Harmonic Series

[Ignis Fatuus]

Hi, could anyone tell me the 11th harmonic of the series (where the fundamental is considered to be the first harmonic) on, for example C1. On wikipedia ( http://en.wikipedia.org/wiki/Harmonic_series_%28music%29 ) the image shows it to be Gb4 and this website ( http://www.music.sc.edu/fs/bain/atmi02/hs/index-audio.html ) shows it to be F#4. However in Schoenbergs Harmonielehre it's stated to be F4, which seems a little strange considering it is minor second (from E4, the 10th harmonic) followed by a major third.

Maybe it's because the note is so far from a tempered note that it could be considered both?

EDIT: Also appologies for not checking the forums as often as a should do :)

Thanks in advance for any help.

[danpowers]

It's roughly a quarter tone between F and F sharp. In other words, there's no way to notate it using conventional notation, which is why you get such different results depending on who you consult.

There's a similar situation with the 7th and 13th partials, which are slightly flat (roughly a sixth tone) from B flat and A respectively.

[nickysnd]

Maybe it's because the note is so far from a tempered note that it could be considered both?
That is the closest answer to your question. :)

If you look on wiki, above the Gb there is a number indication: -49, which represents "the number of cents it deviates from tempered tuning." So, if there were -50 cents, then that harmonic would have been precisely at half distance between F and Gb. As it is, the balance slightly inclines one tiny little cent towards Gb. So technically, Gb would be more "scientifically" right.

My take is that Shoenberg was right to consider it as an F though. I may be wrong, but I remember that he did that in order to explain the importance of the forth interval, the sub-dominant. As opposed to that, Gb is the triton - less important in tonal music that is based on the harmonic series. I am with Schoenberg against all mathematical measurements.

So let's just say that the 11th harmonic refers to a sub-dominant that is slightly attracted by its dominant neighbor. ;) Don't you find interesting that in jazz they are notating that interval as 11 as well?

[Ignis Fatuus]

Ah yeh! Thanks for the quick replies. Thats right about Schoenberg except mostly he explains the importance of the sub dominant by treating it as the dominant but in the oposite diretion, saying C is the dominant of F.
His books really opened up my ears.

[V o n h ö g e n]

My take is that Shoenberg was right to consider it as an F though. I may be wrong, but I remember that he did that in order to explain the importance of the forth interval, the sub-dominant. As opposed to that, Gb is the triton - less important in tonal music that is based on the harmonic series. I am with Schoenberg against all mathematical measurements.


Careful Nicky, someone has told me that Schoenberg was not a pro! :)

Jerome

[nickysnd]

Careful Nicky, someone has told me that Schoenberg was not a pro! :)

Jerome

Touché! But not big damage, only a small scratch. :p

Not being a pro has nothing to do with the quality of one's products. Not being a pro only means one little thing: one is not making a living out of his/her products.

OTOH, I think I have stated several times that I am a huge admirer of Schoenberg as a vertical man, as an open minded person, as true/uncompromising revolutionary, as a fine intellectual, as a teacher, as a writer, as a composer. I have only pointed that he - unlike Haydn, Mozart, Beethoven, and others - didn't make a living as a composer, which automatically keeps him out of the professional composers category. Which is not a negative, but neutral info - many great composers were/are not professional composers. The opposite is just as true: many professional composers (i.e. making a living out of it) are not that great. Just compare James Horner to Franz Schubert and you will get my meaning.

I am a big fan of many non-professionals, like, say - Gandhi. :cool:

[Ignis Fatuus]

many great composers were/are not professional composers

If only the world we lived in allowed that to be more true though!

[Ragingkirb]

Just tell a Viola player to play an F# :p

[fongi]

Will a "Viola" player know what you mean ??? O.K. just a joke :rolleyes: