Leonard Bernstein 77 tones per octave

I recently viewed a DVD of a Harvard Lecture where Bernstein chose to
announce that there were 77 different tones in the octave. He used the piano to
demonstrate how cumbersome that would be.

Anyone ever hear anything about why someone of his acumen would choose to
represent the totality of tuning divisions of the octave to 77?

best, Johnny

Aside from the supposedly magical qualities of the number seven? Beats me.

Now, if he were to admit to 79 on the other hand...
----- Original Message -----
From: Afmmjr@aol.com
To: tuning@yahoogroups.com
Sent: 08 Aralık 2006 Cuma 23:08
Subject: [tuning] Leonard Bernstein 77 tones per octave

I recently viewed a DVD of a Harvard Lecture where Bernstein chose to announce that there were 77 different tones in the octave. He used the piano to demonstrate how cumbersome that would be.

Anyone ever hear anything about why someone of his acumen would choose to represent the totality of tuning divisions of the octave to 77?

best, Johnny

--- In tuning@yahoogroups.com, Afmmjr@... wrote:
>
> I recently viewed a DVD of a Harvard Lecture where Bernstein chose to
> announce that there were 77 different tones in the octave. He used
the piano to
> demonstrate how cumbersome that would be.
>
> Anyone ever hear anything about why someone of his acumen would
choose to
> represent the totality of tuning divisions of the octave to 77?

Interesting question. It's not a candidate for least perceptible
difference, it isn't near any well-known comma, and it's not the
number of notes in any tonality diamond, I can say that much. It's an
excellent valentine tuning, but the chance that influenced Bernstein
is zero.

--- In tuning@yahoogroups.com, Afmmjr@... wrote:
>
> I recently viewed a DVD of a Harvard Lecture where Bernstein chose to
> announce that there were 77 different tones in the octave. He used
the piano to
> demonstrate how cumbersome that would be.
>
> Anyone ever hear anything about why someone of his acumen would
choose to
> represent the totality of tuning divisions of the octave to 77?
>
> best, Johnny
>

Oh, I'd have every reason to believe he was just pulling a large
number out of the air to get the idea across of the compromise that is
the piano. If you say, "I have 100 books on my bookshelf" it really
doesn't catch the attention of the listener the way it does if you say
"I have 93 books..." Or another example, "imagine 50 chimps in a
room" vs "imagine 52 chimps in a room." The latter makes you really
think more about how many that is and about each one, instead of just
a vague "bunch."
I bet he was just saying "a lot" in a different way.

--- In tuning@yahoogroups.com, "Aaron Wolf" <backfromthesilo@...> wrote:

> Oh, I'd have every reason to believe he was just pulling a large
> number out of the air to get the idea across of the compromise that is
> the piano.

Why do you have every reason to believe that? I think he picked on 77
for some reason, not necessarily a good one.

If you say, "I have 100 books on my bookshelf" it really
> doesn't catch the attention of the listener the way it does if you say
> "I have 93 books..."

Which proves nothing about Bernstein.

> I bet he was just saying "a lot" in a different way.

I dunno. I do know I could write music just fine using 77 notes to the
octave, even though I haven't listened to a note of it yet. It's that
on-paper thing. Maybe I'll give it a shot, but did 46 not too long ago
and there's 58 to consider, and these share a family relationship.

Hi all,

--- In tuning@yahoogroups.com, "Gene Ward Smith" wrote:
>
> --- In tuning@yahoogroups.com, "Aaron Wolf" wrote:
>
> > Oh, I'd have every reason to believe he was just pulling a large
number out of the air to get the idea across of the compromise that
is the piano.
>
> Why do you have every reason to believe that? I think he picked on
77 for some reason, not necessarily a good one.
>
> If you say, "I have 100 books on my bookshelf" it really doesn't
catch the attention of the listener the way it does if you say "I
have 93 books..."
>
> Which proves nothing about Bernstein.
>
> > I bet he was just saying "a lot" in a different way.
>
> I dunno. I do know I could write music just fine using 77 notes to
the octave, even though I haven't listened to a note of it yet. It's
that on-paper thing. Maybe I'll give it a shot, but did 46 not too
long ago and there's 58 to consider, and these share a family
relationship.

77 notes to the octave? Well, lessee: the lowest note
on the piano is about as low a note as we use in music.
Its first 77 harmonics range up to 6 octaves and a
major third above it. The modern piano has 88 notes,
or 7 octaves and a minor third. The notes of the top
octave or so have a thinness of timbre that suggest that
most listeners would not hear any overtones above the
fundamentals. So my guess is that Bernstein was
estimating the *useful* harmonics at being only about
77 in number. Combine that with our near-global
assumption of octave-equivalence, and that means that
you'd be wasting your time using any more than 77 notes
in an octave.

That's my theory, anyway ... Now, I wonder what the
REAL answer is? ;-)

Regards,
Yahya

That's a reasonable guess too... I guess I oversimplified my
explanation, but the overall idea still stands. I think he certainly
didn't mean 77edo or anything like that. He simply felt that 77 was
IN THE RANGE of how many important or useful or distinct notes there
are, and I bet he didn't mean it very strongly. In other words, I
doubt he would have bothered arguing with someone who came up and
said, "I think there's only 76 useful notes" or "I'm pretty sure
there's at least 81 real notes per octave." My point is that he'd
respond, "well, my point is that we can identify distinct notes and
there's at least around 77 or so worth discussing. Certainly it is
more than 30 or 40, and there's no way we can distinguish 250
meaningfully different notes."

