F sharp and G flat are not the same note - Bradley Lehman

[shilltheshillXXX]

This is all nothing new Jimi Hendrix and Led Zeppelin used F# and G♭on several occasions. They were well aware of what they were doing!!!

[thebpl]

@shilltheshillXXX There's no claim that this is new; Bach, Handel, and their predecessors were doing this more than 250 years ago.

[shilltheshillXXX]

@thebpl Well that just proves what I was sayiing. Jimi Hendrix and Jimmy Page were both guitarists rooted in American Blues Music which in turn was very much influenced by Bach, Handel, Teleman (I think Fender named an electric guitar after him), Albinoni, Scarlatti, Rameau, and Purcell: Just to name a few.

[HEAVYMETALGODS86feb9]

just gave me a idea for a ac/dc song

[stitchkaboodle999]

Thank you so much for this video. It has explained a lot that I had wondered about.

[shiningnight73]

Great video! I think it will be very helpful to share with my piano students. Thanks.

[eaglemo08]

This is sooo confusing....

[jsmoore1]

Db higher than C#!??!?!Totally wrong...

[cangjie12]

@jsmoore1 If you want to form a good major 3rd with F, Db-F (correctly spelled), then Db must be higher than C#, otherwise C#-F (wrongly spelled) will be too wide. Likewise, A-C# (correct spelling) is a good major third, but A-Db (wrongly spelled) is too wide because Db is higher than C#. Of course, on a keyboard (with equal temperament or well-temperament), there isn't such a issue...

[imperiumdiaboli]

Awesome.

[nukepcr]

If those 55 divisions of the octave are equal, I think you might actually be talking about a 53 equal division, also knows as the Mercator-Holder system, which as I know, gives the two different semitone sizes just like you said: diatonic is 5 commas and chromatic is 4 commas. Correct me if I'm wrong!

[thebpl]

@nukepcr The 55-note division and the 53-note are two different things. The 53-note division has NARROW major 3rds (smaller than 5:4), and slightly wide 5ths (larger than 3:2). The 55 system has the opposite: gently wide major 3rds and narrow 5ths. My theoretical discussion here is clearly about the 55.

[NorrisChuckling]

"Chromatic semitones are usually not used very much within tonal music."

...excluding Jazz. Why does everyone forget the Jazz?!

As for my voice on 12-edo, I don't think it's THAT bad. I'm sure it did turn a lot of people away from classical music, since classical bears the most abuse from it, but it has its uses like any other temperament/tuning, and if the music you're playing isn't very chordal, the difference is much less noticeable.

[xesionprince]

Well, when I had piano lessons as a child and later did grade V theory, I was taught the equal tempered scaled - and nothing else!! So, F# IS the same frequency as Gb as it IS the same note on a piano!!

[flyfishJJA]

Excellent survey of history, thanks, I can use this to definitively win an argument I was having recently.

[heinrich66priapism]

It shouldn't be so hard today to build a piano that has both F# and Gb, for example. You split the black key just before the very tip so that the tip plays the Gb and the rest of the key plays the F#.

To my ear, your discovery of what may have been Bach's tuning is a revolution. It sounds cleaner, clearer, more resonant, and more historically alive. Keep up the good work.

[pligana]

very interesting...but so difficult to understand ...shouldn't music come from the soul? it's amazing to see how many rules and numbers behind a sonata....unbelievable!

[shiningnight73]

@pligana That soul's gotta interface with physical reality somehow if you're gonna make music.

[anisometropie]

you say G♭ is 1 comma higher than F♯ but this is exactly the contrary.

enharmonic ♯ is always higher than ♭ !

for example is the pythagorician tuning, if A = 440 hz

C = 260,74 hz ;

D♭ = 274,69 hz ; 

C♯ = 278,44 hz ;

D = 293,33 hz ;

[thebpl]

In all the regular systems that have 5ths tighter than equal temperament's (i.e. narrower than 1/12th comma of tempering), sharps are LOWER than flats. That's what is discussed here: specifically, the area around 1/6 comma tempering, or the 55-note division of the octave.

By contrast, in regular systems that have 5ths wider than equal temperament's, for example Pythagorean's pure 5ths (as you point out here), sharps are higher than flats...but these systems sound very bad on keyboards.

[daharja]

I found this so interesting.

But then, I'm a *loather* of equal temperament! It's nice to learn some of the history behind the mess we're currently stuck with. Thanks.

[daharja]

Why not just add an extra key to the keyboard?

[thebpl]

That's been done, occasionally over the past 500 years, having split accidentals where the front half plays (for example) G# and the back half plays Ab...heading toward 19 or 31 notes in the octave. Telemann and some others described a 55-note-per-octave system, not necessarily for keyboards. There's a recent book by Patrizio Barbieri covering all this, thoroughly: "Enharmonic instruments and music, 1470-1900".

[brownbear5258]

can u let me know where u learned this at i want to get into theories like this

[thebpl]

Sure - read my papers and the bibliographies in them - at my larips web site.

[recnecsenave]

Arh I'm an idiot!!! I can barely hear the difference:(

[1337dav31337]

Holy... crap.

I love music.

[dianestarner]

Thank you, I needed this explanation for Schubert's Unfinished Symphony. Well done!

[kuj4z]

brainscrewed

[thebpl]

If C-G-D-A-E are all exactly the same size 5th as one another (geometrically), that middle note D in there is mean, no matter what comma we're trying to deal with. That is, the steps C-D and D-E are the same size as one another.

See also the lecture notes from a presentation I gave a few days ago. They are at my "larips" web site.

[TheCrazyCello]

Yeah I understand that meantone literally means averaging the major and minor tones. What I meant is that I assumed meantone always referred to a syntonic temperament, seeing as tempering the fifths C-G-A-D-E with 1/4 of the pythagorean comma wouldn't give exactly pure major 3rds which characterise 1/4 comma meantone. I understand now, sorry.

[thebpl]

1/6 PYTHAGOREAN comma works out to be the same in practice as the 55-note division; and 1/6 syntonic comma is very nearly the same, with less than a cent of difference anywhere. Great question!

[TheCrazyCello]

Ah I see. I just assumed meantone implies tempering the syntonic comma, I guess 1/6 pythagorean comma is kinda "schismatic meantone". I suppose it makes sense - not noticeably affecting the "good" thirds and leaving the wolf 5th with less of a howl hehe.

[TheCrazyCello]

" (regular 1/6 comma meantone, also known as the 55-comma division of the octave) "

I was under the impression that 1/6 comma meantone and 55-division are not exactly the same (but close) as meantone tempers the syntonic comma but equal divisions are effectively schismatic temperaments, (the same applying for 1/4 and 1/5 comma with 31- and 43-division respectively) is this wrong?

[gammypage]

wow that was a lot to get my head round but it was exactly what id been looking for thanks! =D 5 star

[snowypetrel]

Eureka! The reasoning behind the sense that different keys sound variously individual.

Thank you

[Glemser]

wow - very nice done edutainment

[AstAMoore]

Excellent! Thank you for this video. Five-starred.