The musical scale is made up of seven notes: do; re; mi; fa; so; la; ti. These notes are then repeated on a higher scale, then again on a higher scale "ad infinitum." Each seven note scale is equal to one cycle. In Judaism, the number seven is significant for several reasons. One is that there are seven Kabbalistic spheres (sefirot) each of which corresponds to one week of the Omer, which is itself seven weeks of seven days each, from Pesach to Shavuoth: Each letter of the Hebrew alphabet is parallel to a different note of the scale, and hence to the appropriate sphere. Each sphere has its own position being either to the right, left or middle. Therefore the corresponding letters of the alphabet, and notes of the scale are in the same position as its complementary sphere.
It is interesting to note that the difference between the major key and the minor key is explained through the build up of the notes in the key. In the minor key the middle tones (i.e., the "mi" and the "la") are nearer to the left side (being only a semitone away) which is the side representing the heart.
The Hebrew words for the three positions of the spheres are emtza, middle, yemin, right; and smol, left. If we take the initials of these words, it spells the word ish, man. Ish has the connotation of the perfect man; for example Moshe is called ish HaElokim, "man of G-d": Deuteronomy 33:1, also see Psalms 90:1, Samuel 2:27, 9:6; Kings I 12:22; 31:1; Kings II 1:13, 4:9; Nehemiah 12:24; Chronicles II 25:7. Consequently, we see that when the middle, right, and left are together they form a perfect combination.
The spheres also represent midot, Divine attributes, through which we understand Hashem's actions and creations. In astrology, the seven midot that we have seen are parallel to the seven mazalot, celestial bodies (see chart below). Jupiter is parallel to chesed, the first sphere, on the right, and to the letter alef; Mars corresponds to gevura, the second sphere on the left, and to bet; the Sun to tipheret in the middle and to gimel; Venus to netzach and to daled; Mercury to hod and to heh; the Moon to yesod and to vuv; and the Earth to malchut and to zayin.
According to the Ramchal (Rabbi Moshe Chaim Luzzato) in his book Adir BaMarom (page 40) the planets are moved by musical waves. These are his words: "All those things above are carried out by music and all the luminaries, when they go out from their source, are motivated by music." Each planet has its music. It is interesting to note that recently in the United States they discovered that each planet produces different melodies. As has been seen, according to the Ramchal, it is really the music itself which effects and hence moves the planets. The Zohar (Exodus, Parshat Sh'lach) says that the constellations themselves create music. According to the Zohar (Exodus, VaYakel) the music of the sun is so wonderful that if the ears of man would not be blocked then he would be capable of hearing this music. He would, however, not be able to exist as his soul would leave his body. The Rambam, in his book "The Guide for the Perplexed" (part two, chapter 8), also mentions this and other theories of how the stars create different sounds
The major key is the plan of the cycle of the nineteen years which contain seven leap years. The seven leap years occur on the third, the sixth, the eighth, the eleventh, the fourteenth, the seventeenth and the nineteenth years respectively. Observing the order of these years one can notice that they follow the same sequence as the intervals between the notes (or tones) in the major key, for example two years correspond to one tone, for example between the "do" and the "re" there is a "full space", a tone. When there is only one year difference this relates to the semi-tone, for example the space between the "mi" and the "fa."
In the second scale, the same principles apply. The chet which stands for chayim, life, signifies the note "do" in a higher key, and the attribute, chesed, and hence is on the right. The tet stands for tahara; purity, which is analogous to "re", and gevura; and so is on the left. The yud matches "mi", and tipheret and is in the middle, etc. We see then that the second scale is of a similar structure to the first.
The last seven letters forming the third scale are constructed in the same manner (see the chart above). The book Hafla'a of the Baal HaKane says that exactly the same insight and erudition which applies to connecting letters into words, applies to connecting notes into song.
The Tikunei Zohar mentions three things that music effects: the Torah; the Shechina (the Divine Glory), and the Geula (redemption). These three things in turn are parallel to the mind, heart, and body, respectively. Firstly, the Torah represents the moach, the mind, brain. This is because music has the power to open one's mind and improve one's seich'l, mind. In his book, Pirkei Hatzlacha, the Rambam writes that if a man wants to feel elevated he should sing. Singing has the prepotency to elevate a man as it opens his mind. The Talmud says that one should learn Torah with (a tune) music as this aids one's studies. Hence, one can frequently hear men learning in a sing-song manner in yeshivot.