Re: Intervals enharmony question

[Hans Åberg]

> On 1 May 2018, at 09:23, Malte Meyn <address@hidden> wrote:
> 
> Am 30.04.2018 um 22:11 schrieb Hans Åberg:
>>> On 30 Apr 2018, at 21:47, Malte Meyn <address@hidden> wrote:
>>> 
>>> Am 30.04.2018 um 21:32 schrieb Hans Åberg:
>>>> One has to adapt the pitch on every note played, and the reference is 
>>>> typically the string section, which in turn is tuned in Pythagorean,
>>> 
>>> Many string players tune their perfect fifths a bit small so that they’re 
>>> near to equal temperament (700 ct) or even smaller instead of just (702 ct).
>> So how do they tune their violins?
> 
> Tune a fifth perfectly just and then make it a little bit smaller. This of 
> course needs experience so that it’s only 2 ct smaller.

But they still bow when tuning, and not using a chromatic tuner.

>> And why would an orchestra do this: it increases the beats in the chords.
> 
> It increases beats only in the fifths of open strings. All other fifths and 
> other intervals in general can be adjusted by the players. And it’s nicer to 
> have a 400 ct third C–E than 408 ct as a starting point for such adjustments.

If they do not play the retuned fifths harmonically that might be OK in 
harmony, but in melody, Pythagorean tuning sounds better to me than E12.

>>>> but can adapt into 5-limit Just Intonation if the music played follows the 
>>>> Traditional Harmony rules.
>>> 
>>> They could, yes. But I think that most intonation in choir and orchestra is 
>>> not just intonation but more or less an approximation; for example leading 
>>> notes are often played higher than just because they have more of the 
>>> leading character then. And just intonation has other problems that make it 
>>> impractical.
>> It is adaptive JI: If pivoting the chord sequence C F Dm G C, it slips a 
>> syntonic comma. So the orchestra must slide the pitch somewhere. Sounds 
>> terrible on music like organs, though.
> 
> That’s one of the problems I had in mind.

Some synth software has adaptive tuning as choice, for example, MainStage, so 
one can check what it sounds like on an organ.

> There are other reasons why just intonation, even adaptive JI isn’t really an 
> option and is not what orchestras use to play:

There is no problem for an orchestra, though. Some measurements suggest that 
when performing twelve tone music, they will actually slip into something like 
Pythagorean tuning. It does not matter, though: if there is no harmony, pithces 
can be chosen quite freely.

> for example, enharmonic equivalents in modulation (like <c e g bes> = <c e g 
> ais>) cannot really be intonated perfectly just.

Some measurements I made suggest they just play the stacked thirds which can be 
adjusted for, that is 5-limit JI. So if you do not spell it out correctly, they 
will play the stacked thirds instead.

>>>> That becomes more difficult in distant keys.
>>> 
>>> Why should it? Just intonation works in every key.
>> Because there is no reference to the Pythagorean notes.
> 
> I’m not sure what you’re talking about here: What are these Pythagorean 
> notes? Pythagorean tuning means using only perfect fifths, that’s not just 
> intonation.

The string section open strings. There seems to be no other absolute pitch 
references in an orchestra.