Open key No Key and Atonality

I haven’t the foggiest notion of what this means. I guess I don’t know what an open key is. All of the atonal music that I have ever seen is written in C major with accidentals. This must have something to do with transposing instruments. An atonal piece in C major would still require transposition of Horn in F, clarinet, English horn, etc. I’m just not sure how it works in an open key.

muratkayi said:

Hi guys,

From the Staffpad blog

StaffPad now creates new scores in an open key. Previously, all new scores were created in C Major. Do remember to change your key signature if your piece really is in C Major, otherwise transposing instruments won't show their transposed key signature correctly! You'll notice there's now a "No Key" option in the "Change Key Signature" control.

Can someone explain the implications of these options both for the workflow within Staffpad as well as for a real world score reading situation?

I have been trying to understand how composing atonal music influences decision making and working with the score and the subject matter is surprisingly diffuse or unclear.

For example, if I know I will avoid any key in my music, I could just as well keep it in C and decide on whether to use Bs or #s (and keep it uniform across the score so as not to piss the musicians off) and there it is. An atonal score. So what's the open and atonal options about and is it actually necessary to somehow declare that leaving out key signatures is different from a score in C although they look the same or what?

And if you think my questions are particularly stupid, could you please name a book or an online Ressource that explains this subject matter concisely?

Click to expand...

Its a good question! Think of the key of C as a position on a circle of fifths in which the accidentals go sharp in one direction and flat in the other. Then, if you go too far, the flats become double flat or the sharps become double sharp, and so forth.

This would be because in fractional tunings when the circle goes from C to G to D to A and so on, it's just cumulative 3:2 ratios, with the pitch as if moving "out of phase" with the equal tempered counterpart on an ET tuned piano. So if you have a transposing instrument it will matter.

"Music is often written in transposed form for these groups of instruments so that the fingerings correspond to the same written notes for any instrument in the family, even though the sounding pitches will differ. A musician who plays several instruments in a family can thus read music in the same way regardless of which particular instrument is being used."



So if you are writing a TONAL piece in the key of C, then F# is F# but this is different than Gb, because Gb is in the other direction on the circle of fifths. So the deviation accumulates in the other direction when you travel in that direction.

But if you're writing atonal music this isn't necessary - because such music isn't conceived of as adhering to such historic pure harmonies.

* * *

This is a sample conversation about the issue (but in MuseScore) that I found helpful:

Orig. OP QUESTION:

"
With atonal music, the tradition of creating a score in C but parts in the correct transposition has been customary. However, there seems to be some inconsistency with playback in MuseScore. I have a B-flat clarinet part, written in "C" in the score, but not playing back as intended. Any solutions?

HELPFUL ANSWER:

Are you aware of the atonal 'key signature'?

Anyway, a sample score is needed.

The difference between C and atonal is how transposing instruments are handled. Both show no key signature when viewing with concert pitch on, but with concert pitch off, with C key signature, then an Eb alto saxophone part (for instance) will show three sharps when transposed. With atonal, it will continue to show no key signature. So, exactly what one would want when writing atonal music.

But I think you may be misunderstanding something. From what you describe, I think you simply don't have concert pitch set the way you want. I think you simply want the score in concert pitch mode - by turning on the concert pitch button. Then you can write what you want to hear. The parts will still be transposed.

As mentioned, if you continue to need help, just attach your score so we can understand and assist better.

"

Thanks @Jett Hitt - sometimes it's good to hear that others are mystified by a question also, especially if it's someone like you who I consider quite knowledgeable

@jesussaddle thanks for your great and comprehensive explanation! I was actually thinking that it might have to do with enharmonic equivalences.

So, does this mean that for any fretless instrument or those without mechanics, the musician always has to make a decision of whether to play the purest interval possible as pertains to notation in the key of the score OR adhere to ET in order to either be able to not mess up intonation when playing with fretted/mechanic instruments or follow an atonal score?

(As a little digression, I once was at a concert of Jordi Savall and a baroque harp player where it took me five minutes of thinking "when's he gonna tune his harp?" like a dork, before I realised he was using an older tuning, so not ET, and it sounded really beautiful, but it took me a bit of getting used to)

I guess I would like to understand if an orchestra adheres to ET and if not in which situations and what problems they face when playing with instruments which are locked to ET.

Also, if in an orchestra enharmonic equivalences are audible as the two different notes they actually are(other than on a fretted or keyed or mechanic instrument), does that actually make the intervals of keys with many accidentals hard to listen to (which was the reason of inventing ET, if I got that right, to be able to play in those keys too, without the thirds being so ugly. So the ugliness was spread equally across all keys to make atrocities like F# major accessible)?

Which also means: none of this is audible on Staffpad, right? Because the samples are meant to be triggered originally via keyboard (in their source products) and thus the recordings will have taken place with an ET reference for each note, I guess?

I would really like to understand this thoroughly, before trying to go for atonal work, not really because a real world situation is actually at hand (unfortunately not), but because I think the more I know the better I can actually handle the concept.

