[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:04.56,Default,,0000,0000,0000,,in addition to providing us with an\Nefficient system for approximating JI
Dialogue: 0,0:00:04.56,0:00:09.12,Default,,0000,0000,0000,,two-dimensional regular\Ntemperaments also generate scales with
Dialogue: 0,0:00:09.12,0:00:14.25,Default,,0000,0000,0000,,very specific and useful melodic properties\Nthese scales are called
Dialogue: 0,0:00:14.25,0:00:21.42,Default,,0000,0000,0000,,"moment of symmetry scales"\Na moment of symmetry scale or MoS for short
Dialogue: 0,0:00:21.42,0:00:25.68,Default,,0000,0000,0000,,is defined by having exactly two different\Nintervals that span one step in the scale
Dialogue: 0,0:00:25.68,0:00:31.26,Default,,0000,0000,0000,,one large, one small and by being\Nderivative of a continuous chain of generators
Dialogue: 0,0:00:31.26,0:00:36.63,Default,,0000,0000,0000,,that is the same way the\Ndiatonic scale contains only a major and
Dialogue: 0,0:00:36.63,0:00:41.40,Default,,0000,0000,0000,,minor second and can be derived from\Nseven continuous fifths repeated within
Dialogue: 0,0:00:41.40,0:00:46.53,Default,,0000,0000,0000,,the octave, all MoS scales must have only\Ntwo types of second and they must be
Dialogue: 0,0:00:46.53,0:00:51.24,Default,,0000,0000,0000,,derivative of a continuous chain of some\Ngenerator repeated within some .
Dialogue: 0,0:00:52.88,0:00:58.76,Default,,0000,0000,0000,,since it has those defining properties\Nthe diatonic scale is an MoS. as it turns
Dialogue: 0,0:00:58.76,0:01:02.78,Default,,0000,0000,0000,,out our other standard Western scales\Nare also moment of symmetry scales
Dialogue: 0,0:01:02.78,0:01:07.31,Default,,0000,0000,0000,,including the pentatonic scale whose two\Nstep sizes are the major second in the
Dialogue: 0,0:01:07.31,0:01:12.23,Default,,0000,0000,0000,,minor 3rd and the chromatic scale whose\Nto step sizes are the minor second and
Dialogue: 0,0:01:12.23,0:01:16.85,Default,,0000,0000,0000,,the Augmented unison. both derived from a\Ncontinuous chains of fifths from the
Dialogue: 0,0:01:16.85,0:01:21.68,Default,,0000,0000,0000,,circle of fifths. so we don't know for\Nsure why historically we arrived so
Dialogue: 0,0:01:21.68,0:01:27.05,Default,,0000,0000,0000,,naturally at MoS scales we can use that\Nfact to theorize that other scales that
Dialogue: 0,0:01:27.05,0:01:32.81,Default,,0000,0000,0000,,share similar properties would be\Nsimilarly fruitful. MoS scales are
Dialogue: 0,0:01:32.81,0:01:38.45,Default,,0000,0000,0000,,categorized by their number of large and\Nsmall seconds. for example the diatonic scale
Dialogue: 0,0:01:38.45,0:01:42.98,Default,,0000,0000,0000,,scale would be prefer to as the 5\Nlarge and 2 small MoS, because it has five
Dialogue: 0,0:01:42.98,0:01:48.38,Default,,0000,0000,0000,,major seconds and two minor seconds\Neach MoS has what is referred to as a valid
Dialogue: 0,0:01:48.38,0:01:54.41,Default,,0000,0000,0000,,tuning range. the range of generator\Nsizes over which that MoS is generated
Dialogue: 0,0:01:54.41,0:01:58.10,Default,,0000,0000,0000,,as you vary the size of the generator\Nacross that range the large and small
Dialogue: 0,0:01:58.10,0:02:03.17,Default,,0000,0000,0000,,steps vary in size compared to each other\Nat one extreme a small steps
Dialogue: 0,0:02:03.17,0:02:06.89,Default,,0000,0000,0000,,shrink towards being non-existent, while\Nthe large steps take over the whole
