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Q re: 1/2 valves and the harmonic series



 
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teacherdad
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Location: Baltimore, MD

PostPosted: Sun Feb 10, 2019 12:44 pm    Post subject: Q re: 1/2 valves and the harmonic series Reply with quote

Hi all,

Playing at the top of the staff with the 1st and 2nd valves in the mix...

Why does the pitch go from E to G (a minor third) and not E to F# (a Maj 2nd)?

(Here's my understanding of the harmonic series... first, an octave (lowlowA to lowA), then a P5 (lowA to first-line E), then a P4 (E to 2nd-space A), then a M3 (to C# in the staff), then a m3 (to top-space E), and then a M2nd (to F#, right?) But that next note that comes from the horn is a G, not an F#.)

How does the ledger line A come out, too? I mean: I know A is the octave repeatedly, and the P4 of top-space E, but...

Where's my misconception?

And, if anyone would be willing to give an example from their own playing of when they use/how they choose some of these alternate fingerings up there... Thanks!
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JayKosta
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PostPosted: Sun Feb 10, 2019 1:22 pm    Post subject: Reply with quote

When both 1 & 2 valves are down -
Starting with the OPEN G above the staff,
2nd valve - F#
1st - F
1&2 - E

if you then slide UP to the next 1&2 harmonic, that harmonic is the one that is a based on a 'bad Bb' played OPEN.
And from there down -
2nd - bad A (corrected from earlier)
1st - bad Ab (corrected from earlier)
1&2 - bad G, (corrected from earlier)
Regardless - all the valve combinations based on that bad OPEN Bb are not typically usable.

The important thing about adding valves is that it 'works' from the higher OPEN harmonic and going down. When you go UP by adding 'valve slide length', you are sliding UP to another OPEN harmonic.
e.g. the middle C under the staff is played OPEN, and the C# above it is 123, that C# is based on the 'in the staff' OPEN G - and then adding valves 2/1/1&2/2&3/1&3/1&2&3 lowers the pitch to the C#.

Regarding alternate fingering -
Sometimes it's useful when trying to avoid 'cross fingering' in fast passages.
And in some key signatures it helps make the pitches sound better. e.g in Eb (3 flats) playing in-the-staff C with 2&3 sounds better than OPEN, especially when moving around Eb Ab C . If the C doesn't sound quite right played OPEN, try 23 (it changes the pitch slightly, and can affect the 'mood' of the sound).

Jay
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Last edited by JayKosta on Sun Feb 10, 2019 3:34 pm; edited 1 time in total
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teacherdad
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PostPosted: Sun Feb 10, 2019 2:47 pm    Post subject: Reply with quote

Thanks for the reply!

I get that there are overlapping, coinciding series and notes up there, so then I guess why does the open series go: C-G (P5), G-C (P4), C-E (M3), E-G (m3) [good so far]... and then G-to-B-flat?! (another minor 3rd, instead of a M2)?
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astadler
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PostPosted: Sun Feb 10, 2019 3:17 pm    Post subject: Reply with quote

The 7th partial note you're talking about ("bad" B-flat) lies somewhere between A and B-flat; on a natural trumpet in C, the pitch could be lipped down to produce F natural, or up to produce F#, which is why both pitches are used in music written for that instrument. So it isn't a M2 or a m3, but somewhere in between the two. As for why, physics. There's not really any practical reason why one would need to know the physics behind it, it's just the pitches that make up the harmonic series.

As for your first question, when you're using first and second valve, you're getting a flat G on B-flat trumpet. G above the staff can tend to be a sharp note anyway, so using the 1/2 flat fingering often ends up not being too terribly out of tune.
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JayKosta
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PostPosted: Sun Feb 10, 2019 3:28 pm    Post subject: Reply with quote

I think this image illustrates your question -
https://www.google.com/imgres?imgurl=https://upload.wikimedia.org/wikipedia/commons/thumb/e/e8/Harmonic_series_intervals.png/550px-Harmonic_series_intervals.png&imgrefurl=https://en.wikipedia.org/wiki/Harmonic_series_(music)&h=235&w=550&tbnid=CKSqHi-aYhzuPM:&q=harmonic+series+musical+pitch&tbnh=91&tbnw=214&usg=AI4_-kTnbBYE0QQIRDklEIAiRU9Oj3q5ag&vet=1&docid=0Y7bVFheeNIrVM&client=firefox-b-1&sa=X&ved=2ahUKEwiqqoq-pbLgAhWo1lkKHdD9AHYQ9QEwAHoECAMQBg

As far as 'why does it work that way', I don't know the details - but I think it has to do with needing the ratio of -
'air column length' : 'pitch wave length'
to be a WHOLE number - a non-whole number ratio would not maintain a stable wave pattern.

