Do all semitones have the same width?
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ashcat_lt
Well-known member
I've never heard that term before, but farview is still correct. In modern equal tempered western music there is no comma, every semitone is the same "size".
Or at least that's how things are supposed to be tuned. Most guitars are different for every semitone on the neck, and of course a lot of instruments (orchestral strings, trombones...) have not inherently fixed intonation, so each semitone almost has to be a little different every time it's played.
Or at least that's how things are supposed to be tuned. Most guitars are different for every semitone on the neck, and of course a lot of instruments (orchestral strings, trombones...) have not inherently fixed intonation, so each semitone almost has to be a little different every time it's played.
Farview
Well-known member
I guess the answer depends on what instrument you play and what type of music. In western music, we use equal temperament. In that temperament, all semitones are equal.
That won't be the case with any other temperament, but it isn't something that you will run into a whole lot.
That won't be the case with any other temperament, but it isn't something that you will run into a whole lot.
SeaGtGruff
Member
The term "comma" by itself is somewhat ambiguous, since there are different kinds-- e.g., Pythagorean versus Ptolemaic.
I think "comma" without a qualifier is usually taken to mean a Ptolemaic ("ordinary" or "syntonic") comma, the interval between a "just major third" (5:4) and "Pythagorean major third" (81:64), which is equal to 81:80-- i.e., (81/64) / (5/4) = (81/64) * (4/5) = (81/64) * (64/80) = 81/80.
On the other hand, a Pythagorean ("diatonic") comma is the interval between twelve Pythagorean semitones (531441:262144, or [3^12]:[2^12]) and a perfect octave (2:1), which is equal to 531441:524288 (sometimes given as approximately 74:73).
In any case, a particular type of comma always has the same ratio, and an equal temperament semitone likewise always has the same ratio, so if we express an equal temperament semitone in terms of a comma then it will always be the same no matter which two adjacent notes we're considering-- C to C#, C# to D, D to D#, etc.
Since the two types of commas mentioned above are defined as the ratio between two different "versions" of a particular interval, by extension we could define other types of commas based on other intervals and whatever ratios we happen to be using to define them-- e.g., there is Archytas' comma. But as I understand it, a "comma" is relevant only in reference to some type of tuning system-- it's irrelevant in equal temperament, since by definition every equal temperament semitone is exactly equal to every other semitone-- 2^(1/12):1.
I think "comma" without a qualifier is usually taken to mean a Ptolemaic ("ordinary" or "syntonic") comma, the interval between a "just major third" (5:4) and "Pythagorean major third" (81:64), which is equal to 81:80-- i.e., (81/64) / (5/4) = (81/64) * (4/5) = (81/64) * (64/80) = 81/80.
On the other hand, a Pythagorean ("diatonic") comma is the interval between twelve Pythagorean semitones (531441:262144, or [3^12]:[2^12]) and a perfect octave (2:1), which is equal to 531441:524288 (sometimes given as approximately 74:73).
In any case, a particular type of comma always has the same ratio, and an equal temperament semitone likewise always has the same ratio, so if we express an equal temperament semitone in terms of a comma then it will always be the same no matter which two adjacent notes we're considering-- C to C#, C# to D, D to D#, etc.
Since the two types of commas mentioned above are defined as the ratio between two different "versions" of a particular interval, by extension we could define other types of commas based on other intervals and whatever ratios we happen to be using to define them-- e.g., there is Archytas' comma. But as I understand it, a "comma" is relevant only in reference to some type of tuning system-- it's irrelevant in equal temperament, since by definition every equal temperament semitone is exactly equal to every other semitone-- 2^(1/12):1.