Transpose from Am to A

[crumhorn]

Thanks stringtapper!, must remember to post more random musicology noob questions from time to time when you're around.

[crumhorn]

@angstrom

I'm with you on that. The whole idea that music theory has adopted C major (and it's modes) as the "default setting" and that everything else has to be described in terms of how it differs from that default leads to much confusion.

As soon as you start to stray away from "normal" diatonic tonal music with 7 note scales the system breaks down IMO

Even fairly common tricks like tritone substitution lead to wierd things like F having to be written as E# so that it can be the 3rd of a C#7 chord (in key of C).

But it has to be admitted that the system has been enormously successful and human ingenuity seems to be up to the task of adapting it endlessly.

[stringtapper]

However there is a problem with this system, the tuning depends on the scale, so the tuning for C major is not the same as the tuning for D major. So to get something more usable for things like keyboards, the equal tempered scale was developed, which is a compromise tuning scheme. I expect people like stringtapper are also familiar with the Pythagorean, Mean-tone scale, and the Werckmeister scales which were also devised over the centuries. There are many others, all with their own tunings and scales. For example the Spanish Gypsy Scale: 1-3-1-2-1-2-2 can only be approximated on a modern keyboard as the tuning would not be authentic.

The differences between the tunings of the just and equal temperament scales are in the order of 1-2 Hz which is distinguishable by the human ear. Eg D4 = 294.33 Hz on the just scale and 293.66 Hz on the equal temperament scale.

Pythagorean tuning is the earliest we know of and the "problem" funken speaks of persisted for centuries. Pythagorean tuning is derived by dividing a string upward in 5ths and downward in 4ths. The problem is that when the two sides meet on an enharmonic pitch their ratios will not coincide. So if C was your center pitch you would get an F# on the 5ths side and a Gb on the 4ths side but they would not sound the same! Some early keyboards tried to get around this by having keys for both F# and Gb side by side. That difference between the F# and the Gb is known as the Pythagorean Comma.

The other problem is the 3rds. If you ever get a chance to do a side by side comparison of Pythagorean, Just, and ET 3rds you should. ET 3rds are sharp enough compared to Just 3rds, but Pythagorean 3rds just sound insane. They were basically unusable and this is probably why 3rds were considered "imperfect consonances."

In both just and equal tempered scales, C4 is actually 261.63 Hz.

I'll have to check my Max patches that calculate this stuff, but I believe this would be dependent on which note was used to derive the tuning. So if the just scale was derived from A=440, which is pretty much the modern standard tuning frequency (but not the only!), then you would probably get a middle C that was closer to around 264.



Pythagorean tuning when the op question was how to modulate? Ok NOW I have to say we've used a chainsaw to remove a splinter.

But it's all so fascinating…

[stringtapper]

Even fairly common tricks like tritone substitution lead to wierd things like F having to be written as E# so that it can be the 3rd of a C#7 chord (in key of C).

No no NO!

You wouldn't spell the chord on C#, but rather on Db. Why? Because the root of the Tritone sub leads down to the root of the I chord. Then you don't have problems like that.

The idea of sharps leading up and flats leading down is a very useful way to think in terms of voice leading, especially when chromatids are involved. It's also a very real thing that composer have done for centuries in practice. Even once atonal music emerged you would find Schoenberg using different enharmonic spellings of the same (ET) pitch depending on which direction the note was going, even though there was no real functional reason to do so. In tonal music there is a functional reason. Sharpened chromatic pitches are most often going to be functioning as the 3rd of a secondary dominant which needs to lead up to the root of the chord of resolution. Conversely flatted chromatics will often as the 7th of a secondary dominant or secondary diminished seventh, and would need to resolve down to the 3rd or fifth of the chord respectively.


@Angstrom: it's indeed a legit beef you've got with notation. But let me tell you as someone who recently went through a truly "hellish" seminar on transcribing medieval polyphonic notation that we are in paradise now compared to the mess that was going on c. 1200-1600.

Yes it's imperfect, but it's obviously the best humans could come up with and more importantly agree on in the last 2,000 years. So I think it's as good as it will get, although the possibility of something like piano roll notation becoming a standard could be possible, probably after the singularity hits and the robots take over.

[Angstrom]

Yeah, I agree.
I looked around for alternatives and they were all worse in one way or another.
It turns out that music is complicated. Who knew!?

[stringtapper]

And in Ableton C4 is 523 Hz, some weird Midi way of labeling the notes, everything is an octave out.

Ableton uses the C3=middle C for MIDI octave designation. It's not weird just another standard. I think one or the other was developed by Yamaha. Can't remember what system the other DAWs use. In Ma xthe int number boxes default to C3 but have an option to switch to C4.

[Tone Deft]

oh man... learn before you try to teach. you've unwittingly opened yet another can of worms.

equal temperament is for pussies.

Friday popcorn everyone!

[crumhorn]

but it i call my tritone sub Db7 instead of C#7 - which I'm happy to accept - then my B becomes a Cb.

[stringtapper]

but it i call my tritone sub Db7 instead of C#7 - which I'm happy to accept - then my B becomes a Cb.

Which is functionally correct in the key of Bb. Of course if you were in the key of A# minor then a Tritone sub on B would be correct too.

A Tritone sub is most often used as a harmonic device that creates a descending chromatic bass line. So in a ii-V-I progression the bass line is 2-b2-1.

[crumhorn]

my example is in C major. substituting Db7 for G7 - resolving to C.

[crumhorn]

thanks

serious problems with the notation drawing code which I must have written when stoned. it works but needs rewriting before I can really move forward with the project. Trying to embody music theory in code is a real learning experience.

[stringtapper]

my example is in C major. substituting Db7 for G7 - resolving to C.

But then you said that your "B would have to become Cb." I assumed you meant that a Tritone sub on B would really need to be spelled as Cb.

If you meant that the viio chord (on B) in C major would have to be spelled from Cb, then no. A Tritone sub is a chromatic chord and has no bearing on the spelling of any diatonic chords.

Unless I'm misunderstanding you?

[beatmunga]

Anyone here like The Human League?

They invented music.

http://youtu.be/bKwQ_zeRwEs

[crumhorn]

I think i'm failing to communicate clearly.

i'm talking about the note Cb, that is the 7 in the Db7 chord. Writing it as Cb in the key of C just seems wrong especially since it leads to the tonic exactly like the B in a G7 chord.

[stringtapper]

I think i'm failing to communicate clearly.

i'm talking about the note Cb, that is the 7 in the Db7 chord. Writing it as Cb in the key of C just seems wrong especially since it leads to the tonic exactly like the B in a G7 chord.

Ok well that's true, either way you're going to have an incorrect spelling based on the voice leading. I would still go with the b2 spelling because that chromatic bass descent is the defining feature, the "special effect" if you will.

This problem actually stems from the origin of the Tritone substitution, which is the augmented sixth chord.

So if we move over to the key of F for a minute, the German Augmented Sixth is spelled Db-F-Ab-B. the Db and the B both encapsulate the root of the V chord, C. This is essentially the same chord as the Tritone sub in C major but that chord functions differently and is spelled Db-F-Ab-Cb. So yeah it's a bit of a kludge and the reason is that it's stretching the diatonic system beyond its own limits. In jazz you can get around this problem by just making the I chord a C7 instead of a Cmaj7, so the Cb resolves down to Bb, the seventh of C7.