Dialogue: 0,0:02:06.89,0:02:10.70,Default,,0000,0000,0000,,scale at which point you reach an equal\Ntemperament equal to the number of large steps
Dialogue: 0,0:02:10.70,0:02:15.50,Default,,0000,0000,0000,,at the other extreme the small steps\Nget larger and a large steps
Dialogue: 0,0:02:15.50,0:02:19.58,Default,,0000,0000,0000,,shrink until both are the same size at\Nwhich point you reach an equal
Dialogue: 0,0:02:19.58,0:02:22.85,Default,,0000,0000,0000,,temperament equal to the number of total\Nsteps in the scale
Dialogue: 0,0:02:23.46,0:02:28.59,Default,,0000,0000,0000,,outside of those parameters the scales\Ngenerated with no longer be of the same
Dialogue: 0,0:02:28.59,0:02:37.89,Default,,0000,0000,0000,,MoS structure. for example the diatonic\Nscale a.k.a. the 5 large 2 small MoS is
Dialogue: 0,0:02:37.89,0:02:40.86,Default,,0000,0000,0000,,valid with the generator ranging from\Napproximately 685 cents
Dialogue: 0,0:02:40.86,0:02:46.98,Default,,0000,0000,0000,,to 720 cents. in the middle of\Nthese two around 700 cents you arrive at
Dialogue: 0,0:02:46.98,0:02:51.54,Default,,0000,0000,0000,,scales or the scale structure is\Nobviously LLsLLLs
Dialogue: 0,0:02:51.54,0:02:57.72,Default,,0000,0000,0000,,as you approach 720 cents\Nhowever the small steps shrink towards
Dialogue: 0,0:02:57.72,0:03:01.74,Default,,0000,0000,0000,,nothing until the minor second\Ndisappears completely and you get 5-tet
Dialogue: 0,0:03:01.74,0:03:05.88,Default,,0000,0000,0000,,here is what that progression in generator size
Dialogue: 0,0:03:05.88,0:03:08.65,Default,,0000,0000,0000,,sounds like
Dialogue: 0,0:03:59.91,0:04:05.99,Default,,0000,0000,0000,,conversely if your generator approaches\N685 cents your major and minor seconds
Dialogue: 0,0:04:05.99,0:04:09.83,Default,,0000,0000,0000,,approach each other in size until\Nthey're equal at which point you have 7-tet
Dialogue: 0,0:04:09.83,0:04:13.79,Default,,0000,0000,0000,,here's what that progression in generator size
Dialogue: 0,0:04:13.79,0:04:16.79,Default,,0000,0000,0000,,sounds like
Dialogue: 0,0:04:58.05,0:05:02.49,Default,,0000,0000,0000,,the sizes and structures of the\Ndifferent MoS scales you reach given a
Dialogue: 0,0:05:02.49,0:05:06.81,Default,,0000,0000,0000,,period and a generator combination are\Ndetermined by the ratio in size between
Dialogue: 0,0:05:06.81,0:05:10.89,Default,,0000,0000,0000,,those two intervals. though the\Nintricacies of that relationship are
Dialogue: 0,0:05:10.89,0:05:16.38,Default,,0000,0000,0000,,beyond the scope of this video. to put it\Nas simply as possible the number of
Dialogue: 0,0:05:16.38,0:05:22.44,Default,,0000,0000,0000,,notes in each successive MoS scale a.k.a.\Ntheir cardinalities follow a Fibonacci
Dialogue: 0,0:05:22.44,0:05:27.09,Default,,0000,0000,0000,,ESCA pattern or each new scales\Ncardinality is an addition of two
Dialogue: 0,0:05:27.09,0:05:31.98,Default,,0000,0000,0000,,previous cardinalities. also the number\Nof large and small steps in your new
Dialogue: 0,0:05:31.98,0:05:38.67,Default,,0000,0000,0000,,scale will match those two previous\Ncardinalities. for example when using a
Dialogue: 0,0:05:38.67,0:05:43.62,Default,,0000,0000,0000,,pure 3/2 and a pure 2/1\Napproximation 702 cents and 1200 cents
Dialogue: 0,0:05:43.62,0:05:49.02,Default,,0000,0000,0000,,as our generator and period we have MoS\Nscales after one note, which in this case
Dialogue: 0,0:05:49.02,0:05:54.27,Default,,0000,0000,0000,,is just octaves, then at two notes a\Nscale of one large one small
