1. How the Note Names Started as "Ut, Re, Mi, Fa, Sol, La" Before "Do"
In the current Do-Re-Mi-Fa-Sol-La-Si-Do scale, six of the names (all except Si) were originally "Ut, Re, Mi, Fa, Sol, La" [2]. "Ut" was reportedly changed to "Do" later because it was difficult to sing [4]. The word "Ut" itself has no musical meaning. So where did these names come from? The clue lies in a song from about a thousand years ago.
2. Guido of Arezzo, the Italian Monk Behind the Note Names
Guido of Arezzo was an Italian monk in the first half of the 11th century. He was born around 991–992 and died after 1033, though the exact year is unclear [1]. The song that inspired the names is a hymn sung on June 24, the birthday of John the Baptist. The lyrics are attributed to the 8th-century historian Paul the Deacon [2]. In the first verse, the starting note of each line rises in order: C, D, E, F, G, A [2][3]. The first syllables of these lines—"Ut," "Re," "Mi," "Fa," "Sol," "La"—became the note names. This naming is "usually attributed to Guido," but the sources do not provide definitive proof that he did it [2].
3. The Hymn of St. John and Its Prayer for a Sore Throat
The hymn’s lyrics ask that "your servants may sing your great deeds without their voices weakening" [2]. There is a legend that people with sore throats sang this hymn and were cured. However, this story was not recorded until the 13th century, much later than the hymn itself [3]. It is a curious connection that note names were born from a song where singers wished to protect their voices.
4. How Guido's Method Cut Music Training from About 10 Years to 1–2 Years
At that time, choir members had to learn songs by ear, which took about 10 years to become proficient. Guido claimed that his method using staff notation and note names could reduce this time to 1–2 years [1]. His writings include *Micrologus* and *Epistle on Unknown Songs*, from around 1025–1026 [1].
5. Why "Ut" Became "Do" and How "Si" Was Added
"Ut" changed to "Do" in the 17th century. It is said to have been renamed by Giovanni Battista Doni because "Ut" was hard to pronounce [4]. There are several theories about the origin of the name "Do." "Si" was added much later, and the exact year is not clearly stated [4]. The Do-Re-Mi we sing today is a form that has changed little by little from the version of a thousand years ago.
6. Pythagorean Tuning: Building a Scale by Stacking Perfect Fifths
Pythagorean tuning creates a scale by stacking "perfect fifths" with a frequency ratio of 3:2 within an octave [5]. When the ratio of vibrations between two notes is a simple integer, the sound is clear. Although it bears Pythagoras’s name, this method dates back to ancient Mesopotamia, and some argue that attributing it to Pythagoras is incorrect [5]. Here, we simply call it an "ancient method."
7. The Wolf Fifth: Why 12 Perfect Fifths Do Not Fit 7 Octaves
If you stack 12 perfect fifths, the total height is about 23.46 cents larger than 7 octaves. One cent is 1/100 of a semitone, so this is a difference of about a quarter of a semitone [6]. This difference is called the Pythagorean comma. If you try to make an octave with 12 notes, one fifth must absorb this error. That fifth becomes narrow (about 678.5 cents) and produces a strong beating sound when played as a chord. It is called the "wolf fifth" because it resembles a wolf’s howl [6]. This single error ruins the sound in that key, which was a major problem in old tuning systems.
8. Why Pythagorean Thirds Sound Rough and What Just Intonation Does
In Pythagorean tuning, fifths and fourths are clear, but major thirds have a complex ratio of 81:64. Compared to the pure third of 5:4, they sound rough. The difference is small (81 ÷ 64 ≒ 1.266 vs. 5 ÷ 4 = 1.25), but the ear hears it as beating [5]. From around 1510, thirds became important in chords, and "meantone" tuning, which adjusts thirds, became popular [5]. "Just intonation," which uses simple integer ratios, also makes chords clear. However, if you fix pitches for specific keys in just intonation, errors (commas) accumulate when you change keys (modulate). With a small number of fixed notes, it is difficult to play cleanly in all keys [7].
9. Equal Temperament: Dividing the Octave into 12 Equal Parts
Equal temperament divides an octave into 12 equal parts by frequency ratio. The ratio between adjacent notes is the 12th root of 2 (about 1.0595), making the sound the same in any key [8]. The trade-off is that compared to just intonation, fifths are about 2 cents narrow, and major thirds are about 13.7 cents wide. The fifth error is small, but the third error is noticeable [8]. The mathematical concept was shown early by Zhu Zaiyu in China in 1584 in *New Theory of Music*. In Europe, Simon Stevin wrote about it in a draft around 1605, and Marin Mersenne published it in 1636 [8][9]. It is unclear if Zhu Zaiyu’s ideas reached Europe.
10. Bach's Well-Tempered Clavier and the A=440Hz Standard
Bach’s *Well-Tempered Clavier* has an original title meaning "well-tempered (tuning)," which does not necessarily mean equal temperament. It is now generally viewed that we cannot say "Bach popularized equal temperament" [8]. The reference note "La" (A) was set to 440 Hz at the 1939 London International Conference, approved as ISO 16 in 1955, and reconfirmed in 1975 [10]. This is an agreement, not a natural height. Before that, 435 Hz was used in Paris (1859) and Vienna (1885). Today, some use 442 Hz, and Baroque performances may use 415 Hz [10].
11. Things to Try and Look Up About Do-Re-Mi and Pitch
You can try these things. Choose a song you know and sing it using Do-Re-Mi. Sing with family and compare the starting pitch to a piano or other instrument. If you have a piano or keyboard harmonica, play Do and Sol, then Do and Mi, simultaneously. Listen to the difference in clarity and note which sounds calmer in your own words. In a school music room or library, look up books on music history. Compare the entries for "solmization" and "tuning." If the explanations differ from those used here, that difference can be your next research topic.