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teacherdad Regular Member
Joined: 20 Jan 2012 Posts: 27 Location: Baltimore, MD
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Posted: Sun Feb 10, 2019 12:44 pm Post subject: Q re: 1/2 valves and the harmonic series |
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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 Heavyweight Member
Joined: 24 Dec 2018 Posts: 3302 Location: Endwell NY USA
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Posted: Sun Feb 10, 2019 1:22 pm Post subject: |
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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 _________________ Most Important Note ? - the next one !
KNOW (see) what the next note is BEFORE you have to play it.
PLAY the next note 'on time' and 'in rhythm'.
Oh ya, watch the conductor - they set what is 'on time'.
Last edited by JayKosta on Sun Feb 10, 2019 3:34 pm; edited 1 time in total |
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teacherdad Regular Member
Joined: 20 Jan 2012 Posts: 27 Location: Baltimore, MD
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Posted: Sun Feb 10, 2019 2:47 pm Post subject: |
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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 Veteran Member
Joined: 11 Feb 2014 Posts: 129 Location: Little Rock, AR
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Posted: Sun Feb 10, 2019 3:17 pm Post subject: |
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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 Heavyweight Member
Joined: 24 Dec 2018 Posts: 3302 Location: Endwell NY USA
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iiipopes Heavyweight Member
Joined: 29 Jun 2015 Posts: 554
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Posted: Sun Feb 10, 2019 4:41 pm Post subject: |
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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. _________________ King Super 20 Trumpet; Sov 921 Cornet
Bach cornet modded to be a 181L clone
Couesnon Flugelhorn and C trumpet |
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Derek Reaban Heavyweight Member
Joined: 08 Jul 2003 Posts: 4221 Location: Tempe, Arizona
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Posted: Mon Feb 11, 2019 5:28 am Post subject: |
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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. _________________ Derek Reaban
Tempe, Arizona
Tempe Winds / Symphony of the Southwest |
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iiipopes Heavyweight Member
Joined: 29 Jun 2015 Posts: 554
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Posted: Sat Feb 16, 2019 7:52 am Post subject: |
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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. _________________ King Super 20 Trumpet; Sov 921 Cornet
Bach cornet modded to be a 181L clone
Couesnon Flugelhorn and C trumpet |
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JayKosta Heavyweight Member
Joined: 24 Dec 2018 Posts: 3302 Location: Endwell NY USA
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Posted: Sat Feb 16, 2019 2:05 pm Post subject: |
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iiipopes wrote: | ...
If A=440 Hz, then the seventh partial is 440*7, 3080 Hz.
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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 _________________ Most Important Note ? - the next one !
KNOW (see) what the next note is BEFORE you have to play it.
PLAY the next note 'on time' and 'in rhythm'.
Oh ya, watch the conductor - they set what is 'on time'. |
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iiipopes Heavyweight Member
Joined: 29 Jun 2015 Posts: 554
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Posted: Sat Feb 16, 2019 4:28 pm Post subject: |
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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. _________________ King Super 20 Trumpet; Sov 921 Cornet
Bach cornet modded to be a 181L clone
Couesnon Flugelhorn and C trumpet |
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