Converting BPM to Measures Per Minute

How often have you sat down to record something, and wondered--how many measures will I need at this bpm?  And, what happens to my 7 minute song if I increase/decrease the tempo?

@ 4/4, the following table spells it all out.  This is actually part of a Mac Numbers document which is a little more interactive.  Since I can't upload documents to blogger (BOOO) I figured I'd just walk folks through the basic math.

BPM to Measure Length

bpm	seconds per measure	Measures per minute
120	2.0	30.00
50	4.8	12.50
51	4.7	12.75
52	4.6	13.00
53	4.5	13.25
54	4.4	13.50
55	4.4	13.75
56	4.3	14.00
57	4.2	14.25
58	4.1	14.50
59	4.1	14.75
60	4.0	15.00
61	3.9	15.25
62	3.9	15.50
63	3.8	15.75
64	3.8	16.00
65	3.7	16.25
66	3.6	16.50
67	3.6	16.75
68	3.5	17.00
69	3.5	17.25
70	3.4	17.50
71	3.4	17.75
72	3.3	18.00
73	3.3	18.25
74	3.2	18.50
75	3.2	18.75
76	3.2	19.00
77	3.1	19.25
78	3.1	19.50
79	3.0	19.75
80	3.0	20.00
81	3.0	20.25
82	2.9	20.50
83	2.9	20.75
84	2.9	21.00
85	2.8	21.25
86	2.8	21.50
87	2.8	21.75
88	2.7	22.00
89	2.7	22.25
90	2.7	22.50
91	2.6	22.75
92	2.6	23.00
93	2.6	23.25
94	2.6	23.50
95	2.5	23.75
96	2.5	24.00
97	2.5	24.25
98	2.4	24.50
99	2.4	24.75
100	2.4	25.00
101	2.4	25.25
102	2.4	25.50
103	2.3	25.75
104	2.3	26.00
105	2.3	26.25
106	2.3	26.50
107	2.2	26.75
108	2.2	27.00
109	2.2	27.25
110	2.2	27.50
111	2.2	27.75
112	2.1	28.00
113	2.1	28.25
114	2.1	28.50
115	2.1	28.75
116	2.1	29.00
117	2.1	29.25
118	2.0	29.50
119	2.0	29.75
120	2.0	30.00
121	2.0	30.25
122	2.0	30.50
123	2.0	30.75
124	1.9	31.00
125	1.9	31.25
126	1.9	31.50
127	1.9	31.75
128	1.9	32.00
129	1.9	32.25
130	1.8	32.50
131	1.8	32.75
132	1.8	33.00
133	1.8	33.25
134	1.8	33.50
135	1.8	33.75
136	1.8	34.00
137	1.8	34.25
138	1.7	34.50
139	1.7	34.75
140	1.7	35.00
141	1.7	35.25
142	1.7	35.50
143	1.7	35.75
144	1.7	36.00
145	1.7	36.25
146	1.6	36.50
147	1.6	36.75
148	1.6	37.00
149	1.6	37.25
150	1.6	37.50
151	1.6	37.75
152	1.6	38.00
153	1.6	38.25
154	1.6	38.50
155	1.5	38.75
156	1.5	39.00
157	1.5	39.25
158	1.5	39.50
159	1.5	39.75
160	1.5	40.00
161	1.5	40.25
162	1.5	40.50
163	1.5	40.75
164	1.5	41.00
165	1.5	41.25
166	1.4	41.50
167	1.4	41.75
168	1.4	42.00
169	1.4	42.25
170	1.4	42.50
171	1.4	42.75
172	1.4	43.00
173	1.4	43.25
174	1.4	43.50
175	1.4	43.75
176	1.4	44.00
177	1.4	44.25
178	1.3	44.50
179	1.3	44.75
180	1.3	45.00
181	1.3	45.25
182	1.3	45.50
183	1.3	45.75
184	1.3	46.00
185	1.3	46.25
186	1.3	46.50

Exercise for the Reader

In my Numbers document (which is GREAT btw, for stuff like this simply beats the pants off Microsoft/Open Office), I have the following tables...the math is very basic, and the following equations should convert quite easily to almost any format.

BPM 

This is a very basic table that converts BPM to Seconds per Measure and Measure Per Minute...

• BPM (120, an input cell)
• Notes per beat (4, an input cell)
• Measure (4, an input cell)
• Seconds per Measure = Measure / bpm * 60
• Measure per Minute = 60 / Seconds Per Measure

Song Length -  Input

This is a table we can use to define the basic structure of our song (intro-verse-chorus-verse-outro, for example)

• BPM = BPM::BPM
• Intro (min)  = 1 for 1 minute intros
• Verse (min) = 2 for 2 minute verses
• Verse Count = 2 for 2 verses
• Chorus (min) = 1 for 1 minute chorus
• Chorus Count = 1 for 1 chorus
• Outro (min) = 1 for 1 minute outro

Song Length - Output
This table calculates how many measures we'll need to meet our song obligations.

• Measures Per Minute = BPM::Measures per Minute
• Intro (measures) = Measures Per Minute / Intro (min)
• Verse (measures) = Measures Per Minute / Verse (min)
• Chorus (measures) = Measures Per Minute / Chorus (min)
• Outro (measures) = Measures Per Minute / Outro (min)
• Song Length (Measures) = Intro (measures) + Verse Count * Verse (measures) + Chorus Count * Chorus(measures) + Outro (measures) 
• Song Length (Time) = Time(0,intro (min) + verse (min) * verse count + chorus (min) * chorus count + outro (min),0)

Measure Input
Now...what happens if we have a song of X measures, and we want to change the tempo? What will that do to our song length, for example, if we have Y minutes to fill?  This table contains our basic song structure, assuming all verses/choruses are the same.  It should be trivial to change per song if you need to (eg Verse 1, Verse 2, Chorus 1, fill, etc...add whatever parts you need!)

• BPM = BPM
• Intro (measures) = 30
• Verse (measures) = 60
• Chorus (measures) = 30
• outro (measures) = 30

Measures Output

Converts measures above into minutes.

• Seconds Per Measure = BPM::Seconds Per Measure
• Intro (minutes) = Time(0,0,Intro (measures) * Seconds Per Measure)
• Verse (minutes) = Time(0,0,Verse (measures) * Seconds Per Measure)
• Chorus (minutes) = Time(0,0,Chorus (measures) * Seconds Per Measure)
• Outro (minutes) =  Time(0,0,Outro(measures) * Seconds Per Measure)

Settings this up, note--very easy.  It took a lot longer to type up this blog entry then create the document, as automatic formula copy/paste is a beautiful thing. 

Thats it for a few weeks....