# Are the intervals do-re and re-mi equal in size if we are tuning re-fa to be a minor third and re-sol to be a perfect fourth? [closed]

On a modern piano (in well-tempered tuning) the interval between do-re and re-mi are equal in size. Can they be equal in size if we use the harmonic series to make re-fa a minor third and re-sol a perfect fourth? (With size I mean how big the interval is between two notes in percent. An examole would be from A1 to A2 we have an octave and A5 to A6 is also an octave in size.)

If I sing a chord eg Do-mi-sol I would use the perfect intervals from the harmonic series. How would the harmonic series fit with the intervals of major seconds?

## closed as unclear what you're asking by Todd Wilcox, Tim, David Bowling, Dom♦Mar 6 at 17:12

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• I have a few clarifying questions: 1) Isn’t re-fa a minor third and re-sol a perfect fourth already? 2) What do you mean by “size”? Are you referring to physical distance on a modern piano as measured in, say, inches? Do you mean in terms of the ratios of their frequencies? Or something else? – Alex Basson Mar 6 at 9:26
• If I understand the question correctly, the answer is no: if you are using integral ratios from the harmonic series, do-re and re-mi are different sizes of whole tone, most commonly 9/8 and 10/9. If you divide the 5/4 ratio of the just major third in half, you get √5/2, which never appears in the harmonic series, because it's irrational. – Scott Wallace Mar 7 at 9:57
• To my knowledge, in any well temperament, do-re and re-mi are likely not equal in size, as not all semitones in a well temperament are equal in size either. (I believe that statement to be the result of a suspect edit.) – Dekkadeci Mar 7 at 15:16

Do-Re and Re-Mi are whole tones (mind the black keys between the white keys) and therefore major seconds.

Re-Fa and Mi-So are minor thirds because of the halftone between MiFa (sum of a minor second and a major second).

Therefore Do-Fa and Re-So are always a perfect fourth by definition as they are the sum of a major second and minor third.

Can they be equal in size if we are to make re-fa a minor third and re-sol a perfect fourth?

What ever you make with the white keys of the piano these intervals remain the same.

• Albrecht: note that the question is about intervals in the harmonic series, not in equal temperament. – Scott Wallace Mar 7 at 16:55
• Oh, has the question been edited or have I overseen the temperature? – Albrecht Hügli Mar 7 at 19:17
• Du has nichts übersehen, die Frage ist nicht sehr eindeutig formuliert. – Scott Wallace Mar 12 at 13:43