this temperament is
indeed a
>gift from the gods.=20

The gods aren't cool enough to have invented dissonance

>The major semitone (164 cents) and minor semitone (55 cents) are=20
>utterly divergent from western habits, though the former is melodically
>usable.=20

But the other isn't melodically usable?

>Another and simpler way of expressing the non-cyclic character of the
>22-tone equal is to observe that the three consonant cycles (those of
>the fifth, major third and minor third with their inversions) are
>incommensurable. What this really entails is often overlooked. Some
>theorists simply look at the 327- 382- & 709-cent intervals of 22-tone
>equal, and conclude that this temperament has good representations of
>the consonances. In doing this, they forget that as soon as one
>modulates (or proceeds by any number of melodic phrases that involve the
>simultaneous use of the 5- and 3- limits) one obtains highly dissonant
>thirds, so long as the fifths are held consonant. This is doubtless
>obvious to many theorists, but not to all. Mandelbaum, for example, a
>person of no inconsiderable theoretical attainments, fell into this
>trap.

I don't understand.

>I do however categorically deny that any singers whatever (allowance
>made for the occasional alien with 31-tone equal ears)
>can reliably reproduce intervals narrower than 55-60 cents in melody.

Narower from what?

Carl


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