Dialogue: 0,0:05:54.27,0:05:55.98,Default,,0000,0000,0000,,a perfect fifth and a perfect fourth
Dialogue: 0,0:05:55.98,0:06:00.75,Default,,0000,0000,0000,,our next MoS has reached at three\Nnotes a.k.a. 2+1 giving us
Dialogue: 0,0:06:00.75,0:06:05.97,Default,,0000,0000,0000,,2L1s MoS scale including two\Nperfect fourth and a major second
Dialogue: 0,0:06:05.97,0:06:11.64,Default,,0000,0000,0000,,after that we had an MoS of five notes a.k.a.\N2+3 giving us a 2L3s MoS scale
Dialogue: 0,0:06:11.64,0:06:17.34,Default,,0000,0000,0000,,which is our pentatonic scale\Nthe next MoS is reached seven notes just
Dialogue: 0,0:06:17.34,0:06:22.98,Default,,0000,0000,0000,,5+2 giving us a 5L 2s MoS scale\Nwhich is our diatonic scale
Dialogue: 0,0:06:22.98,0:06:28.59,Default,,0000,0000,0000,,and then 12 notes - 7+5 giving us a 5L 7s MoS scale\Nand uneven
Dialogue: 0,0:06:28.59,0:06:32.85,Default,,0000,0000,0000,,chromatic scale. after that the bag\Npattern continues onto 17 notes,
Dialogue: 0,0:06:32.85,0:06:40.08,Default,,0000,0000,0000,,29 notes etc. if you generate with the\Npure 6/5 and a 2/1 however you
Dialogue: 0,0:06:40.08,0:06:43.74,Default,,0000,0000,0000,,arrive at a different combination of MoS\Nscales that they follow a similar
Dialogue: 0,0:06:43.74,0:06:50.46,Default,,0000,0000,0000,,pattern. they would occur at one note,\Ntwo notes, three notes (just 2+1), 4 notes
Dialogue: 0,0:06:50.46,0:07:00.84,Default,,0000,0000,0000,,(3+1), 7 notes (3+4), 11 notes (7+4)\N15 notes (11+4) and so on
Dialogue: 0,0:07:00.84,0:07:04.41,Default,,0000,0000,0000,,the closer to generators are in size the\Nmore scale structures they'll have in
Dialogue: 0,0:07:04.41,0:07:09.00,Default,,0000,0000,0000,,common before they diverge. for example\Nwhen generating scales using a flatted 3/2
Dialogue: 0,0:07:09.00,0:07:14.19,Default,,0000,0000,0000,,or 696 cents, as often happens in\Nmintone temperament, we arrived at the
Dialogue: 0,0:07:14.19,0:07:18.84,Default,,0000,0000,0000,,same MoS scales as when generating with\Nthe pure 3/2 until we get to the 12
Dialogue: 0,0:07:18.84,0:07:22.89,Default,,0000,0000,0000,,notes scale which will instead have\Nseven large steps and five small steps
Dialogue: 0,0:07:22.89,0:07:26.34,Default,,0000,0000,0000,,making it an uneven chromatic scale with\Na reverse structure
Dialogue: 0,0:07:26.95,0:07:34.51,Default,,0000,0000,0000,,that scale is followed by MoS scales of\N19 notes (a.k.a. 12+7), 26 notes (19+7)
Dialogue: 0,0:07:34.51,0:07:40.24,Default,,0000,0000,0000,,and then the pattern diverges from then on\Nhere is what several alternative MoS
Dialogue: 0,0:07:40.24,0:07:43.24,Default,,0000,0000,0000,,scale structure sound like
Dialogue: 0,0:08:25.29,0:08:31.19,Default,,0000,0000,0000,,those are just several examples among an\Ninfinite number of MoS scales which are
Dialogue: 0,0:08:31.19,0:08:35.96,Default,,0000,0000,0000,,theoretically ripe for exploration.\Nbut how on earth should one go about playing
Dialogue: 0,0:08:35.96,0:08:39.47,Default,,0000,0000,0000,,these new musical structures if they can\Ndiffer on such a basic level from our
Dialogue: 0,0:08:39.47,0:08:43.49,Default,,0000,0000,0000,,familiar scales? certainly many of them\Nwould not be playable on traditional
Dialogue: 0,0:08:43.49,0:08:48.11,Default,,0000,0000,0000,,musical instruments. next video I'll be\Ncovering the most ergonomic way to
Dialogue: 0,0:08:48.11,0:08:51.56,Default,,0000,0000,0000,,represent these musical structures\Nphysically for musical performance