I highly, highly doubt that Bernstein ever sat down to ceck about all
these possible notes and carefully decided that anything beyond his 77
were not valid but that each of the 77 were. I've seen Bernstein's
lecture style and he is certainly one to use specific numbers like
that to make a point when he knows and would not hesitate to admit
that it may be a simplification or generalization. In a discussion
with any of us, he would undoubtedly agree that it is a complex and
not yet fully answered or answerable question regarding exact number
of functional notes. I suggest nobody try to read more into his 77
claim than this, because I really doubt that there's truly something
there.

--- In tuning@yahoogroups.com, "yahya_melb" <yahya@...> wrote:
>
>
> Hi all,
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" wrote:
> >
> > --- In tuning@yahoogroups.com, "Aaron Wolf" wrote:
> >
> > > Oh, I'd have every reason to believe he was just pulling a large
> number out of the air to get the idea across of the compromise that
> is the piano.
> >
> > Why do you have every reason to believe that? I think he picked on
> 77 for some reason, not necessarily a good one.
> >
> > If you say, "I have 100 books on my bookshelf" it really doesn't
> catch the attention of the listener the way it does if you say "I
> have 93 books..."
> >
> > Which proves nothing about Bernstein.
> >
> > > I bet he was just saying "a lot" in a different way.
> >
> > I dunno. I do know I could write music just fine using 77 notes to
> the octave, even though I haven't listened to a note of it yet. It's
> that on-paper thing. Maybe I'll give it a shot, but did 46 not too
> long ago and there's 58 to consider, and these share a family
> relationship.
>
> 77 notes to the octave? Well, lessee: the lowest note
> on the piano is about as low a note as we use in music.
> Its first 77 harmonics range up to 6 octaves and a
> major third above it. The modern piano has 88 notes,
> or 7 octaves and a minor third. The notes of the top
> octave or so have a thinness of timbre that suggest that
> most listeners would not hear any overtones above the
> fundamentals. So my guess is that Bernstein was
> estimating the *useful* harmonics at being only about
> 77 in number. Combine that with our near-global
> assumption of octave-equivalence, and that means that
> you'd be wasting your time using any more than 77 notes
> in an octave.
>
> That's my theory, anyway ... Now, I wonder what the
> REAL answer is? ;-)
>
> Regards,
> Yahya
>

How about this then:

0: 1/1 0.000 unison, perfect prime
1: 77/76 22.631 approximation to 53-tone comma
2: 77/75 45.561
3: 77/74 68.800
4: 77/73 92.354
5: 77/72 116.234
6: 77/71 140.447
7: 11/10 165.004 4/5-tone, Ptolemy's second
8: 77/69 189.915
9: 77/68 215.188
10: 77/67 240.837
11: 7/6 266.871 septimal minor third
12: 77/65 293.302
13: 77/64 320.144
14: 11/9 347.408 undecimal neutral third
15: 77/62 375.108
16: 77/61 403.259
17: 77/60 431.875
18: 77/59 460.972
19: 77/58 490.567
20: 77/57 520.676
21: 11/8 551.318 undecimal semi-augmented fourth
22: 7/5 582.512 septimal or Huygens' tritone, BP
fourth
23: 77/54 614.279
24: 77/53 646.639
25: 77/52 679.616
26: 77/51 713.233
27: 77/50 747.516
28: 11/7 782.492 undecimal augmented fifth
29: 77/48 818.189
30: 77/47 854.637
31: 77/46 891.870
32: 77/45 929.920
33: 7/4 968.826 harmonic seventh
34: 77/43 1008.626
35: 11/6 1049.363 21/4-tone, undecimal neutral seventh
36: 77/41 1091.081
37: 77/40 1133.830
38: 77/39 1177.661
39: 77/38 1222.631 approximation to 53-tone comma + 1
octave

Oz.

*******

That's a reasonable guess too... I guess I oversimplified my
explanation, but the overall idea still stands. I think he certainly
didn't mean 77edo or anything like that. He simply felt that 77 was
IN THE RANGE of how many important or useful or distinct notes there
are, and I bet he didn't mean it very strongly. In other words, I
doubt he would have bothered arguing with someone who came up and
said, "I think there's only 76 useful notes" or "I'm pretty sure
there's at least 81 real notes per octave." My point is that he'd
respond, "well, my point is that we can identify distinct notes and
there's at least around 77 or so worth discussing. Certainly it is
more than 30 or 40, and there's no way we can distinguish 250
meaningfully different notes."

I highly, highly doubt that Bernstein ever sat down to ceck about all
these possible notes and carefully decided that anything beyond his 77
were not valid but that each of the 77 were. I've seen Bernstein's
lecture style and he is certainly one to use specific numbers like
that to make a point when he knows and would not hesitate to admit
that it may be a simplification or generalization. In a discussion
with any of us, he would undoubtedly agree that it is a complex and
not yet fully answered or answerable question regarding exact number
of functional notes. I suggest nobody try to read more into his 77
claim than this, because I really doubt that there's truly something
there.