Edit/add: I was pestering Google's Bard with questions like these and one of the pieces of info it dumped on me was that composers in atonal pieces choose B's or #s depending whether they want an overall brilliant/bright or mellow/dark sound in the orchestra which also only really makes sense if enharmonic substitution is not taking place (i.e. when noone follows ET), but then I immediately wondered about the woodwinds with mechanics (or playing with fretted instruments).
Actually, when thinking about woodwinds with mechanics: could it be that they have to adjust their audible pitch according to the same questions, their mechanics notwithstanding? I am sorry, I realize I sound like a five year old who can't stop asking, but I can't help it...

muratkayi said:

Thanks @Jett Hitt - sometimes it's good to hear that others are mystified by a question also, especially if it's someone like you who I consider quite knowledgeable

@jesussaddle thanks for your great and comprehensive explanation! I was actually thinking that it might have to do with enharmonic equivalences.

So, does this mean that for any fretless instrument or those without mechanics, the musician always has to make a decision of whether to play the purest interval possible as pertains to notation in the key of the score OR adhere to ET in order to either be able to not mess up intonation when playing with fretted/mechanic instruments or follow an atonal score?

(As a little digression, I once was at a concert of Jordi Savall and a baroque harp player where it took me five minutes of thinking "when's he gonna tune his harp?" like a dork, before I realised he was using an older tuning, so not ET, and it sounded really beautiful, but it took me a bit of getting used to)

I guess I would like to understand if an orchestra adheres to ET and if not in which situations and what problems they face when playing with instruments which are locked to ET.

Also, if in an orchestra enharmonic equivalences are audible as the two different notes they actually are(other than on a fretted or keyed or mechanic instrument), does that actually make the intervals of keys with many accidentals hard to listen to (which was the reason of inventing ET, if I got that right, to be able to play in those keys too, without the thirds being so ugly. So the ugliness was spread equally across all keys to make atrocities like F# major accessible)?

Which also means: none of this is audible on Staffpad, right? Because the samples are meant to be triggered originally via keyboard (in their source products) and thus the recordings will have taken place with an ET reference for each note, I guess?

I would really like to understand this thoroughly, before trying to go for atonal work, not really because a real world situation is actually at hand (unfortunately not), but because I think the more I know the better I can actually handle the concept.

Edit/add: I was pestering Google's Bard with questions like these and one of the pieces of info it dumped on me was that composers in atonal pieces choose B's or #s depending whether they want an overall brilliant/bright or mellow/dark sound in the orchestra which also only really makes sense if enharmonic substitution is not taking place (i.e. when noone follows ET), but then I immediately wondered about the woodwinds with mechanics (or playing with fretted instruments).
Actually, when thinking about woodwinds with mechanics: could it be that they have to adjust their audible pitch according to the same questions, their mechanics notwithstanding? I am sorry, I realize I sound like a five year old who can't stop asking, but I can't help it...

Click to expand...

I can only give my opinions without any experience talking to young orchestral players. My opinions come from seeing something online & from talking to a couple of much older players.

All I know is that, if strings or fretless instruments are alone, there are 2 categories - 1) playing melody to a single bass or note and 2) playing to chords. If the melody is NOT accompanied by chords it can sound good to play Pythagorean tuning (3:2). If playing to chords it depends on if the chords are fitted to 12ET or just intonation (and string players can sometimes play chords per just intonation). You would then just follow that - not use Pythagorean tuning.

So other than in places where the accompaniment has a significant presence of non-string instruments, one can do these 2 things, which often does sound right.

Also the emotion can decide it. For instance, Major triads in Pythagorean tuning have a 3rd that's a bit higher than 12ET, sounding brighter, whereas Major triads in Just intonation sound more balance and stable (on a synth, without fluid vibrato, they can sound unnatural and too stable, too square or "forced" [basically they sound like a standing wave pattern] relative to the undulating processes we're used to from nature). If you have a synth patch (often virtual synths copy the analog version, that had aesthetic instabilities, along with vibrato, so these can sound very, very good in just intonation. 12ET are a happy medium, but not as stable or vibrant.

Modulation from one key to another is made easier by 12ET. "Wolf" notes happen in certain chords if they're built from just intonation (and more so with Pythagorean tuning) - and moving from one chord to another in this system can be hit or miss depending on the notes of the chord. So in barbershop the lead singer moves to positions relative to 12ET to facilitate what would be the more problematic transitions, but the other singers form just intonated intervals based on these positions.

Partly based on noticing this form of order everywhere around me, & to help promote this kind of mathematics in nature, I patented a music-to-color conversion for lighting & music visualization software -not that colors are like individual notes, but that color harmony is based on music-like relationships that have a physics mathematics (different from music but similar). So in that way of thinking, one can transpose music into any color "key" the same way the Beatles songbook can be transposed to different keys by singers (so as to be more fitting to their voice or mood or whatever). One thing that's missing is that in my approach higher pitch doesn't necessarily mean warmer colors. But if desired a hybrid approach can try to choose color keys that specifically accomplish that only where desired. In any regard, when converted to colors per my discovery, the 12ET allows key modulation, but man, to me the just intonation versions of individual color chords so much more vibrant - visually analogous to "ringing" chords. (See video #1 below, where he talks about "ringing chords". (like in music, modulating or including too many chords makes certain changes rough and less harmonious, but my feeling is that tuning systems shouldn't force a constant tuning, but rather should flow the way that barbershop quartet singers flow - that's the best explanation I've heard as to how pure tunings can be adhered to over many chord changes.



