# A441 Harmonic Series

• Feb 1, 2017 - 21:23

Hey. I'm back.

Does anyone know where I can find a chart for A441? This link has a few charts but not 441. http://www.phy.mtu.edu/~suits/notefreqs.html

If not, then how can I figure the series, based upon 441, using a calculator?

#### Comments

What you linked to is not representative of the Harmonic Series; it is a chromatic key-set mapped to the corresponding wavelengths in Hz or Cm. If the latter is what you want but for 441Hz, a quick Internet search will result in something similar with the added function of user-supplied base frequency for calculation.
E.g., (http://www.gamutstrings.com/calculators/quick_calc/quickcalc.htm).

For an harmonic series, use the mathematical function to obtain the frequencies:

Wikipedia.org gives a generic visual correlation:

In reply to by worldwideweary

Excellent. This is good for starters. I see that the results do not include the full range. When transposing to 441, the lowest note is 27.5, but the highest it goes is to 882. That seems odd. But thanks. This will be very useful.

EDIT: the Wiki diagram is Just intonation.

In reply to by worldwideweary

That looks like an even better calculator. Talking about this topic has been tricky on other boards because people forget about Just and Equal temperment. Just intonation is pretty easy to calculate, even with a paper and pencil.

Also, I think someone mentioned something about the MS tuning features. That might give some info on the series?

In reply to by Joe H

Hrm... So far I've noticed in the inspector that when a note is selected, there are 100 degrees between half-steps; 100 = one half-step or semi-tone. If you have a G and put 100 in the tuning box, you get a G# upon playback. Also, in View->Synthesizer->Tuning it is easy to shift the base frequency into something like 441Hz, 432, 424, etc. The arrows are graded by 1-Hz, so if you want some special partial Hz usage you have to manually type in the floating point on the right-hand side.

P.S. my understanding of harmonic series is something like
Tonic + Octave + 5th + 4th + Major 3rd + Minor 3rd + Small Minor 3rd + Large Major 2nd

PP.S. A little secret: the sound of dying in the arcade game Pac-Man, after some sort of chromatic falling downward, uses something like this harmonic series played super-fast to give a sound effect rather than a musical passage. I.E:

Don't ask me what I was doing to figure that one out :)

P.P.P.S I may be mistaken with terminology here and am actually referring to what is called Fundamental Harmonic Overtones. Either way, I hope it's interesting.

http://www.sengpielaudio.com/calculator-centsratio.htm

Near to bottom of Page, with title "Octave division in 12-tone equal temperament TET" :

in short:

```Octave division in 12-tone equal temperament TET:
+------------------+------------+
| Interval         | Ratio      |
+------------------+------------+
| Unison           | 1.000000:1 |
| minor second     | 1.059463:1 |
| Major second     | 1.122462:1 |
| minor third      | 1.189207:1 |
| Major third      | 1.259921:1 |
| Perfect fourth   | 1.334840:1 |
| diminished fifth | 1.414214:1 |
| Perfect fifth    | 1.498307:1 |
| minor sixth      | 1.587401:1 |
| Major sixth      | 1.681793:1 |
| minor seventh    | 1.781797:1 |
| Major seventh    | 1.887749:1 |
| Octave           | 2.000000:1 |
+------------------+------------+
```

In reply to by Ziya Mete Demircan

OK. I have been here before asking about the tuning features and synthesizer. So, I'm just going to have to study up on these things when I have time and with these additional materials, I should be able to get oriented.

My question is because I am using analog instruments to record. But I use MS to notate and to playback in a kind of scratchpad arrangement, to get started on a composition. And I also use audacity to piece things together. the transposing tools on audacity are not exact. They only get you within hitting distance. That's because Audacity transposes the whole line or series together (using a simple addition of hertz) - which renders a complicated result. I'm going to have to correct my transpositions here and there.

In reply to by Joe H

2.1 may be the answer to your conundrum. In 2.1 you can select notes by the line they lie on in a staff (e.g. every A 3). You can select every note with the same pitch and adjust it appropriately for your tuning. 2.1 is considered non stable, but the current release has the format for future 2.1 scores. It also opens all 2.0.3 files and vice-versa.

In reply to by mike320

How would that affect the transposition of analog instruments? I realize this question is out of the realm of MS, but I'm asking it as a musician, realizing that there are many musicians here. If I record a melody with an anolog instrument using an audio editor, the transposition of the deries of notes (or even a stack of notes - a chord) is not a neat task as it is in MS. MS has an assigned value for each individual note. It will even adjust those values based upon the fundamental you enter.

It's not really a musescore issue. I'm just hoping to get some foundational info under me, regarding the harmonic series.

In reply to by Joe H

I obviously didn't give my entire thought. You can use MS to write and play back the music with whatever temperament you want. The process of tuning each note is greatly simplified when you can chose every instance of a given note and tune it, which is possible starting in 2.1.

The problem is not to transpose a single note, but the series, which is a mathematical impossibility. Nevertheless, transposition is a necessary and messy task in analog.

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