Jay
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iiipopes
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PostPosted: Sun Feb 10, 2019 4:41 pm    Post subject: Reply with quote

The harmonic referred to by the OP is the flat 7th partial. It is not in tune with anything. In the "A" harmonic series, yes, it is roughly a G, but so flat it is more like a sharp F#.

Going back to the "C" harmonic series, yes, it is roughly a Bb, but so flat it sounds more like a sharp A.

This is why in any method book the 7th partials are not listed as alternate fingerings.

If A=440 Hz, then the seventh partial is 440*7, 3080 Hz.
But with equally tempered tuning, the closest octave is 440*8, 3520.
Divide 3520 by two semitones, 2^(2/12), and you get approx 3189 Hz, which is significantly sharper for the "whole tone below the octave" than is the 7th partial under the 8th partial octave.
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Derek Reaban
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PostPosted: Mon Feb 11, 2019 5:28 am    Post subject: Reply with quote

iiipopes wrote:
If A=440 Hz, then the seventh partial is 440*7, 3080 Hz.
But with equally tempered tuning, the closest octave is 440*8, 3520.
Divide 3520 by two semitones, 2^(2/12), and you get approx 3189 Hz, which is significantly sharper for the "whole tone below the octave" than is the 7th partial under the 8th partial octave.


Just correcting the approach to the math. For A=440 Hz an octave above this simply doubles the frequency, or A = 880 Hz (for the A at just above the top of the staff). To get the frequencies for the harmonic above 440 Hz and below 880 Hz you use ratios from the harmonic series:

5:4 (M3) (or the C# above the A) is 440 Hz x 1.25 = 550 Hz
3:2 (P5) (or the E above the A) is 440 Hz x 1.5 = 660 Hz
7:4 (m7) (or the G/F# above the A) is 440 Hz x 1.75 = 770 Hz
2:1 (O) (or the A above the A) is 440 Hz x 2.0 = 880 Hz

FYI.
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iiipopes
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PostPosted: Sat Feb 16, 2019 7:52 am    Post subject: Reply with quote

Derek Reaban wrote:
iiipopes wrote:
If A=440 Hz, then the seventh partial is 440*7, 3080 Hz.
But with equally tempered tuning, the closest octave is 440*8, 3520.
Divide 3520 by two semitones, 2^(2/12), and you get approx 3189 Hz, which is significantly sharper for the "whole tone below the octave" than is the 7th partial under the 8th partial octave.


Just correcting the approach to the math. For A=440 Hz an octave above this simply doubles the frequency, or A = 880 Hz (for the A at just above the top of the staff). To get the frequencies for the harmonic above 440 Hz and below 880 Hz you use ratios from the harmonic series:

5:4 (M3) (or the C# above the A) is 440 Hz x 1.25 = 550 Hz
3:2 (P5) (or the E above the A) is 440 Hz x 1.5 = 660 Hz
7:4 (m7) (or the G/F# above the A) is 440 Hz x 1.75 = 770 Hz
2:1 (O) (or the A above the A) is 440 Hz x 2.0 = 880 Hz

FYI.

I know that. I was pointing out the differences in terms of ascending partials, not the Pythagorean ratios. To use your ratios, an equally tempered G above A=440 would be 440*(2^10/12), or @794 Hz, which, again, is significantly sharper than the Pythagorean ratio.
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JayKosta
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PostPosted: Sat Feb 16, 2019 2:05 pm    Post subject: Reply with quote

iiipopes wrote:
...
If A=440 Hz, then the seventh partial is 440*7, 3080 Hz.

--------------------------
I think this is confusing because of the difference in understanding and meaning of 'partials' versus the 'harmonic series'.

an illustration of type of partials -


and an illustration of harmonic series, showing the bad 7th harmonic -
It is important to remember that the 'trumpet C below the staff' is labeled "2" in the illustration.



These are from wikipedia -
https://en.wikipedia.org/wiki/Harmonic_series_(music)

Jay
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iiipopes
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PostPosted: Sat Feb 16, 2019 4:28 pm    Post subject: Reply with quote

JayKosta wrote:
I think this is confusing because of the difference in understanding and meaning of 'partials' versus the 'harmonic series'.

Yes, the entire discussion can be quite confusing. Thanks for posting the chart which illustrates the difference in nomenclature.
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