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7

We first need to categorize each interval, assign it a "consonance amount". That's the first problem we find. In the case of the fourth, for example, some consider it perfect consonance, and others consider it a dissonance, depending context (and who you ask). For simplicity, let's define ours based on Wikipedia's: 1: Perfect consonances: unison, octave, ...


6

Maybe somewhat controversial. There is definitely some serious hokum going on here, you're right. BUT, I think you're underestimating the color differences a number of keys have on some instruments. The string section is the most dramatic—they generally have three strings that are free to vibrate sympathetically when they are playing a single pitch on the ...


5

As some of the other answers have eluded to, there are two basic problems with your question: The first is the question of how you generalize a "tritone" in a non-12-TET based system. One possibility is to interpret it literally as three whole tones (which then begs the question as to how you define a whole tone in a non 12-tone system). Another ...


5

Yes, and one can go a little bit further. The traditional qualities associated with common keys in the 18th century can be correlated with orchestration, in that different instruments sounded better (or, sometimes, could only really play well) in certain keys. Examples: A and E major had the reputation of being "fiery" -- probably because both keys would ...


5

"Are there other examples of common practice period manuscripts, or other documents that provide some indications on how to tune the instrument?" I think you're mostly looking for examples of scores/manuscripts, but as far as "other documents" go, there are certainly period treatises that describe various temperaments. One such example is "Lettre touchant ...


5

ALL notes in a JI system are a series of ratios in relation to the tonic. So what path you choose to get to any particular note is important in determining what its tuning is going to be. This means in JI a modulation is possible, but will bear little resemblance to a modulation in a tempered tuning system. The consonance of a secondary dominant is ...


4

For your specific points: 1) For most/all* instruments, the amplitude of the partials decreases as the partial number (i.e. frequency goes up). Thus, for almost all musical sounds there is "more of" the (first) octave and the fifth and less of the higher harmonics. So adding a second sound whose fundamental is at one of the lower harmonics reinforces ...


4

There might be a second question here, which regards the internal tuning of the cello strings, relative to itself. Cellos are typically tuned in fifths (C-G-D-A) of course, but there are pieces that require a different tuning (a technique called scordatura). In this case, wikipedia mentions that Bach's 5th Cello Suite was written for a scordatura in which ...


4

These days many musicians who play Baroque music such as Bach tune their instruments down to the lower pitch of A=415, which is exactly one half-step below the modern standard of A=440. It is generally accepted by modern performers of early music in the historically-informed style that A=415 was the tuning that Bach himself used for the string pieces he ...


3

It is significant when you are trying to tune an instrument by ear, using the purity of intervals as your guide. You (and the pages you link) refer to jumping up 7 octaves vs. 12 fifths, but don't forget that any notes you reach that way can also be brought down by one or more octaves as well. To illustrate this, let's bring all the notes down into the same ...


3

It is only significant to someone designing an instrument with a finite set of fixed pitches like a keyboard. Tuning such an instrument in a system based on pure fifths causes octaves to not be equivalent - which is terrible because the octave is the only truly pure interval, you can hear the beats from a mile away because it doesn't form a difference tone ...


3

The point of unequal well-tempered tunings is that the keys don't sound the same. Temperaments like Werckmeister III or Vallotti or 18th century French ordinaire are meant to be usable in any key while letting each have its own colour. (Vallotti is quite commonly used on fortepianos.) For most of what you're doing, you could probably get away with a mean ...


2

As MarkM pointed out, your claim is unsubstantiated. Consider further that "concert pitch" is not a fixed value. In the Good Old Days of Yesteryear, middle-A could be anything from 409Hz on up ( Wikipedia). Whether any particular YouTube recording was pitch-shifted in postprocessing is unknown.


2

Maybe you could point out which videos you're listening to. Period tuning is sometimes lower than A 440, but from a random sample of top results in youtube I found: Mischa Maisky : ...


2

Equal temperament is key-agnostic. Well-tempered tuning isn't. The point of well-tempered tuning is that all keys are tolerable, but some are still better than others and each has its own character. This own character was pretty much the whole point of Bach's "Wohltemperirtes Clavier" (it is usually assumed that some Werckmeister tuning reflects the ...


1

Any single string creates harmonics as it rings. Up to eight parts a C would generate C C G CEG Bb and C, essentially a dominant 7th chord. The lower partials are louder and than the upper partials due to string length influencing volume. A longer portion of the string vibrating will be louder. Tempered tuning requires that octaves and fifths sound good ...


1

Strings are tuned in perfect fifths, brass uses the overtone series and valving compromises in its scales. While instruments with per-note strings, keyholes, tines or whatever can be tuned in equal temperament, quite a bit of the characteristic substance of an orchestra does not belong in that class. This also affects orchestration, further adding to the ...



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