In postgresql, how to count runs in a sequence across repeating partitions?

Try this. It uses the Tabibitosan method ( grouping sequence ranges ) : Toolbox

SQL Fiddle

PostgreSQL 9.6 Schema Setup:

CREATE TABLE user_events
    (user_name varchar(3), eventname varchar(1), event_time time)
;

INSERT INTO user_events
    (user_name, eventname, event_time)
VALUES
    ('Ted', 'a', '12:01'),
    ('Ted', 'b', '12:02'),
    ('Ted', 'b', '12:03'),
    ('Ted', 'b', '12:04'),
    ('Ted', 'c', '12:05'),
    ('Ted', 'b', '12:06'),
    ('Ted', 'b', '12:07'),
    ('Ted', 'c', '12:08'),
    ('Ted', 'b', '12:09'),
    ('Ted', 'b', '12:11'),
    ('Ted', 'b', '12:12')
;

Query 1:

SELECT t.user_name
    ,t.eventname
    ,row_number() OVER (
        ORDER BY MIN(event_time)
        ) AS event_sequence_number
    ,MIN(event_time) AS time_started
    ,COUNT(*) as frequency
FROM (
    SELECT user_name
        ,eventname
        ,event_time
        ,row_number() OVER (
            ORDER BY event_time
            ) - row_number() OVER (
            PARTITION BY eventname ORDER BY event_time
                ,eventname
            )  seq
    FROM user_events
    ) t
GROUP BY user_name
    ,eventname
    ,seq
ORDER BY time_started

Results:

| user_name | eventname | event_sequence_number | time_started | frequency |
|-----------|-----------|-----------------------|--------------|-----------|
|       Ted |         a |                     1 |     12:01:00 |         1 |
|       Ted |         b |                     2 |     12:02:00 |         3 |
|       Ted |         c |                     3 |     12:05:00 |         1 |
|       Ted |         b |                     4 |     12:06:00 |         2 |
|       Ted |         c |                     5 |     12:08:00 |         1 |
|       Ted |         b |                     6 |     12:09:00 |         3 |