--- In tuning@yahoogroups.com, "yahya_melb" <yahya@...> wrote:
>
>
> Hi all,
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" wrote:
> >
> > --- In tuning@yahoogroups.com, "Aaron Wolf" wrote:
> >
> > > Oh, I'd have every reason to believe he was just pulling a large
> number out of the air to get the idea across of the compromise that
> is the piano.
> >
> > Why do you have every reason to believe that? I think he picked on
> 77 for some reason, not necessarily a good one.
> >
> > If you say, "I have 100 books on my bookshelf" it really doesn't
> catch the attention of the listener the way it does if you say "I
> have 93 books..."
> >
> > Which proves nothing about Bernstein.
> >
> > > I bet he was just saying "a lot" in a different way.
> >
> > I dunno. I do know I could write music just fine using 77 notes to
> the octave, even though I haven't listened to a note of it yet. It's
> that on-paper thing. Maybe I'll give it a shot, but did 46 not too
> long ago and there's 58 to consider, and these share a family
> relationship.
>
> 77 notes to the octave? Well, lessee: the lowest note
> on the piano is about as low a note as we use in music.
> Its first 77 harmonics range up to 6 octaves and a
> major third above it. The modern piano has 88 notes,
> or 7 octaves and a minor third. The notes of the top
> octave or so have a thinness of timbre that suggest that
> most listeners would not hear any overtones above the
> fundamentals. So my guess is that Bernstein was
> estimating the *useful* harmonics at being only about
> 77 in number. Combine that with our near-global
> assumption of octave-equivalence, and that means that
> you'd be wasting your time using any more than 77 notes
> in an octave.
>
> That's my theory, anyway ... Now, I wonder what the
> REAL answer is? ;-)
>
> Regards,
> Yahya
>

Hi

77-edl ?, we havn,t any octave as the cardinality is odd number , but what about 77-ADO (-;?
1/1 --------------- 0
78/77 --------------- 22.3388138
79/77 --------------- 44.39304898
80/77 --------------- 66.16986503
81/77 --------------- 87.67615463
82/77 --------------- 108.9185567
83/77 --------------- 129.9034688
12/11 --------------- 150.6370585
85/77 --------------- 171.1252745
86/77 --------------- 191.3738568
87/77 --------------- 211.3883462
8/7 --------------- 231.1740935
89/77 --------------- 250.7362683
90/77 --------------- 270.0798668
13/11 --------------- 289.2097194
92/77 --------------- 308.1304984
93/77 --------------- 326.8467245
94/77 --------------- 345.3627732
95/77 --------------- 363.6828812
96/77 --------------- 381.811152
97/77 --------------- 399.7515618
14/11 --------------- 417.5079641
9/7 --------------- 435.0840953
100/77 --------------- 452.4835789
101/77 --------------- 469.7099305
102/77 --------------- 486.7665615
103/77 --------------- 503.6567838
104/77 --------------- 520.3838129
15/11 --------------- 536.9507724
106/77 --------------- 553.3606966
107/77 --------------- 569.6165348
108/77 --------------- 585.7211538
109/77 --------------- 601.6773409
10/7 --------------- 617.4878074
111/77 --------------- 633.1551908
16/11 --------------- 648.6820576
113/77 --------------- 664.0709061
114/77 --------------- 679.3241682
115/77 --------------- 694.4442123
116/77 --------------- 709.4333453
117/77 --------------- 724.2938147
118/77 --------------- 739.0278104
17/11 --------------- 753.6374671
120/77 --------------- 768.1248659
11/7 --------------- 782.4920359
122/77 --------------- 796.7409562
123/77 --------------- 810.8735576
124/77 --------------- 824.8917236
125/77 --------------- 838.7972928
18/11 --------------- 852.5920594
127/77 --------------- 866.2777753
128/77 --------------- 879.8561512
129/77 --------------- 893.3288577
130/77 --------------- 906.6975268
131/77 --------------- 919.963753
12/7 --------------- 933.1290944
19/11 --------------- 946.1950738
134/77 --------------- 959.1631797
135/77 --------------- 972.0348676
136/77 --------------- 984.8115607
137/77 --------------- 997.4946507
138/77 --------------- 1010.085499
139/77 --------------- 1022.585438
20/11 --------------- 1034.995772
141/77 --------------- 1047.317774
142/77 --------------- 1059.552695
13/7 --------------- 1071.701755
144/77 --------------- 1083.766153
145/77 --------------- 1095.747059
146/77 --------------- 1107.645622
21/11 --------------- 1119.462965
148/77 --------------- 1131.20019
149/77 --------------- 1142.858376
150/77 --------------- 1154.43858
151/77 --------------- 1165.941838
152/77 --------------- 1177.369167
153/77 --------------- 1188.721562
2/1 --------------- 1200

Shaahin Mohajeri

Tombak Player & Researcher , Microtonal Composer

My web site?? ???? ????? ??????

My farsi page in Harmonytalk ???? ??????? ?? ??????? ???

Shaahin Mohajeri in Wikipedia ????? ?????? ??????? ??????? ???? ????

