I've got a tempo expressed as "one dotted quarter note = 100" and I want to convert this to BPM. I'm thinking it should be 150 BPM, but I'm not sure. Could someone confirm this?
No, it is not 150 bpm.
A tempo indication is an indication of beats per minutes. A tempo of 100 means 100 beat in a minute. It's how a metronome plays beats. Your watch moves the second at a bpm of 60, because there are 60 seconds in a minute, hence 60 beats.
A tempo of 100, be them quarter notes, eight notes, dotted quarter notes, is a tempo of a hundred, which is a 100 beats per minutes. The value of the notes being played (quarter, eight) have no influence on the beats per minutes, only on the number of notes being played.
In the tempo you provided,
one dotted quarter note = 100
the 100 refers to the BPM. Usually, the person (composer) used this value (dotted quarter) because it would help the song to count it this way.
The usual way to display the tempo is 'one quarter note = X BPM', but this can vary, especially when the time signature is not 4/4. For instance, in a song that is in 6/8, you might see the tempo marking in eighths or in dotted quarters, like the one you mentioned. Also, in some very fast songs you might see that the tempo marks the half note and not the quarter.
I'm guessing the time sig. on this song is 12/8 or maybe 6/8. Both use a dotted crotchet (quarter note) as the 'beat', which gets sub-divided into 3 quavers (eighth notes). That will be the pulse of the song. If you use a metronome set to this, at 100, it IS your b.p.m. Don't think that b.p.m. has to be quarter notes. See Shev's answer. If the number is at the start of the song, it will signify b.p.m., but using a 'beat' as whatever the composer decided - in this case, dotted crotchet.
When writing in asymmetric meters (i.e. 5/8, 7/8, etc.), composers often use the dotted quarter as a metronome marking pulse (i.e. dotted quarter = 100). You shouldn't always think of the word "beat" in BPM as being a quarter note.
Even in a common meter such as 6/8, often the beat (pulse) is often either a dotted quarter OR an 8th note and the metronome marking, for example, would indicate either dotted quarter = 100 or 8th note = 100.
But to answer your question, if a metronome marking reads dotted quarter = 100, that means 100 dotted quarter note pulses every 60 seconds, OR 300 8th pulses every 60 seconds. You could use a metronome marking of 8th = 300. Most DAW's allow you to change the beat (pulse) to 8ths. But if you REALLY want to use a quarter note "pulse", then set the metronome to quarter = 150 as you correctly calculated :)
My guess is that you need to express the tempo for a MIDI editor. MIDI expresses tempo in microsecond per MIDI quarter, but editors usually present it in MIDI quarters per minute.
If that is the case, then you are right:
100 dotted-quarter/minute * 1.5 quarter/dotted-quarter = 150 quarter/minute
BPM - beats per minute - doesn't necessarily mean quarter notes per minute. The beat might not be a quarter note. In this case, as the tempo is given as 'dotted quarter=100' we can assume the beat is a dotted quarter. We're in 6/8, 9/8 or 12/8 time, where the music swings along with a triplet feel rather than marching with 'straight 8' subdivisions.
I'm guessing that you have a basic sequencer that only accepts tempo as 'quarter=x' settings? First, check to see if that really IS the case. There may be the facility to make other note-lengths the count. Then ask yourself if you really want to set the sequence up with a quarter-note count. The clicks won't be in the right place if you have a quarter count but enter notes based on a dotted-quarter beat. Better to get the count right and think in triplets.
Not exactly the same, but you could use a 2/4 meter or a 2/2 meter and divide them into triplets on the quarter note, resp. half note. BPM stays 100 on the quarter note, resp. half note. Maybe your software could do that.
The better thing to do (if possible) is learning your DAW that the beat is a quarter-dotted note and stay in the 6/8 meter(at 100 BPM).
Setting the quarter at 150 BPM only means that the song will have the same length, but you will have 2,5 beats in a bar. Very inconvenient. Succes.