RE: [tuning] Re: Questions on chords

John deLaubenfels wrote,

>>Pierre, if these two seventh chords were regarded as consonant, they
>>would not have need for resolution.

>I very much disagree! I'm taking this statement out of context, and
>haven't heard Pierre's work, but to my ear, a well-tuned 7-limit
>dominant 7th (4:5:6:7, or some inversion thereof) is both beautifully
>consonant AND in pressing need of resolution. This combination of
>qualities gives it, and the transition, irresistible beauty (again, to
>my ear).

John, if you read Blackwood, you would know that a better word for
describing your pure 4:5:6:7 dominant seventh would be _concordant_.
Consonance, in the analysis of Western tonal music, does imply a lack of
need for resolution, which the seventh and tritone in the dominant seventh
chord could never possess, however well-tuned. Since you seem to agree with
Blackwood in principle, it might be clearer, especially when conversing with
those trained in the Western tradition, to use this terminological
distinction.

_However_, I part with both you an Blackwood in that I see some fluidity in
what constitutes consonance, depending on musical style. In Gothic music,
for example, a triad was felt to be dissonant, and had to resolve to a
3-limit dyad. In blues and rock the dominant seventh can be used for all the
chords in the I-IV-I-V-IV-I progression, and it has no need to resolve to a
triad. Similarly, much latin jazz in a mixed-minor mode ends on a minor
chord with added major sixth. In this spirit, my paper
(http://www-math.cudenver.edu/~jstarret/22ALL.pdf) proposes a new type of
"tonal" music where approximations to 4:5:6:7 and 1/7:1/6:1/5:1/4 tetrads
can, with enough exposure, become recognized as the canonical "consonances",
to which other chords would resolve, and compared to which, triads would
sound incomplete.

At 05:40 AM 8/15/00 -0600, you wrote:
>[Paul Erlich wrote:]
>>>>Pierre, if these two seventh chords were regarded as consonant, they
>>>>would not have need for resolution.
>
>[I wrote:]
>>>I very much disagree! I'm taking this statement out of context, and
>>>haven't heard Pierre's work, but to my ear, a well-tuned 7-limit
>>>dominant 7th (4:5:6:7, or some inversion thereof) is both beautifully
>>>consonant AND in pressing need of resolution. This combination of
>>>qualities gives it, and the transition, irresistible beauty (again, to
>>>my ear).
>Jay here,
Much of the time I would agree that 7ths, 9ths, and 11ths imply some sort of
resolution. But this discussion made me thing: "What if the 7th chord that
concludes the Sanctus in the Stravinsky "Mass" or the 11th chord that
concludes the whole piece were tuned as pure intervals?" To my ear they
would be perfectly acceptible as resolved sonorities, in fact, quite
beautiful. As is, in e.t. tuning, they always leave me with a slight
up0in-the-air feeling which I don't mind, but wonder what Stravinsky
really had in mind.
>
>
>
>
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I am having difficulty with the notion that the 4567
needs to resolve. If the stasis of the overtone series does does not need to resolve, why should a straight ordering with the root in the bass need to resolve? There must be a rule of inertia involved.

Johnny Reinhard

I wrote,

>>John, if you read Blackwood, you would know that a better word for
>>describing your pure 4:5:6:7 dominant seventh would be _concordant_.
>>Consonance, in the analysis of Western tonal music, does imply a lack
>>of need for resolution, which the seventh and tritone in the dominant
>>seventh chord could never possess, however well-tuned.

John deLaubenfels wrote,

>So, you're saying that the word consonance == "doesn't need resolution".
>What word ("non-consonance?") is the opposite? I've always thought
>that consonance and dissonance were opposites, but dissonance implies
>actual beating intervals, does it not?

In the analysis of Western tonal music, the perfect fourth is considered
dissonant if it occurs between the bass and another voice. So in that
context, dissonance does not mean actual beating intervals. Sethares uses
the term "sensory dissonance" for the latter, and Blackwood used
"discordant".

>A single piano note is struck by the
>hammer in such as way as to minimize, if not eliminate, the 7th
>harmonic, so a chord deliberately tuned to 4:5:6:7 would seem to be a
>completely different animal.

That is a myth. It may have been true at one point -- hammers hitting the
string 1/7 of the way along their length -- but today's piano hammers strike
much closer to the end of the string. Anyway, I still suggest your feeling
of a need for resolution is based on excessive [:)] exposure to diatonic
tonal music -- and perhaps most egregiously [:) :) :)], your 7-limit
adaptive retunings of classical pieces, where dominant seventh chords are
deliberately pulled toward 4:5:6:7. Listen to the blues for a while and see
if you still feel that 4:5:6:7 needs to resolve.

>I do listen to the blues, as it happens, but please tell me: where does
>one find blues music with 7ths properly tuned? I'm sure I don't have to
>tell you, Paul that a 12-tET dom 7th is very different from 4:5:6:7.

Exactly, but if the 12-tET dom 7th doesn't need to resolve, isn't it true
that retuning to 4:5:6:7 makes it need _even less_ to resolve? At least
that's my perception.

Hi,

Paul Erlich wrote, regarding hammer strike points:
> >That is a myth. It may have been true at one point -- hammers hitting
> >the string 1/7 of the way along their length -- but today's piano
> >hammers strike much closer to the end of the string.

at which John deLaubenfels exclaimed:

> No kidding! Can the piano tuners on this list confirm this?

John Broadwood rationalized strike points to 1/8 string length in the
late 18th century; Robert Wornum topped him thirty years later with an
equal tension stringing scale using a single string guage for all plain
wire unisons.

Modern piano manufacturers are far more empirical, but myths abound. I
keep intending to measure every instrument we rebuild - here's a start.

Approximate strike lengths measured from a handy 1931 Chickering scale
135:

note String ~Strike ~ratio
88 51 3 1/17
80 75 5 1/15
70 126 9 1/14
60 222 20 1/11
50 395 38 1/10
40 633 68 1/9
30 920 114 1/8
20 1068 129 1/8
10 1140 143 1/8
1 1182 152 1/8

Regards,

Clark