-----Original Message-----
From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf Of Ozan Yarman
Sent: Sunday, December 10, 2006 2:31 AM
To: Tuning List
Subject: [tuning] Re: Leonard Bernstein 77 tones per octave

How about this then:

0: 1/1 0.000 unison, perfect prime
1: 77/76 22.631 approximation to 53-tone comma
2: 77/75 45.561
3: 77/74 68.800
4: 77/73 92.354
5: 77/72 116.234
6: 77/71 140.447
7: 11/10 165.004 4/5-tone, Ptolemy's second
8: 77/69 189.915
9: 77/68 215.188
10: 77/67 240.837
11: 7/6 266.871 septimal minor third
12: 77/65 293.302
13: 77/64 320.144
14: 11/9 347.408 undecimal neutral third
15: 77/62 375.108
16: 77/61 403.259
17: 77/60 431.875
18: 77/59 460.972
19: 77/58 490.567
20: 77/57 520.676
21: 11/8 551.318 undecimal semi-augmented fourth
22: 7/5 582.512 septimal or Huygens' tritone, BP
fourth
23: 77/54 614.279
24: 77/53 646.639
25: 77/52 679.616
26: 77/51 713.233
27: 77/50 747.516
28: 11/7 782.492 undecimal augmented fifth
29: 77/48 818.189
30: 77/47 854.637
31: 77/46 891.870
32: 77/45 929.920
33: 7/4 968.826 harmonic seventh
34: 77/43 1008.626
35: 11/6 1049.363 21/4-tone, undecimal neutral seventh
36: 77/41 1091.081
37: 77/40 1133.830
38: 77/39 1177.661
39: 77/38 1222.631 approximation to 53-tone comma + 1
octave

Oz.

*******

That's a reasonable guess too... I guess I oversimplified my explanation, but the overall idea still stands. I think he certainly didn't mean 77edo or anything like that. He simply felt that 77 was IN THE RANGE of how many important or useful or distinct notes there are, and I bet he didn't mean it very strongly. In other words, I doubt he would have bothered arguing with someone who came up and said, "I think there's only 76 useful notes" or "I'm pretty sure there's at least 81 real notes per octave." My point is that he'd respond, "well, my point is that we can identify distinct notes and there's at least around 77 or so worth discussing. Certainly it is more than 30 or 40, and there's no way we can distinguish 250 meaningfully different notes."

I highly, highly doubt that Bernstein ever sat down to ceck about all these possible notes and carefully decided that anything beyond his 77 were not valid but that each of the 77 were. I've seen Bernstein's lecture style and he is certainly one to use specific numbers like that to make a point when he knows and would not hesitate to admit that it may be a simplification or generalization. In a discussion with any of us, he would undoubtedly agree that it is a complex and not yet fully answered or answerable question regarding exact number of functional notes. I suggest nobody try to read more into his 77 claim than this, because I really doubt that there's truly something there.

--- In tuning@yahoogroups.com, "yahya_melb" <yahya@...> wrote:
>
>
> Hi all,
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" wrote:
> >
> > --- In tuning@yahoogroups.com, "Aaron Wolf" wrote:
> >
> > > Oh, I'd have every reason to believe he was just pulling a large
> number out of the air to get the idea across of the compromise that is
> the piano.
> >
> > Why do you have every reason to believe that? I think he picked on
> 77 for some reason, not necessarily a good one.
> >
> > If you say, "I have 100 books on my bookshelf" it really doesn't
> catch the attention of the listener the way it does if you say "I have
> 93 books..."
> >
> > Which proves nothing about Bernstein.
> >
> > > I bet he was just saying "a lot" in a different way.
> >
> > I dunno. I do know I could write music just fine using 77 notes to
> the octave, even though I haven't listened to a note of it yet. It's
> that on-paper thing. Maybe I'll give it a shot, but did 46 not too
> long ago and there's 58 to consider, and these share a family
> relationship.
>
> 77 notes to the octave? Well, lessee: the lowest note on the piano is
> about as low a note as we use in music.
> Its first 77 harmonics range up to 6 octaves and a major third above
> it. The modern piano has 88 notes, or 7 octaves and a minor third. The
> notes of the top octave or so have a thinness of timbre that suggest
> that most listeners would not hear any overtones above the
> fundamentals. So my guess is that Bernstein was estimating the
> *useful* harmonics at being only about
> 77 in number. Combine that with our near-global assumption of
> octave-equivalence, and that means that you'd be wasting your time
> using any more than 77 notes in an octave.
>
> That's my theory, anyway ... Now, I wonder what the REAL answer is?
> ;-)
>
> Regards,
> Yahya
>

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Well well... see you the meantone and superpythagorean wholetones & fifths I
use in 79 MOS 159-tET? This is quite a functional scale...

