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<u>'''Modulation</u> ''' is the practice of changing keys. The source and destination keys are important. Many composers only modulate into destination keys based on the 4th or 5th of the source key, as these are the most harmonic keys.
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{{Intermediate Lesson Crumbs|8}}
The <u>'''circle of fifths</u> ''' lays out the 12 tones in a circle, just like the 12 hours on an analog clock face, moving clockwise in perfect fifths. If C is 12 o'clock, its fifth, G, is 1 o'clock. G's fifth, D, is two o'clock. And so on.
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The whole-half pattern from G to G in the key of C Major is w-w-h-w-w-h-w. If we sharp the 7th note, the F, we get w-w-h-w-w-w-h - the major scale pattern.
Remember that F is a fifth below C and G is a fifth above. We notice that if we change the key by moving the root note by perfect fifths, only one note changes. While no two major scales will have different tonic notes but identical sets of notes, some scales are more ''inter-related'' or relatively harmonic than others.
The circle of fifths lists keys in 5ths, which is useful to determine how interrelated any two keys are. The points opposite each other (12 :00 vs. 6:00, 3 :00 vs. 9:00, 11 :00 vs. 5:00, etc.) are the least related, while the points nearest each other (12 :00 and 1:00, 1 :00 and 2:00, etc.) are most related. As we go right or clockwise, we sharp the 4th of the current key to get the next key. For example in C Major, sharping the 4th (F) gives us the scale of G Major. As we move left or counter-clockwise, we flatten the 7th of the current key to get the next key. For C Major, we flat the B to get F Major.
So each movement is a single note difference, always adjusting the leading tone of the key on the clockwise side of the pair. Note that the major scale has two half-steps, which means two notes right next to each other. Every other major or natural minor scale has to contain at least one of these notes, since the largest movement between neighboring notes is a whole step. So the least related scales will share 2 notes. For example, C and C{{s}} don't share any notes by name - every note in C is the same note in C{{s}} but sharped. However, E{{s}} = F and B{{s}} = C; so they still have two notes in common.
Db - Ab - Eb - Bb - F - C - G - D - A - E - B
Gb - Db - Ab - Eb - Bb - F - C - G - D - A - E - B - F#
F# {{s}} is the same pitch as GbG{{b}}, which means we've completed the circle. If we keep going, we still get unique key names, but the pitches will match other keys already in the circle. For example, continuing left (counter-clockwise), we reach CbC{{b}}, which is the same as B. Going right (clockwise), we reach C#{{s}}, which is the same as DbD{{b}}.
So assuming C is "12 o'Clock", our circle of fifths looks like this:
{| class="wikitable"
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! Key !!Cb C{{b}} !! Gb G{{b}} !! Db D{{b}} !! Ab A{{b}} !! Eb E{{b}} !! Bb B{{b}} !! F !! C !! G !! D !! A !! E !! B {{b}} !! F# {{s}} !! C#{{s}}
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| Flats/Sharps||7 {{b}}'s||6 {{b}}'s || 5 {{b}}'s || 4 {{b}}'s || 3 {{b}}'s || 2 {{b}}'s || 1 {{b}}'s || 0 {{b}}/#{{s}}'s || 1 #{{s}}'s || 2 #{{s}}'s || 3 #{{s}}'s || 4 #{{s}}'s || 5 #{{s}}'s || 6 #{{s}}'s || 7 #{{s}}'s
|-
! Unison ||Cb C{{b}} || Gb G{{b}} || Db D{{b}} || Ab A{{b}} || Eb E{{b}} || Bb B{{b}} || F || C || G || D || A || E || B {{b}} || F# {{s}} || C#{{s}}
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| 2nd ||Db D{{b}} || AbA{{b}}|| Eb E{{b}} || Bb B{{b}} || F || C || G || D || A || E|| B {{b}} || F#{{s}}|| C# {{s}} || G# {{s}} || D#{{s}}
|-
| 3rd ||Eb E{{b}} || Bb B{{b}} || F || C || G || D || A || E || B {{b}} || F# {{s}} || C# {{s}} || G#{{s}}|| D# {{s}} || A# {{s}} || E#{{s}}
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! 4th ||Fb F{{b}} || Cb C{{b}} || Gb G{{b}} || Db D{{b}} || Ab A{{b}} || Eb E{{b}} || Bb B{{b}} || F || C || G || D || A|| E || B {{b}} || F#{{s}}
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| 5th ||Gb G{{b}} || Db D{{b}} || Ab A{{b}} || Eb E{{b}} || Bb B{{b}} || F || C || G || D || A || E|| B{{b}}|| F# {{s}} || C# {{s}} || G#{{s}}
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| 6th ||Ab A{{b}} || Eb E{{b}} || Bb B{{b}} || F || C || G || D || A || E || B {{b}} || F#{{s}}|| C#{{s}}|| G# {{s}} || D# {{s}} || A#{{s}}
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! 7th ||Bb B{{b}} || F || C || G || D || A || E || B {{b}} || F# {{s}} || C# {{s}} || G#{{s}}|| D#{{s}}|| A# {{s}} || E# {{s}} || B#{{b}}{{s}}
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| Oct ||Cb C{{b}} || Gb G{{b}} || Db D{{b}} || Ab A{{b}} || Eb E{{b}} || Bb B{{b}} || F || C || G || D || A|| E|| B {{b}} || F# {{s}} || C#{{s}}
|}
Above is the list of the keys from Cb C{{b}} to C#{{s}}. Note that this is actually 15 tones. Since C# {{s}} = DbD{{b}}, Cb C{{b}} = B, and F# {{s}} = GbG{{b}}, we can eliminate them, leaving with only the 12 distinct tones on the circle of fifths.
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Below is a table to show the most interrelated keys. It says how many notes the two keys will have in common, modulating to the key of the named interval above the current key. For example, the key of C Major will only have 2 notes in common with the major keys a M7, m2, or d5 above C (C{{f}} or B Major, C{{s}} or D{{f}} Major, and G{{f}} or F{{s}} Major).