Note the +/- numbers relative to the notes in the following video - these are the departures, in musical cents, from 12ET.

You'll notice, where it says -31, that this is the 7:4 harmonic functioning as a (VERY) minor 7th for that dom7 chord.

Wow, this answers a lot of questions on tuning systems and intonations! I had heard of the barbershop intricacies before and vaguely knew it had to do with stacking pure intervals, but hadn't ever seen or heard it demonstrated like this! Thanks so much for finding it!

Also, there is this crucial info that the bass singer moves in ET to close the Pythagorean gap and the others use just intonation above that!! Mind blown.
Now, I wonder if this kind of work is what conductors also have to to during rehearsals, namely deciding on whether a passage, a motif or other structural elements need tuning adjustments like the one described in the barbershop video and if an orchestra during a sinfonic performance within one and the same piece possibly changes its approach from part to part.

So much food for thought - thanks a lot!

Also, it now strikes me as something crucial on the long list of things we kind of miss out on when producing with virtual instruments and singers

muratkayi said:

Wow, this answers a lot of questions on tuning systems and intonations! I had heard of the barbershop intricacies before and vaguely knew it had to do with stacking pure intervals, but hadn't ever seen or heard it demonstrated like this! Thanks so much for finding it!

Also, there is this crucial info that the bass singer moves in ET to close the Pythagorean gap and the others use just intonation above that!! Mind blown.
Now, I wonder if this kind of work is what conductors also have to to during rehearsals, namely deciding on whether a passage, a motif or other structural elements need tuning adjustments like the one described in the barbershop video and if an orchestra during a sinfonic performance within one and the same piece possibly changes its approach from part to part.

So much food for thought - thanks a lot!

Also, it now strikes me as something crucial on the long list of things we kind of miss out on when producing with virtual instruments and singers

Click to expand...

I would also like to know - is this common practice for string players to simply adapt their "ear" to the orchestral pieces in play at the time? Or does the conductor sometimes (or a lot of times) get more specific with how the piece sounds best? A lot of questions!

I would like to sit in on some prep and hear that discussed!

I forgot to mention in my long post that just intonation minor 3rds sound less somber. If you apply that to a philosophical analogy of, essentially "male" vs "female", as Viktor Schauberger seemed to, this shows the power of receptivity in terms of those (less morose) minor chords.

The Pythagorean minor 3rd is "sadder" it is 6 cents below the 12 ET version, whereas the just intonation version is 16 cents above (much less sad than even the 12 ET version).

All of these are useful. The problem with traditional tuning concepts is that they imagine this "field" to be static, whereas it's contextual derivation is exciting in its continual evolution. IOW THAT's the music, the music is NOT some static tuning field.

I've envisioned creating software for musicians that would take user decision-making in how to respond to the evolving harmony, melody, and rhythm. It's a bit hard to afford just now, but I plan to do it in combination with my color visualization methods at some future point.

As a guitarist, if I play an E- minor on an ET12 guitar, and then play the third up high somewhere, I'll always adjust it to fit the pure 6/5 harmonic. To not do so (even with the 12ET third below - which one would think would be very clashing) sounds like a wrong note right away. It needs to be bent up. I'm pretty sure a lot of players I like do that subconsciously with their vibrato and bending.

I don't have the opportunity to do with the just intonation major 3rd as much. To do so requires a bend up from the 12ET minor 3rd to just under the fretted 12ET major third. I suppose if I were a better player I'd do that more often, but I think that there are a lot of "good" notes in vibrato, and going a bit sharper reaches the Pythagorean Major third anyway.

The best book on all this is called "Harmonic Experience" by Walter Mathieu, and there's an appendix page at the back with about 59 available "notes" per octave, and what musical contexts can call them into appropriate use. (It's based on Indian names for do, re, mi... which are sa, re, ga, ma, pa, dha, ni.) For example, if you're playing the minor 7th, a pure version of that could be 9:5 (above the ET version) or 16:9 (below ET) or 7:4 (way below ET = barbershop 7). The derivation of the minor version of "ni" (equivalent to our Western minor seventh note) 16:9 is 'sourced' or contextually derived as what he calls "grand pa below". Pa = the Perfect Fifth & grand pa a= 3:2 * 3:2 or two fifths. On the circle of fifths this would be moving 2 positions up in Fifths. "below" means go the other direction. Bb would be the grand pa below C, but the pure version (in this case the Pythagorean tuning version) would be different than the 12ET version. So every note of these 59 or so, has a context, and you can use that context to compose. It's very fun.




That's the first page, up to the Perfect Fourth.

(Sorry, my programming notes are scribbled all over).

Maybe you can support the author, or if needed pick up that book for cheap on some used bookstore website. IMHO it's certainly among the most enlightening music theory books ever produced.