----- Original Message -----
From: "Mohajeri Shahin" <shahinm@kayson-ir.com>
To: <tuning@yahoogroups.com>
Sent: 10 Aral�k 2006 Pazar 6:06
Subject: RE: [tuning] Re: Leonard Bernstein 77 tones per octave

> Hi
>
> 77-edl ?, we havn,t any octave as the cardinality is odd number , but
what about 77-ADO (-;?
> 1/1 --------------- 0
> 78/77 --------------- 22.3388138
> 79/77 --------------- 44.39304898
> 80/77 --------------- 66.16986503
> 81/77 --------------- 87.67615463
> 82/77 --------------- 108.9185567
> 83/77 --------------- 129.9034688
> 12/11 --------------- 150.6370585
> 85/77 --------------- 171.1252745
> 86/77 --------------- 191.3738568
> 87/77 --------------- 211.3883462
> 8/7 --------------- 231.1740935
> 89/77 --------------- 250.7362683
> 90/77 --------------- 270.0798668
> 13/11 --------------- 289.2097194
> 92/77 --------------- 308.1304984
> 93/77 --------------- 326.8467245
> 94/77 --------------- 345.3627732
> 95/77 --------------- 363.6828812
> 96/77 --------------- 381.811152
> 97/77 --------------- 399.7515618
> 14/11 --------------- 417.5079641
> 9/7 --------------- 435.0840953
> 100/77 --------------- 452.4835789
> 101/77 --------------- 469.7099305
> 102/77 --------------- 486.7665615
> 103/77 --------------- 503.6567838
> 104/77 --------------- 520.3838129
> 15/11 --------------- 536.9507724
> 106/77 --------------- 553.3606966
> 107/77 --------------- 569.6165348
> 108/77 --------------- 585.7211538
> 109/77 --------------- 601.6773409
> 10/7 --------------- 617.4878074
> 111/77 --------------- 633.1551908
> 16/11 --------------- 648.6820576
> 113/77 --------------- 664.0709061
> 114/77 --------------- 679.3241682
> 115/77 --------------- 694.4442123
> 116/77 --------------- 709.4333453
> 117/77 --------------- 724.2938147
> 118/77 --------------- 739.0278104
> 17/11 --------------- 753.6374671
> 120/77 --------------- 768.1248659
> 11/7 --------------- 782.4920359
> 122/77 --------------- 796.7409562
> 123/77 --------------- 810.8735576
> 124/77 --------------- 824.8917236
> 125/77 --------------- 838.7972928
> 18/11 --------------- 852.5920594
> 127/77 --------------- 866.2777753
> 128/77 --------------- 879.8561512
> 129/77 --------------- 893.3288577
> 130/77 --------------- 906.6975268
> 131/77 --------------- 919.963753
> 12/7 --------------- 933.1290944
> 19/11 --------------- 946.1950738
> 134/77 --------------- 959.1631797
> 135/77 --------------- 972.0348676
> 136/77 --------------- 984.8115607
> 137/77 --------------- 997.4946507
> 138/77 --------------- 1010.085499
> 139/77 --------------- 1022.585438
> 20/11 --------------- 1034.995772
> 141/77 --------------- 1047.317774
> 142/77 --------------- 1059.552695
> 13/7 --------------- 1071.701755
> 144/77 --------------- 1083.766153
> 145/77 --------------- 1095.747059
> 146/77 --------------- 1107.645622
> 21/11 --------------- 1119.462965
> 148/77 --------------- 1131.20019
> 149/77 --------------- 1142.858376
> 150/77 --------------- 1154.43858
> 151/77 --------------- 1165.941838
> 152/77 --------------- 1177.369167
> 153/77 --------------- 1188.721562
> 2/1 --------------- 1200
>
> Shaahin Mohajeri

--- In tuning@yahoogroups.com, "Ozan Yarman" wrote:
>
> How about this then:
>
> 0: 1/1 0.000 unison, perfect prime
> 1: 77/76 22.631 approximation to 53-tone comma
> 2: 77/75 45.561
> 3: 77/74 68.800
> 4: 77/73 92.354
> 5: 77/72 116.234
> 6: 77/71 140.447
> 7: 11/10 165.004 4/5-tone, Ptolemy's second
> 8: 77/69 189.915
> 9: 77/68 215.188
> 10: 77/67 240.837
> 11: 7/6 266.871 septimal minor third
> 12: 77/65 293.302
> 13: 77/64 320.144
> 14: 11/9 347.408 undecimal neutral third
> 15: 77/62 375.108
> 16: 77/61 403.259
> 17: 77/60 431.875
> 18: 77/59 460.972
> 19: 77/58 490.567
> 20: 77/57 520.676
> 21: 11/8 551.318 undecimal semi-augmented
fourth
> 22: 7/5 582.512 septimal or Huygens' tritone,
BP
> fourth
> 23: 77/54 614.279
> 24: 77/53 646.639
> 25: 77/52 679.616
> 26: 77/51 713.233
> 27: 77/50 747.516
> 28: 11/7 782.492 undecimal augmented fifth
> 29: 77/48 818.189
> 30: 77/47 854.637
> 31: 77/46 891.870
> 32: 77/45 929.920
> 33: 7/4 968.826 harmonic seventh
> 34: 77/43 1008.626
> 35: 11/6 1049.363 21/4-tone, undecimal neutral
seventh
> 36: 77/41 1091.081
> 37: 77/40 1133.830
> 38: 77/39 1177.661
> 39: 77/38 1222.631 approximation to 53-tone
comma + 1
> octave

But Oz!

That (77-EDL) only gives 38 notes per octave.
Don't you mean 154-EDL? (Or 155 or 156-EDL.) ;-)

Still, I tend to agree with Aaron - Bernstein always
strikes me as a very practical person.

