Enharmonics...WTF?!?! Oh god another tuning question.

[Matt Walsh]

I was at choir last week and the main work we are doing for our upcoming concert is Rautavaara's Vigilia. If you are unfamiliar, it is ridiculous, monumental, awesome, ethereal yet earthly, mindbendingly complex (yet the deeper I go the simpler a lot of it seems... but then again...), and it is the all around craziest work I have had to sing in to date! This work (choral-ly, I guess) puts Michael Jordan's first free-throw line dunk (athletically) to utter shame. This insane Finn composes in quarter beats and quarter tones (mind you only in places, but still I mean COME ON haha...)! This is kind of what I am getting at. I asked my voice teacher/ choir director why is the use of enharmonics important in the structure because it definitely does not help from a voice leading perspective in certain parts (that is enharmonics against each other, or in close succession, in both different lines and in one line). For instance at any given point you could have the altos singing a Bb to a C and the tenors singing an A# to a G#. Oh it hurts. Now my teacher said theres actually a difference in pitch between an A# and a Bb of a quarter tone because of the equal temperament system...I think. I really need to understand the concept of temperament better. Help? He would have to be rounding I would think, but really I mean a quarter tone in the middle of like an 11 part harmony in a capella choral music? ...not even mentioning that its pianissimo for half the choir and mezzo forte for a quarter of the choir with one section freaking whispering gibberish and a solo bass doing his best to blare brown notes (like low Bb's) over the top of everybody...all in Finnish!!! Ok I exaggerate a little but if you are familiar with the score you know what I'm talking about. 

I love a lot of 20th century music but Jesus H Christ!

[Douglas Edward]

lol nice 20th century rant!

If the piece or section you mention favors sharps, then Bb to C makes a decent amount of sense as an exception- otherwise you would either be reading A# to C which would urge one to leap instead of step, or A# to B# which would urge one to briefly scratch one's head before asking "why didn't they just notate it Bb to C"?.

Yes there is a difference between A# and Bb (except for that scene in Goonies when she says she doesn't know if it's A# or Bb, in which case it is exactly the same thing), but I am not familiar with it being as big of a difference as a quarter tone. Possibly your teacher is referring to the extreme, as in a high soprano part would need to adjust as much as a quarter tone to match the bass part when singing in just intonation (or vise versa depending on where the ensemble sits in relation to equal temperament). Regardless, it might be a good way to look at it when singing, so as to help produce that difference between one and the other when vocalizing.

Now that being said, it sounds like you are coming away with the thought that the altos Bb should be a quarter tone off from the tenors A# as they sing the notes together at the same time. Is that what you are asking? Unless specified otherwise, I would say this isn't the case. You already mentioned the piece has quarter tone markings in specific sections, so certainly the composer would of used those notations had they wanted it to sound so harmoniously so lol. Imho, I believe this to simply be a way to best tell each section what to sing in relation to their part.

[Jim Aikin]

It's definitely not a quarter-tone. People who are not familiar with the details of tuning systems sometimes use the term "quarter-tone" (incorrectly) because they assume or imagine that the only pitch between two of the pitches in the 12-note equal-tempered scale must be exactly halfway between them. A quarter-tone is one of the pitches in 24-note equal temperament (not a very interesting scale, in point of fact) that isn't found in 12-note equal temperament.

Whether there's a difference between a Bb and an A# depends entirely on what instrument(s) you're using, and on the sensitivity of your performers to pitch. Players of fretless stringed instruments will sometimes (consciously or unconsciously) fudge their intonation up or down slightly (less than a quarter-tone!) so as to produce intervals that are closer to the simple ratios of just intonation. You can't do this dance on a piano, of course.

The question of whether a note is spelled in the score as a Bb or an A# has no necessary connection to the intonation with which the note is played.

This is a complex area. Maybe I'll write a book about it someday, but probably not. If you can find a copy of a book called Harmonic Experience, by W. A. Mathieu, you'll learn a great deal.

[Andrew Gleibman]

Let me rephrase a remark from another discussion, as it is relevant here.

Enharmonics is not always related to pitch. We simply do a simple logic with key vs. accidental signatures and subconsciously link our emotions to this logic.

Let us do the following simple experiment. Imagine (or write) a natural Re minor scale with A sharp instead of B flat,

What we have? Concerning (equally tempered) pitches, it is the same Re minor scale. However, note B is absent, while note A is written twice. So, the concept of scale, or ladder with single steps and no omissions, is violated. In melodies we can apply or hear similar violations for stressing some ideas or emotions. The ladder with no such double stops and omissions involves calm and confident feelings, and musicians can have specific emotions related to sharp and flat signs. This can be very individual, e.g., listening to the 2nd movement of Beethoven's 6th, we can imagine that some B flat and E flat signs are small birds (Beethoven wrote about nightingales).

BTW, for A# vs Bb, I perceive that A# is higher than Bb, although my background is only equally tempered pianistic one.

[Marcel de Velde]

Notation is based on the Pythagorean system.
In this system Bb has the ratio of 16/9 to C (about 996 cents) and A# has the ratio of 59049/32768 to C (about 1120 cents).
The difference between Bb and A# is 531441/524288 (about 24 cents) and it is called the Pythagorean comma and it is not a quarter tone.
And 12 stacked pure fifths do not make a pure 2/1 octave, there is no true circle of fifths.

The above is the tuning system our western notation is based on.
In the old days it was believed to be the correct way to tune and most of western music theory was based on it.
However, the Pythagorean system does not correspond to practice. People do not naturally sing or play in the ratios described above.
Ramos de Pareja described in his book Musica Practica in 1482 how actual singers sing for instance the major third as 5/4 (about 386 cents) instead of the 81/64 Pythagorean major third (about 408 cents) (difference 81/80 a Syntonic comma).
Many people have described such things before, but after Ramos his book this 5/4 major third amongst other things became accepted by virtually all music theorists in the west (though it took a while).

Now we enter Just Intonation. A theoretical system on the actual ratios of notes in music.
To this day Just Intonation is not well understood. Nobody knows how to play even simple pieces of music 100% "in tune".
Our ear and or brain knows what is in tune, yet we do not have the theory to describe it in detail.
The best example we have of Just Intonation is how a well practiced and talented trombone quartet plays.

What this all means, is that our notation is based on a wrong system.
The E or Bb or A# or whatever note, does not correspond to any fixed ratio or pitch.
Use notation as your rough guideline, but use your musical understanding of a composition (how you "hear" the composition in your head) as your true guideline on the pitch of the notes.