Ttyjukl

so i need some clarification as this is confusing me terribly..

What are the first 12 harmonic series of a fundamental (Lets say A (440hz)?

Do those harmonic series of the fundamental pertain to every note in an equal temperament scale? Such as if we use A as the fundamental, do the notes B,C,D,E,F,G exist in the harmonic series of A?

and last question,

Could you explain to me in a simplified manner, how we take a fundamentals harmonic series and turn them into intervals? How does that process work exactly?

Much much thanks folks!

Seery

What are the first 12 harmonic series of a fundamental (Lets say A (440hz)?

I assume you mean the first 12 harmonics in the harmonic series.

The theoretical 'perfect' harmonic series is simply the multiples of 440 - 440, 880, 1320... and so on. 12 * 440 is 5280.

In real life, the few instruments actually have overtones following a perfect harmonic series - partly though design, as it sounds very boring and flat.

Do those harmonic series of the fundamental pertain to every note in an equal temperament scale?

The overtone structure of a note determines what the timbre of the sound is. Different notes played on the same instruments often have slightly different overtone structures. In most cases, they will have a strong correlation with the theoretical 'perfect' harmonic series, but this depends on all sorts of factors (such as how the instrument is played).

Such as if we use A as the fundamental, do the notes B,C,D,E,F,G exist in the harmonic series of A?

They do, but in some cases at frequencies much higher than the fundamental. In a note played by a real instrument, those overtones might be entirely absent, or very quiet. On the other hand, there might be lots of overtones present in the sound of a note that don't relate directly to the frequencies of other notes in the scale.

Could you explain to me in a simplified manner, how we take a fundamentals harmonic series and turn them into intervals?

It sounds like you've got the impression that musical scales and intervals are derived in a direct way from the harmonic series, but that isn't really the case. It is true that the important notes in some scales correlate with the frequencies of what are often strong overtones, but other harmonics will be present that don't correlate with notes in the scale.

I hope by this answer your next question will be enlightened too.

A scale or (sound) scale in the music is a series of the pitch of ordered notes, bounded by frame tones beyond which the tone row is usually repeatable.

In most cases, a scale has the circumference of one octave and in many cases follows a heptatonic tone scale construction. How a scale is built up is determined in the sound system.

The most common European and non-European scales are based on five or seven notes within the octave, which are called tone levels. Widely used are diatonic scales in major and minor or the church leaders. Scales are defined by pitches. The tones contained in the concrete scale are called conductor-specific tones.

In non-European music such as classical Arabic or Indian music, there are sound systems and scales that divide the sound space differently. So there are scales that contain more than seven fixed tone levels, such as Mugam, Maqam or Raga.

https://en.wikipedia.org/wiki/Scale_(music)