Regards,
Yahya

> *******
>
[Aaron Wolf wrote:]
> That's a reasonable guess too... I guess I oversimplified my
> explanation, but the overall idea still stands. I think he certainly
> didn't mean 77edo or anything like that. He simply felt that 77 was
> IN THE RANGE of how many important or useful or distinct notes there
> are, and I bet he didn't mean it very strongly. In other words, I
> doubt he would have bothered arguing with someone who came up and
> said, "I think there's only 76 useful notes" or "I'm pretty sure
> there's at least 81 real notes per octave." My point is that he'd
> respond, "well, my point is that we can identify distinct notes and
> there's at least around 77 or so worth discussing. Certainly it is
> more than 30 or 40, and there's no way we can distinguish 250
> meaningfully different notes."
>
> I highly, highly doubt that Bernstein ever sat down to ceck about
all
> these possible notes and carefully decided that anything beyond his
77
> were not valid but that each of the 77 were. I've seen Bernstein's
> lecture style and he is certainly one to use specific numbers like
> that to make a point when he knows and would not hesitate to admit
> that it may be a simplification or generalization. In a discussion
> with any of us, he would undoubtedly agree that it is a complex and
> not yet fully answered or answerable question regarding exact number
> of functional notes. I suggest nobody try to read more into his 77
> claim than this, because I really doubt that there's truly something
> there.
>
> --- In tuning@yahoogroups.com, "yahya_melb" <yahya@> wrote:
> >
> >
> > Hi all,
> >
> > --- In tuning@yahoogroups.com, "Gene Ward Smith" wrote:
> > >
> > > --- In tuning@yahoogroups.com, "Aaron Wolf" wrote:
> > >
> > > > Oh, I'd have every reason to believe he was just pulling a
large
> > number out of the air to get the idea across of the compromise
that
> > is the piano.
> > >
> > > Why do you have every reason to believe that? I think he picked
on
> > 77 for some reason, not necessarily a good one.
> > >
> > > If you say, "I have 100 books on my bookshelf" it really doesn't
> > catch the attention of the listener the way it does if you say "I
> > have 93 books..."
> > >
> > > Which proves nothing about Bernstein.
> > >
> > > > I bet he was just saying "a lot" in a different way.
> > >
> > > I dunno. I do know I could write music just fine using 77 notes
to
> > the octave, even though I haven't listened to a note of it yet.
It's
> > that on-paper thing. Maybe I'll give it a shot, but did 46 not too
> > long ago and there's 58 to consider, and these share a family
> > relationship.
> >
> > 77 notes to the octave? Well, lessee: the lowest note
> > on the piano is about as low a note as we use in music.
> > Its first 77 harmonics range up to 6 octaves and a
> > major third above it. The modern piano has 88 notes,
> > or 7 octaves and a minor third. The notes of the top
> > octave or so have a thinness of timbre that suggest that
> > most listeners would not hear any overtones above the
> > fundamentals. So my guess is that Bernstein was
> > estimating the *useful* harmonics at being only about
> > 77 in number. Combine that with our near-global
> > assumption of octave-equivalence, and that means that
> > you'd be wasting your time using any more than 77 notes
> > in an octave.
> >
> > That's my theory, anyway ... Now, I wonder what the
> > REAL answer is? ;-)
> >
> > Regards,
> > Yahya

Right. Mayhap this is what he meant:

0: 1/1 0.000 unison, perfect prime
1: 65/64 26.841 13th-partial chroma
2: 64/63 27.264 septimal comma, Archytas' comma
3: 33/32 53.273 undecimal comma, al-Farabi's 1/4-tone
4: 32/31 54.964 Greek enharmonic 1/4-tone
5: 67/64 79.307
6: 64/61 83.115
7: 17/16 104.955 17th harmonic
8: 16/15 111.731 minor diatonic semitone
9: 69/64 130.229
10: 64/59 140.828
11: 35/32 155.140 septimal neutral second
12: 32/29 170.423 29th subharmonic
13: 71/64 179.697
14: 64/57 200.532
15: 9/8 203.910 major whole tone
16: 73/64 227.789
17: 8/7 231.174 septimal whole tone
18: 37/32 251.344 37th harmonic
19: 64/55 262.368
20: 75/64 274.582 classic augmented second
21: 32/27 294.135 Pythagorean minor third
22: 19/16 297.513 19th harmonic
23: 77/64 320.144
24: 64/53 326.495
25: 39/32 342.483 39th harmonic, Zalzal wosta of Ibn
Sina
26: 16/13 359.472 tridecimal neutral third
27: 5/4 386.314 major third
28: 64/51 393.090
29: 32/25 427.373 classic diminished fourth
30: 41/32 429.062
31: 64/49 462.348 2 septatones or septatonic major third
32: 21/16 470.781 narrow fourth
33: 4/3 498.045 perfect fourth
34: 43/32 511.518
35: 64/47 534.493
36: 11/8 551.318 undecimal semi-augmented fourth
37: 32/23 571.726 23rd subharmonic
38: 45/32 590.224 diatonic tritone
39: 64/45 609.776 2nd tritone
40: 23/16 628.274 23rd harmonic
41: 16/11 648.682 undecimal semi-diminished fifth
42: 47/32 665.507
43: 64/43 688.482
44: 3/2 701.955 perfect fifth
45: 32/21 729.219 wide fifth
46: 49/32 737.652
47: 64/41 770.938
48: 25/16 772.627 classic augmented fifth
49: 51/32 806.910
50: 8/5 813.686 minor sixth
51: 13/8 840.528 tridecimal neutral sixth
52: 64/39 857.517 39th subharmonic
53: 53/32 873.505
54: 128/77 879.856
55: 32/19 902.487 19th subharmonic
56: 27/16 905.865 Pythagorean major sixth
57: 128/75 925.418 diminished seventh
58: 55/32 937.632
59: 64/37 948.656 37th subharmonic
60: 7/4 968.826 harmonic seventh
61: 128/73 972.211
62: 16/9 996.090 Pythagorean minor seventh
63: 57/32 999.468
64: 128/71 1020.303
65: 29/16 1029.577 29th harmonic
66: 64/35 1044.860 septimal neutral seventh
67: 59/32 1059.172
68: 128/69 1069.771
69: 15/8 1088.269 classic major seventh
70: 32/17 1095.045 17th subharmonic
71: 61/32 1116.885
72: 128/67 1120.693
73: 31/16 1145.036 31st harmonic
74: 64/33 1146.727 33rd subharmonic
75: 63/32 1172.736 octave - septimal comma
76: 128/65 1173.159
77: 2/1 1200.000 octave

