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Hi

I'm new to this site so I hope this is the right part of the forum to post a question like this!

Anyways I'm wondering if anyone has knowledge of where to find/can share a microtonal harmonic chart. I'm looking for something that shows ALL the nodes on a string and what notes/octaves that sound.

I have really been looking hard and the charts I have found don't include certain quarter tone notes like the one in the picture below, which sounds as a quarter flat F if I'm correct (unsure about the octave though).

It would be deeply appreciated if anyone has any tips on where to find something like this!

//William

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Not quite sure what you're looking for, like "harmonic chart?" Are you looking for a list of accidentals? The scores I've looked at usually have a legend facing the first page of the score and I doubt there is a standard set. Those used by e.g. Sculthorpe (Sun Music III, quarter tones) aren't the same as those Haba used in his quarter tone works. Key signatures would seem impossible on a standard great stave. 

However, I hope you find what you're looking for and shed some light here. I've worked with equal temperament microtones on an analogue synthesiser but not with acoustic instruments. There are no doubt those who are interested.

I don't understand either, but there is this.  Sibelius notation software says that the symbol in your attachment above is "1-1/2 half steps flat."

I'm no expert but the only way I know of to flat a string harmonic is to either lower the fundamental string tension or else make the fretted distance longer. There are charts for the nodes of vibrations of overtones on a string but they don't move unless the string length changes. Hope that helps.

Here is an article on playing harmonics on a violin without using microtuning.

http://www.musicalobservations.com/publications/harmonics.html

Yeah sorry I forgot to mention that I'm looking for a chart over natural harmonics on a string, something like this: https://www.themoderndoublebass.org.uk/harmonics---charts.html

Though in this link doesn't include some harmonics, for example not the node I showed in the picture in my first post!

Thanks for the link! Though I can't seem to find the natural harmonic which I provided in the picture on these charts. Or maybe I'm reading them wrong hehe

Ingo Lee said:

Here is an article on playing harmonics on a violin without using microtuning.

http://www.musicalobservations.com/publications/harmonics.html

It's possible to map the natural harmonics of each string along with the notes that, compared with the Equal Temperament scale, are  flattened and sharpened. As far as I recall they aren't exactly 1/4 tones anyway. The frequencies of a Just scale harmonics are easy to calculate as they're straight multiples of the fundamental frequency. The difficulty comes with Equal Temperament.  The formula for finding the frequency of a given note....You need to know the frequency of the fundamental (f1)  and the number of semitone steps(Ns) to the note you want the frequency (f2) for, then f2= f1 x 2^1/12 x Ns.  (that 2^1/12 is meant to be the 12th root of 2 - best way I can notate it here. Take it's value as 1.0595 or if you want to be really scientific it's 1.05946309436 according to google! ) Then you can see how close the frequencies are - and on that harmonic it isn't a quarter tone! 

(I think I've got that right. It goes back to analogue synthesiser construction. Please correct me if I'm wrong).

So it may be better to map the sequence out as "discrepancies" if for example you're trying to locate the exact touch point on a string for a particular harmonic.  

Sounds right to me Dane, thanks!.

As a guitar player I find even natural harmonics of simple ratios to be challenging sometimes, so how useful are these more exotic ones?

Dane Aubrun said:

It's possible to map the natural harmonics of each string along with the notes that, compared with the Equal Temperament scale, are  flattened and sharpened. As far as I recall they aren't exactly 1/4 tones anyway. The frequencies of a Just scale harmonics are easy to calculate as they're straight multiples of the fundamental frequency. The difficulty comes with Equal Temperament.  The formula for finding the frequency of a given note....You need to know the frequency of the fundamental (f1)  and the number of semitone steps(Ns) to the note you want the frequency (f2) for, then f2= f1 x 2^1/12 x Ns.  (that 2^1/12 is meant to be the 12th root of 2 - best way I can notate it here. Take it's value as 1.0595 or if you want to be really scientific it's 1.05946309436 according to google! ) Then you can see how close the frequencies are - and on that harmonic it isn't a quarter tone! 

(I think I've got that right. It goes back to analogue synthesiser construction. Please correct me if I'm wrong).

So it may be better to map the sequence out as "discrepancies" if for example you're trying to locate the exact touch point on a string for a particular harmonic.  

If you want the sort-of-F on G string, it's the 7th, so two octaves plus a slightly flattened minor seventh above the fundamental (it's not exactly quarter tone flat, more like a 1/6th).

As for where to look for all of them, you can generally just divide up the string accordingly and eyeball the rest (you very quickly run out of symbols that accurately represent where exactly to put the finger anyway; quarter tones just won't cut it). Using the style of notation that indicates the pitch you're going for as well as the method of producing it will definitely help your performer.

Thanks for all the answers everyone, and sorry if I'm being unclear in what I'm looking for hehe!

But basically I'm looking for that chart to answer if this natural harmonic sounds as the pitch indicated in the parenthesis? Since I realized that the lower quarter flat-B harmonic doesn't resonate as well as the one an octave up on the same string!

Is the parenthesis note in the right octave?

Yeah, this is correct (assuming treble clef, obviously). And it's indeed easier to pull off up there, I just checked on my violin. Theoritically, you can use any node that matches the partial, so, since this is the 7th, every 1/7th of the string. But some of the nodes will be in close proximity to other, much more prominent harmonics, which ramps up the difficulty considerably. Producing this one the way you notated in this last example is relatively easy (although personally I'd still hesitate to use it in a violin part; cello and bass - no problem).

Hm, come to think of it, maybe notating the diamond as normal flat instead of 3/4 flat would be more accurate. Would need to check on a bigger string instrument. When I play this on violin, I snap down to 5th or even 4th harmonic in that exact same spot, depending solely on finger pressure and angle. It's almost more about how to produce the harmonic than where.

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