Wanna guess how I constructed it?

Oz.

----- Original Message -----
From: "yahya_melb" <yahya@melbpc.org.au>
To: <tuning@yahoogroups.com>
Sent: 10 Aral�k 2006 Pazar 17:25
Subject: [tuning] Re: Leonard Bernstein 77 tones per octave

> --- In tuning@yahoogroups.com, "Ozan Yarman" wrote:
> >
> > How about this then:
> >
> > 0: 1/1 0.000 unison, perfect prime
> > 1: 77/76 22.631 approximation to 53-tone comma
> > 2: 77/75 45.561
> > 3: 77/74 68.800
> > 4: 77/73 92.354
> > 5: 77/72 116.234
> > 6: 77/71 140.447
> > 7: 11/10 165.004 4/5-tone, Ptolemy's second
> > 8: 77/69 189.915
> > 9: 77/68 215.188
> > 10: 77/67 240.837
> > 11: 7/6 266.871 septimal minor third
> > 12: 77/65 293.302
> > 13: 77/64 320.144
> > 14: 11/9 347.408 undecimal neutral third
> > 15: 77/62 375.108
> > 16: 77/61 403.259
> > 17: 77/60 431.875
> > 18: 77/59 460.972
> > 19: 77/58 490.567
> > 20: 77/57 520.676
> > 21: 11/8 551.318 undecimal semi-augmented
> fourth
> > 22: 7/5 582.512 septimal or Huygens' tritone,
> BP
> > fourth
> > 23: 77/54 614.279
> > 24: 77/53 646.639
> > 25: 77/52 679.616
> > 26: 77/51 713.233
> > 27: 77/50 747.516
> > 28: 11/7 782.492 undecimal augmented fifth
> > 29: 77/48 818.189
> > 30: 77/47 854.637
> > 31: 77/46 891.870
> > 32: 77/45 929.920
> > 33: 7/4 968.826 harmonic seventh
> > 34: 77/43 1008.626
> > 35: 11/6 1049.363 21/4-tone, undecimal neutral
> seventh
> > 36: 77/41 1091.081
> > 37: 77/40 1133.830
> > 38: 77/39 1177.661
> > 39: 77/38 1222.631 approximation to 53-tone
> comma + 1
> > octave
>
> But Oz!
>
> That (77-EDL) only gives 38 notes per octave.
> Don't you mean 154-EDL? (Or 155 or 156-EDL.) ;-)
>
> Still, I tend to agree with Aaron - Bernstein always
> strikes me as a very practical person.
>
> Regards,
> Yahya
>

I saw these lectures a while back--they're great. I could have swore
he said '76' not '77', which would make sense, given the propeties of
76-edo. In fact, I remembered admiring him for knowing that fact.

I could be wrong, though, or revising my perception of what he
actually said, though.

-A.

--- In tuning@yahoogroups.com, Afmmjr@... wrote:
>
> I recently viewed a DVD of a Harvard Lecture where Bernstein chose to
> announce that there were 77 different tones in the octave. He used
the piano to
> demonstrate how cumbersome that would be.
>
> Anyone ever hear anything about why someone of his acumen would
choose to
> represent the totality of tuning divisions of the octave to 77?
>
> best, Johnny
>

--- In tuning@yahoogroups.com, "Aaron Krister Johnson" <aaron@...>
wrote:
>
>
> I saw these lectures a while back--they're great. I could have swore
> he said '76' not '77', which would make sense, given the propeties of
> 76-edo.

Which are?

In fact, I remembered admiring him for knowing that fact.

What fact?

Yes this 77 ADO is pretty slick!

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Well well... see you the meantone and superpythagorean wholetones
& fifths I
> use in 79 MOS 159-tET? This is quite a functional scale...
>
> ----- Original Message -----
> From: "Mohajeri Shahin" <shahinm@...>
> To: <tuning@yahoogroups.com>
> Sent: 10 Aralýk 2006 Pazar 6:06
> Subject: RE: [tuning] Re: Leonard Bernstein 77 tones per octave
>
>
> > Hi
> >
> > 77-edl ?, we havn,t any octave as the cardinality is odd
number , but
> what about 77-ADO (-;?
> > 1/1 --------------- 0
> > 78/77 --------------- 22.3388138
> > 79/77 --------------- 44.39304898
> > 80/77 --------------- 66.16986503
> > 81/77 --------------- 87.67615463
> > 82/77 --------------- 108.9185567
> > 83/77 --------------- 129.9034688
> > 12/11 --------------- 150.6370585
> > 85/77 --------------- 171.1252745
> > 86/77 --------------- 191.3738568
> > 87/77 --------------- 211.3883462
> > 8/7 --------------- 231.1740935
> > 89/77 --------------- 250.7362683
> > 90/77 --------------- 270.0798668
> > 13/11 --------------- 289.2097194
> > 92/77 --------------- 308.1304984
> > 93/77 --------------- 326.8467245
> > 94/77 --------------- 345.3627732
> > 95/77 --------------- 363.6828812
> > 96/77 --------------- 381.811152
> > 97/77 --------------- 399.7515618
> > 14/11 --------------- 417.5079641
> > 9/7 --------------- 435.0840953
> > 100/77 --------------- 452.4835789
> > 101/77 --------------- 469.7099305
> > 102/77 --------------- 486.7665615
> > 103/77 --------------- 503.6567838
> > 104/77 --------------- 520.3838129
> > 15/11 --------------- 536.9507724
> > 106/77 --------------- 553.3606966
> > 107/77 --------------- 569.6165348
> > 108/77 --------------- 585.7211538
> > 109/77 --------------- 601.6773409
> > 10/7 --------------- 617.4878074
> > 111/77 --------------- 633.1551908
> > 16/11 --------------- 648.6820576
> > 113/77 --------------- 664.0709061
> > 114/77 --------------- 679.3241682
> > 115/77 --------------- 694.4442123
> > 116/77 --------------- 709.4333453
> > 117/77 --------------- 724.2938147
> > 118/77 --------------- 739.0278104
> > 17/11 --------------- 753.6374671
> > 120/77 --------------- 768.1248659
> > 11/7 --------------- 782.4920359
> > 122/77 --------------- 796.7409562
> > 123/77 --------------- 810.8735576
> > 124/77 --------------- 824.8917236
> > 125/77 --------------- 838.7972928
> > 18/11 --------------- 852.5920594
> > 127/77 --------------- 866.2777753
> > 128/77 --------------- 879.8561512
> > 129/77 --------------- 893.3288577
> > 130/77 --------------- 906.6975268
> > 131/77 --------------- 919.963753
> > 12/7 --------------- 933.1290944
> > 19/11 --------------- 946.1950738
> > 134/77 --------------- 959.1631797
> > 135/77 --------------- 972.0348676
> > 136/77 --------------- 984.8115607
> > 137/77 --------------- 997.4946507
> > 138/77 --------------- 1010.085499
> > 139/77 --------------- 1022.585438
> > 20/11 --------------- 1034.995772
> > 141/77 --------------- 1047.317774
> > 142/77 --------------- 1059.552695
> > 13/7 --------------- 1071.701755
> > 144/77 --------------- 1083.766153
> > 145/77 --------------- 1095.747059
> > 146/77 --------------- 1107.645622
> > 21/11 --------------- 1119.462965
> > 148/77 --------------- 1131.20019
> > 149/77 --------------- 1142.858376
> > 150/77 --------------- 1154.43858
> > 151/77 --------------- 1165.941838
> > 152/77 --------------- 1177.369167
> > 153/77 --------------- 1188.721562
> > 2/1 --------------- 1200
> >
> > Shaahin Mohajeri
>

I have seen these lectures and I too was puzzled by the enigmatic number
77 as, theoretically, given the nature of just intonation systems, I
could easily construct one with more than 77. I think it is futile to
try to answer the question "Why did Bernstein pick 77?" since as Victor
Borge aptly put it, "nobody knows, except Bernstein, and he is dead."
However, we can speculate.

Based on everything I know and read about music theory, it seems that 77
is not a natural number of notes in a JI scale (tonality diamond,
Euler-Fokker genus, Wilson CPS, etc.) but, um, isn't it true that if you
construct 12 chords with interval structure {1/1 12/11 9/8 6/5 5/4 4/3
11/8 3/2 12/7 7/4} with each note of Ellis Duodene as the root, and
combine them together, you get 77 notes to the octave? It is extremely
unlikely that this is what Bernstein was referring to, but it seems like
an interesting scale to work in.

(As for the sequence {1/1 12/11 9/8 6/5 5/4 4/3 11/8 3/2 12/7 7/4}, this
is just the combination of a major and minor chord, extended to the 11
Identity.)

This is definitely food for thought...

Praveen Venkataramana (justin_tone52)

------------------------------------------------------------------------\
-------

Check out my "String Trio for Monophony", that I uploaded to the tuning
list in "Justin Tone's Folder".

--- In tuning@yahoogroups.com, Afmmjr@... wrote:
>
> I recently viewed a DVD of a Harvard Lecture where Bernstein chose to
> announce that there were 77 different tones in the octave. He used
the piano to
> demonstrate how cumbersome that would be.
>
> Anyone ever hear anything about why someone of his acumen would choose
to
> represent the totality of tuning divisions of the octave to 77?
>
> best, Johnny
>